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Chapter 2. Complexity Analysis
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2.1 Algorithm Efficiency Evaluation
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2.2 Iteration and Recursion
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2.3 Time Complexity
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2.4 Space Complexity
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Chapter 3. Data Structures
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3.1 Classification of Data Structures
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3.2 Basic Data Types
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3.3 Number Encoding *
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3.4 Character Encoding *
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3.5 Summary
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Chapter 4. Array and Linked List
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4.1 Array
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4.2 Linked List
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4.3 List
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4.4 Memory and Cache *
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4.5 Summary
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Chapter 5. Stack and Queue
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</a>
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Chapter 5. Stack and Queue
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5.1 Stack
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</span>
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</a>
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5.2 Queue
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5.3 Double-Ended Queue
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5.4 Summary
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</span>
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</a>
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Chapter 6. Hashing
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Chapter 6. Hashing
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6.1 Hash Table
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</span>
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</a>
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6.2 Hash Collision
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</span>
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</a>
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<span class="md-ellipsis">
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6.3 Hash Algorithm
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</span>
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</a>
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6.4 Summary
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</span>
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</a>
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</ul>
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</nav>
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<span class="md-ellipsis">
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Chapter 7. Tree
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</span>
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</a>
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<span class="md-nav__icon md-icon"></span>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_9">
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<span class="md-nav__icon md-icon"></span>
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Chapter 7. Tree
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.1 Binary Tree
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
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<span class="md-ellipsis">
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7.2 Binary Tree Traversal
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.3 Array Representation of Tree
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.4 Binary Search Tree
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.5 AVL Tree *
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</span>
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</a>
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<li class="md-nav__item">
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<span class="md-ellipsis">
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7.6 Summary
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</span>
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</a>
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_heap/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1"/></svg>
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<span class="md-ellipsis">
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Chapter 8. Heap
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</span>
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</a>
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<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_10">
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<span class="md-nav__icon md-icon"></span>
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Chapter 8. Heap
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_heap/heap/" class="md-nav__link">
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<span class="md-ellipsis">
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8.1 Heap
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_heap/build_heap/" class="md-nav__link">
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<span class="md-ellipsis">
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8.2 Building a Heap
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_heap/top_k/" class="md-nav__link">
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<span class="md-ellipsis">
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8.3 Top-K Problem
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_heap/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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8.4 Summary
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</span>
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</a>
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</ul>
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</nav>
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_graph/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59zM6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43s.83.16 1.12.43l4.28-2.53zM12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68s1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25zm2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24z"/></svg>
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<span class="md-ellipsis">
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Chapter 9. Graph
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</span>
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</a>
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<label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_11">
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<span class="md-nav__icon md-icon"></span>
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Chapter 9. Graph
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_graph/graph/" class="md-nav__link">
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<span class="md-ellipsis">
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9.1 Graph
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
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<span class="md-ellipsis">
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9.2 Basic Operations on Graphs
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
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<span class="md-ellipsis">
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9.3 Graph Traversal
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_graph/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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9.4 Summary
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</span>
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</a>
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</ul>
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</nav>
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<div class="md-nav__link md-nav__container">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4zM3 16v-2h6v2zm0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1z"/></svg>
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<span class="md-ellipsis">
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Chapter 10. Searching
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</span>
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</a>
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<label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_12">
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<span class="md-nav__icon md-icon"></span>
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Chapter 10. Searching
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search/" class="md-nav__link">
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<span class="md-ellipsis">
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10.1 Binary Search
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
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<span class="md-ellipsis">
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10.2 Binary Search Insertion
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
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<span class="md-ellipsis">
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10.3 Binary Search Edge Cases
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
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<span class="md-ellipsis">
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10.4 Hash Optimization Strategy
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
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<span class="md-ellipsis">
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10.5 Search Algorithms Revisited
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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10.6 Summary
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</span>
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_sorting/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2z"/></svg>
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<span class="md-ellipsis">
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Chapter 11. Sorting
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</span>
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</a>
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<label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
|
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
|
<label class="md-nav__title" for="__nav_13">
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<span class="md-nav__icon md-icon"></span>
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Chapter 11. Sorting
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
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<span class="md-ellipsis">
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11.1 Sorting Algorithms
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.2 Selection Sort
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.3 Bubble Sort
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.4 Insertion Sort
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.5 Quick Sort
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.6 Merge Sort
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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|
11.7 Heap Sort
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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|
11.8 Bucket Sort
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.9 Counting Sort
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</span>
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</a>
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.10 Radix Sort
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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11.11 Summary
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</span>
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
|
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|
<div class="md-nav__link md-nav__container">
|
|
<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7zM2 9v6h5V9zm10 0v2H9v2h3v2l3-3zm5 2v2h5v-2zm0 4v2h5v-2z"/></svg>
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<span class="md-ellipsis">
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|
Chapter 12. Divide and Conquer
|
|
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</span>
|
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</a>
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<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
|
|
<span class="md-nav__icon md-icon"></span>
|
|
</label>
|
|
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|
</div>
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
|
<label class="md-nav__title" for="__nav_14">
|
|
<span class="md-nav__icon md-icon"></span>
|
|
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|
Chapter 12. Divide and Conquer
|
|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
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<span class="md-ellipsis">
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12.1 Divide and Conquer Algorithms
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
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<span class="md-ellipsis">
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12.2 Divide and Conquer Search Strategy
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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12.3 Building a Binary Tree Problem
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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12.4 Hanoi Tower Problem
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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12.5 Summary
|
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</span>
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--active md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" checked>
|
|
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<div class="md-nav__link md-nav__container">
|
|
<a href="../" class="md-nav__link ">
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Chapter 13. Backtracking
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13.1 Backtracking Algorithm
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13.1 Backtracking Algorithm
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13.1.1 Attempt and Backtrack
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13.1.2 Pruning
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13.1.3 Framework Code
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13.1.4 Common Terminology
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13.1.6 Typical Backtracking Examples
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Chapter 14. Dynamic Programming
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14.4 0-1 Knapsack Problem
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14.5 Unbounded Knapsack Problem
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14.6 Edit Distance Problem
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Chapter 15. Greedy
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15.1 Greedy Algorithm
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<h1 id="131-backtracking-algorithm">13.1 Backtracking Algorithm<a class="headerlink" href="#131-backtracking-algorithm" title="Permanent link">¶</a></h1>
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<p><u>The backtracking algorithm</u> is a method for solving problems through exhaustive search. Its core idea is to start from an initial state and exhaustively search all possible solutions. When a correct solution is found, it is recorded. This process continues until a solution is found or all possible choices have been tried without finding a solution.</p>
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<p>The backtracking algorithm typically employs "depth-first search" to traverse the solution space. In the "Binary Tree" chapter, we mentioned that preorder, inorder, and postorder traversals all belong to depth-first search. Next, we will construct a backtracking problem using preorder traversal to progressively understand how the backtracking algorithm works.</p>
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<div class="admonition question">
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<p class="admonition-title">Example 1</p>
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<p>Given a binary tree, search and record all nodes with value <span class="arithmatex">\(7\)</span>, and return a list of these nodes.</p>
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</div>
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<p>For this problem, we perform a preorder traversal of the tree and check whether the current node's value is <span class="arithmatex">\(7\)</span>. If it is, we add the node to the result list <code>res</code>. The relevant implementation is shown in the following figure and code:</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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<div class="highlight"><span class="filename">preorder_traversal_i_compact.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
|
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""Preorder traversal: Example 1"""</span>
|
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
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<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="k">return</span>
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<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
|
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<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># Record solution</span>
|
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<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
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<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
|
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<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_i_compact.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
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<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
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<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="p">}</span>
|
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<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
|
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">left</span><span class="p">);</span>
|
|
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">right</span><span class="p">);</span>
|
|
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="p">}</span>
|
|
</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_i_compact.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
|
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
|
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
|
|
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
|
|
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_i_compact.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
|
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">PreOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
|
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
|
|
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
|
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_i_compact.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
|
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">preOrderI</span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="p">).(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span>
|
|
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="nx">preOrderI</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
|
|
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="nx">preOrderI</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
|
|
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_i_compact.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
|
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
|
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span>
|
|
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
|
|
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_i_compact.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
|
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
|
|
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_i_compact.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
|
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
|
|
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_i_compact.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
|
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
|
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="p">}</span>
|
|
</code></pre></div>
|
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</div>
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<div class="tabbed-block">
|
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<div class="highlight"><span class="filename">preorder_traversal_i_compact.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
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<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="p">}</span>
|
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<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
|
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
|
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
|
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
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<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_i_compact.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
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<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
|
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">left</span><span class="p">);</span>
|
|
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">right</span><span class="p">);</span>
|
|
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_i_compact.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* Preorder traversal: Example 1 */</span>
|
|
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="n">res</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
|
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
|
|
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
|
|
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_i_compact.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### Pre-order traversal: example 1 ###</span>
|
|
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
|
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">root</span>
|
|
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
|
|
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># Record solution</span>
|
|
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
|
|
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>
|
|
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
|
|
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
|
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">end</span>
|
|
</code></pre></div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_nodes.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Search for nodes in preorder traversal" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_nodes.png" /></a></p>
|
|
<p align="center"> Figure 13-1 Search for nodes in preorder traversal </p>
|
|
|
|
<h2 id="1311-attempt-and-backtrack">13.1.1 Attempt and Backtrack<a class="headerlink" href="#1311-attempt-and-backtrack" title="Permanent link">¶</a></h2>
|
|
<p><strong>The reason it is called a backtracking algorithm is that it employs "attempt" and "backtrack" strategies when searching the solution space</strong>. When the algorithm encounters a state where it cannot continue forward or cannot find a solution that satisfies the constraints, it will undo the previous choice, return to a previous state, and try other possible choices.</p>
|
|
<p>For Example 1, visiting each node represents an "attempt", while skipping over a leaf node or a function <code>return</code> from the parent node represents a "backtrack".</p>
|
|
<p>It is worth noting that <strong>backtracking is not limited to function returns alone</strong>. To illustrate this, let's extend Example 1 slightly.</p>
|
|
<div class="admonition question">
|
|
<p class="admonition-title">Example 2</p>
|
|
<p>In a binary tree, search all nodes with value <span class="arithmatex">\(7\)</span>, <strong>and return the paths from the root node to these nodes</strong>.</p>
|
|
</div>
|
|
<p>Based on the code from Example 1, we need to use a list <code>path</code> to record the visited node path. When we reach a node with value <span class="arithmatex">\(7\)</span>, we copy <code>path</code> and add it to the result list <code>res</code>. After traversal is complete, <code>res</code> contains all the solutions. The code is as follows:</p>
|
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<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_ii_compact.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
|
|
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w"> </span><span class="sd">"""Preorder traversal: Example 2"""</span>
|
|
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a> <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
|
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a> <span class="k">return</span>
|
|
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a> <span class="c1"># Attempt</span>
|
|
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a> <span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
|
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a> <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
|
|
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a> <span class="c1"># Record solution</span>
|
|
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">path</span><span class="p">))</span>
|
|
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a> <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
|
|
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a> <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
|
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a> <span class="c1"># Backtrack</span>
|
|
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a> <span class="n">path</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
|
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">path</span><span class="p">);</span>
|
|
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">left</span><span class="p">);</span>
|
|
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">right</span><span class="p">);</span>
|
|
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
|
|
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
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|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
|
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
|
|
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
|
|
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
|
|
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
|
<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">PreOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
|
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
|
|
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w"> </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
|
|
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
|
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
|
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">preOrderII</span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span>
|
|
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="o">...</span><span class="p">))</span>
|
|
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w"> </span><span class="nx">preOrderII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
|
|
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w"> </span><span class="nx">preOrderII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
|
|
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
|
<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
|
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">path</span><span class="p">)</span>
|
|
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span>
|
|
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
|
|
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
|
|
<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w"> </span><span class="nx">path</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
|
|
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">path</span><span class="p">]);</span>
|
|
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w"> </span><span class="nx">path</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
|
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span>
|
|
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span>
|
|
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w"> </span><span class="nx">path</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span>
|
|
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[][]</span>
|
|
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w"> </span><span class="nx">path</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
|
|
<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">path</span><span class="p">]);</span>
|
|
<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w"> </span><span class="nx">path</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
|
<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span>
|
|
<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">,</span>
|
|
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">path</span><span class="p">,</span>
|
|
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
|
|
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a>
|
|
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
|
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
|
|
<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
|
|
<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span>
|
|
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
|
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w"> </span><span class="n">path</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
|
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w"> </span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
|
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
|
<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
|
<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
|
<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
|
<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
|
<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">pathSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
|
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">pathSize</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
|
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w"> </span><span class="n">resSize</span><span class="o">++</span><span class="p">;</span>
|
|
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">left</span><span class="p">);</span>
|
|
<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">right</span><span class="p">);</span>
|
|
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w"> </span><span class="n">pathSize</span><span class="o">--</span><span class="p">;</span>
|
|
<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* Preorder traversal: Example 2 */</span>
|
|
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w"> </span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
|
<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w"> </span><span class="n">res</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
|
|
<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
|
|
<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
|
|
<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w"> </span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
|
|
<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_ii_compact.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### Pre-order traversal: example 2 ###</span>
|
|
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
|
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">root</span>
|
|
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
|
|
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="c1"># Attempt</span>
|
|
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="vg">$path</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">root</span>
|
|
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>
|
|
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="c1"># Record solution</span>
|
|
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="vg">$path</span><span class="o">.</span><span class="n">dup</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
|
|
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
|
|
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
|
|
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
|
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a>
|
|
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="c1"># Backtrack</span>
|
|
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w"> </span><span class="vg">$path</span><span class="o">.</span><span class="n">pop</span>
|
|
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="k">end</span>
|
|
</code></pre></div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<p>In each "attempt", we record the path by adding the current node to <code>path</code>; before "backtracking", we need to remove the node from <code>path</code>, <strong>to restore the state before this attempt</strong>.</p>
|
|
<p>Observing the process shown in the following figure, <strong>we can understand attempt and backtrack as "advance" and "undo"</strong>, two operations that are the reverse of each other.</p>
|
|
<div class="tabbed-set tabbed-alternate" data-tabs="3:11"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1"><1></label><label for="__tabbed_3_2"><2></label><label for="__tabbed_3_3"><3></label><label for="__tabbed_3_4"><4></label><label for="__tabbed_3_5"><5></label><label for="__tabbed_3_6"><6></label><label for="__tabbed_3_7"><7></label><label for="__tabbed_3_8"><8></label><label for="__tabbed_3_9"><9></label><label for="__tabbed_3_10"><10></label><label for="__tabbed_3_11"><11></label></div>
|
|
<div class="tabbed-content">
|
|
<div class="tabbed-block">
|
|
<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Attempt and backtrack" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step1.png" /></a></p>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step2" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step2.png" /></a></p>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step3" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step3.png" /></a></p>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step4" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step4.png" /></a></p>
|
|
</div>
|
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<div class="tabbed-block">
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<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step5" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step5.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step6" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step6.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step7" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step7.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step8" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step8.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step9" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step9.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step10" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step10.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step11" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step11.png" /></a></p>
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</div>
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</div>
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</div>
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<p align="center"> Figure 13-2 Attempt and backtrack </p>
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<h2 id="1312-pruning">13.1.2 Pruning<a class="headerlink" href="#1312-pruning" title="Permanent link">¶</a></h2>
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<p>Complex backtracking problems usually contain one or more constraints. <strong>Constraints can typically be used for "pruning"</strong>.</p>
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<div class="admonition question">
|
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<p class="admonition-title">Example 3</p>
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<p>In a binary tree, search all nodes with value <span class="arithmatex">\(7\)</span> and return the paths from the root node to these nodes, <strong>but require that the paths do not contain nodes with value <span class="arithmatex">\(3\)</span></strong>.</p>
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</div>
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<p>To satisfy the above constraints, <strong>we need to add pruning operations</strong>: during the search process, if we encounter a node with value <span class="arithmatex">\(3\)</span>, we return early and do not continue searching. The code is as follows:</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_compact.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
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<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w"> </span><span class="sd">"""Preorder traversal: Example 3"""</span>
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<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a> <span class="c1"># Pruning</span>
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<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a> <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
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<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a> <span class="k">return</span>
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<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a> <span class="c1"># Attempt</span>
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<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a> <span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
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<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a> <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
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<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a> <span class="c1"># Record solution</span>
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<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">path</span><span class="p">))</span>
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<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a> <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
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<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a> <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
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<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a> <span class="c1"># Backtrack</span>
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<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a> <span class="n">path</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_compact.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
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<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w"> </span><span class="c1">// Pruning</span>
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<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w"> </span><span class="c1">// Attempt</span>
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<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
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<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w"> </span><span class="c1">// Record solution</span>
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<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">path</span><span class="p">);</span>
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<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">left</span><span class="p">);</span>
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<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">right</span><span class="p">);</span>
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<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w"> </span><span class="c1">// Backtrack</span>
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<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
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<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_compact.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
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<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w"> </span><span class="c1">// Pruning</span>
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<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w"> </span><span class="c1">// Attempt</span>
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<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
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<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
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<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
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<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
|
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<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
|
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<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
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<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
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<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="p">}</span>
|
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_compact.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
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<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">PreOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w"> </span><span class="c1">// Pruning</span>
|
|
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
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<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
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<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
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<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
|
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<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w"> </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
|
|
<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w"> </span><span class="n">PreOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
|
<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
|
<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_compact.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
|
|
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">preOrderIII</span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="c1">// Pruning</span>
|
|
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span>
|
|
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="o">...</span><span class="p">))</span>
|
|
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w"> </span><span class="nx">preOrderIII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
|
|
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w"> </span><span class="nx">preOrderIII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
|
|
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
|
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_compact.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
|
|
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="c1">// Pruning</span>
|
|
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w"> </span><span class="k">guard</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
|
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">path</span><span class="p">)</span>
|
|
<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span>
|
|
<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
|
|
<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
|
|
<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_compact.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
|
|
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="c1">// Pruning</span>
|
|
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w"> </span><span class="nx">path</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
|
|
<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">path</span><span class="p">]);</span>
|
|
<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w"> </span><span class="nx">path</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
|
<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_compact.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
|
|
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span>
|
|
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span>
|
|
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w"> </span><span class="nx">path</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span>
|
|
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[][]</span>
|
|
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w"> </span><span class="c1">// Pruning</span>
|
|
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w"> </span><span class="nx">path</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">root</span><span class="p">);</span>
|
|
<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">path</span><span class="p">]);</span>
|
|
<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w"> </span><span class="nx">path</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
|
<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_compact.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
|
|
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span>
|
|
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="p">,</span>
|
|
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">path</span><span class="p">,</span>
|
|
<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
|
|
<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a>
|
|
<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
|
<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
|
|
<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
|
|
<a id="__codelineno-34-21" name="__codelineno-34-21" href="#__codelineno-34-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_compact.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
|
|
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span>
|
|
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
|
<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w"> </span><span class="n">path</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
|
<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w"> </span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
|
<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w"> </span><span class="c1">// Pruning</span>
|
|
<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
|
<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
|
<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
|
<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">path</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">());</span>
|
|
<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w"> </span><span class="n">path</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
|
<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_compact.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
|
|
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="c1">// Pruning</span>
|
|
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">pathSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
|
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">pathSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
|
<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w"> </span><span class="n">resSize</span><span class="o">++</span><span class="p">;</span>
|
|
<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">left</span><span class="p">);</span>
|
|
<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-></span><span class="n">right</span><span class="p">);</span>
|
|
<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w"> </span><span class="n">pathSize</span><span class="o">--</span><span class="p">;</span>
|
|
<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_compact.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* Preorder traversal: Example 3 */</span>
|
|
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="c1">// Pruning</span>
|
|
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="c1">// Attempt</span>
|
|
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w"> </span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
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<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w"> </span><span class="n">res</span><span class="o">!!</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
|
|
<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">)</span>
|
|
<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">)</span>
|
|
<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w"> </span><span class="c1">// Backtrack</span>
|
|
<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w"> </span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">path</span><span class="o">!!</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
|
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<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="p">}</span>
|
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_compact.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">### Pre-order traversal: example 3 ###</span>
|
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<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
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<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w"> </span><span class="c1"># Pruning</span>
|
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<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">root</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span>
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<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
|
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<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w"> </span><span class="c1"># Attempt</span>
|
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<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w"> </span><span class="vg">$path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
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<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a>
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<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w"> </span><span class="c1"># Record solution</span>
|
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<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="vg">$path</span><span class="o">.</span><span class="n">dup</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
|
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<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a>
|
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<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
|
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<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
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<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a>
|
|
<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="w"> </span><span class="c1"># Backtrack</span>
|
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<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="w"> </span><span class="vg">$path</span><span class="o">.</span><span class="n">pop</span>
|
|
<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="k">end</span>
|
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</code></pre></div>
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</div>
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</div>
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</div>
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<p>"Pruning" is a vivid term. As shown in the following figure, during the search process, <strong>we "prune" search branches that do not satisfy the constraints</strong>, avoiding many meaningless attempts and thus improving search efficiency.</p>
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<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_constrained_paths.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Pruning according to constraints" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_constrained_paths.png" /></a></p>
|
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<p align="center"> Figure 13-3 Pruning according to constraints </p>
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<h2 id="1313-framework-code">13.1.3 Framework Code<a class="headerlink" href="#1313-framework-code" title="Permanent link">¶</a></h2>
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<p>Next, we attempt to extract the main framework of backtracking's "attempt, backtrack, and pruning", to improve code generality.</p>
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<p>In the following framework code, <code>state</code> represents the current state of the problem, and <code>choices</code> represents the choices available in the current state:</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">State</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">choice</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">state</span><span class="p">]):</span>
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<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w"> </span><span class="sd">"""Backtracking algorithm framework"""</span>
|
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<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a> <span class="c1"># Check if it is a solution</span>
|
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<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a> <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
|
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<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a> <span class="c1"># Record the solution</span>
|
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<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a> <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a> <span class="c1"># Stop searching</span>
|
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<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a> <span class="k">return</span>
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<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a> <span class="c1"># Traverse all choices</span>
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<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a> <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
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<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a> <span class="c1"># Pruning: check if the choice is valid</span>
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<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a> <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
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<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a> <span class="c1"># Attempt: make a choice and update the state</span>
|
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<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a> <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a> <span class="c1"># Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a> <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
|
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
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<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Choice</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">State</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
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<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
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<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
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<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
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<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
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<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
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<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
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<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
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<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w"> </span><span class="p">}</span>
|
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<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
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<div class="tabbed-block">
|
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<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Choice</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">State</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Choice</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">State</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w"> </span><span class="n">RecordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w"> </span><span class="n">MakeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a><span class="w"> </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w"> </span><span class="n">UndoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-42-21" name="__codelineno-42-21" href="#__codelineno-42-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="nx">State</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="p">[]</span><span class="nx">Choice</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="nx">State</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
|
|
<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
|
|
<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="n">State</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Choice</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">State</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">State</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">Choice</span><span class="p">[],</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">State</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Choice</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">State</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="n">State</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Choice</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">State</span><span class="o">></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w"> </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w"> </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="w"> </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">Choice</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numChoices</span><span class="p">,</span><span class="w"> </span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numRes</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">numRes</span><span class="p">);</span>
|
|
<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">numChoices</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
|
|
<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">numChoices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">numRes</span><span class="p">);</span>
|
|
<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
|
|
<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* Backtracking algorithm framework */</span>
|
|
<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">State?,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Choice?></span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">State?></span><span class="o">?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w"> </span><span class="c1">// Record the solution</span>
|
|
<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w"> </span><span class="c1">// Stop searching</span>
|
|
<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w"> </span><span class="c1">// Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w"> </span><span class="c1">// Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">### Backtracking algorithm framework ###</span>
|
|
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="c1"># Check if it is a solution</span>
|
|
<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution?</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
|
|
<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="c1"># Record the solution</span>
|
|
<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w"> </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w"> </span><span class="k">return</span>
|
|
<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w"> </span><span class="k">end</span>
|
|
<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a>
|
|
<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w"> </span><span class="c1"># Traverse all choices</span>
|
|
<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span>
|
|
<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w"> </span><span class="c1"># Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid?</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w"> </span><span class="c1"># Attempt: make a choice and update the state</span>
|
|
<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w"> </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w"> </span><span class="c1"># Backtrack: undo the choice and restore to the previous state</span>
|
|
<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w"> </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w"> </span><span class="k">end</span>
|
|
<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w"> </span><span class="k">end</span>
|
|
<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="k">end</span>
|
|
</code></pre></div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<p>Next, we solve Example 3 based on the framework code. The state <code>state</code> is the node traversal path, the choices <code>choices</code> are the left and right child nodes of the current node, and the result <code>res</code> is a list of paths:</p>
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">])</span> <span class="o">-></span> <span class="nb">bool</span><span class="p">:</span>
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<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w"> </span><span class="sd">"""Check if the current state is a solution"""</span>
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<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a> <span class="k">return</span> <span class="n">state</span> <span class="ow">and</span> <span class="n">state</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span>
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<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>
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<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]]):</span>
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<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w"> </span><span class="sd">"""Record solution"""</span>
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<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
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<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>
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<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="o">-></span> <span class="nb">bool</span><span class="p">:</span>
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<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w"> </span><span class="sd">"""Check if the choice is valid under the current state"""</span>
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<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a> <span class="k">return</span> <span class="n">choice</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">choice</span><span class="o">.</span><span class="n">val</span> <span class="o">!=</span> <span class="mi">3</span>
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<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a>
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<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a><span class="k">def</span><span class="w"> </span><span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
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<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a><span class="w"> </span><span class="sd">"""Update state"""</span>
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<a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a> <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a>
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<a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
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<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="w"> </span><span class="sd">"""Restore state"""</span>
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<a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a> <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
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<a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a>
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<a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
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<a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a> <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]]</span>
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<a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a><span class="p">):</span>
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<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a><span class="w"> </span><span class="sd">"""Backtracking algorithm: Example 3"""</span>
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<a id="__codelineno-52-25" name="__codelineno-52-25" href="#__codelineno-52-25"></a> <span class="c1"># Check if it is a solution</span>
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<a id="__codelineno-52-26" name="__codelineno-52-26" href="#__codelineno-52-26"></a> <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
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<a id="__codelineno-52-27" name="__codelineno-52-27" href="#__codelineno-52-27"></a> <span class="c1"># Record solution</span>
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<a id="__codelineno-52-28" name="__codelineno-52-28" href="#__codelineno-52-28"></a> <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-52-29" name="__codelineno-52-29" href="#__codelineno-52-29"></a> <span class="c1"># Traverse all choices</span>
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<a id="__codelineno-52-30" name="__codelineno-52-30" href="#__codelineno-52-30"></a> <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
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<a id="__codelineno-52-31" name="__codelineno-52-31" href="#__codelineno-52-31"></a> <span class="c1"># Pruning: check if the choice is valid</span>
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<a id="__codelineno-52-32" name="__codelineno-52-32" href="#__codelineno-52-32"></a> <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
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<a id="__codelineno-52-33" name="__codelineno-52-33" href="#__codelineno-52-33"></a> <span class="c1"># Attempt: make choice, update state</span>
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<a id="__codelineno-52-34" name="__codelineno-52-34" href="#__codelineno-52-34"></a> <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-52-35" name="__codelineno-52-35" href="#__codelineno-52-35"></a> <span class="c1"># Proceed to the next round of selection</span>
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<a id="__codelineno-52-36" name="__codelineno-52-36" href="#__codelineno-52-36"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="p">[</span><span class="n">choice</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">choice</span><span class="o">.</span><span class="n">right</span><span class="p">],</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-52-37" name="__codelineno-52-37" href="#__codelineno-52-37"></a> <span class="c1"># Backtrack: undo choice, restore to previous state</span>
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<a id="__codelineno-52-38" name="__codelineno-52-38" href="#__codelineno-52-38"></a> <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* Check if the current state is a solution */</span>
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<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">empty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">back</span><span class="p">()</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
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<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="p">}</span>
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<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a>
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<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="cm">/* Record solution */</span>
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<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*>></span><span class="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
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<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="p">}</span>
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<a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a>
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<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
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<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
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<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="p">}</span>
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<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a>
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<a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a><span class="cm">/* Update state */</span>
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<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a><span class="p">}</span>
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<a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a>
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<a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></a><span class="cm">/* Restore state */</span>
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<a id="__codelineno-53-22" name="__codelineno-53-22" href="#__codelineno-53-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-23" name="__codelineno-53-23" href="#__codelineno-53-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
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<a id="__codelineno-53-24" name="__codelineno-53-24" href="#__codelineno-53-24"></a><span class="p">}</span>
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<a id="__codelineno-53-25" name="__codelineno-53-25" href="#__codelineno-53-25"></a>
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<a id="__codelineno-53-26" name="__codelineno-53-26" href="#__codelineno-53-26"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
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<a id="__codelineno-53-27" name="__codelineno-53-27" href="#__codelineno-53-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*>></span><span class="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-28" name="__codelineno-53-28" href="#__codelineno-53-28"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
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<a id="__codelineno-53-29" name="__codelineno-53-29" href="#__codelineno-53-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-30" name="__codelineno-53-30" href="#__codelineno-53-30"></a><span class="w"> </span><span class="c1">// Record solution</span>
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<a id="__codelineno-53-31" name="__codelineno-53-31" href="#__codelineno-53-31"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-53-32" name="__codelineno-53-32" href="#__codelineno-53-32"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-53-33" name="__codelineno-53-33" href="#__codelineno-53-33"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-53-34" name="__codelineno-53-34" href="#__codelineno-53-34"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-53-35" name="__codelineno-53-35" href="#__codelineno-53-35"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-53-36" name="__codelineno-53-36" href="#__codelineno-53-36"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-53-37" name="__codelineno-53-37" href="#__codelineno-53-37"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
|
|
<a id="__codelineno-53-38" name="__codelineno-53-38" href="#__codelineno-53-38"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-53-39" name="__codelineno-53-39" href="#__codelineno-53-39"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
|
|
<a id="__codelineno-53-40" name="__codelineno-53-40" href="#__codelineno-53-40"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">nextChoices</span><span class="p">{</span><span class="n">choice</span><span class="o">-></span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="o">-></span><span class="n">right</span><span class="p">};</span>
|
|
<a id="__codelineno-53-41" name="__codelineno-53-41" href="#__codelineno-53-41"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">nextChoices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-53-42" name="__codelineno-53-42" href="#__codelineno-53-42"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-53-43" name="__codelineno-53-43" href="#__codelineno-53-43"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-53-44" name="__codelineno-53-44" href="#__codelineno-53-44"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-53-45" name="__codelineno-53-45" href="#__codelineno-53-45"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-53-46" name="__codelineno-53-46" href="#__codelineno-53-46"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_template.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* Check if the current state is a solution */</span>
|
|
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">boolean</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">).</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
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<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="p">}</span>
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<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a>
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<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="cm">/* Record solution */</span>
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<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
|
|
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="p">}</span>
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|
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a>
|
|
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
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|
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="kt">boolean</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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|
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
|
|
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="p">}</span>
|
|
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a>
|
|
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="cm">/* Update state */</span>
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|
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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|
<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="p">}</span>
|
|
<a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a>
|
|
<a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="cm">/* Restore state */</span>
|
|
<a id="__codelineno-54-22" name="__codelineno-54-22" href="#__codelineno-54-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-54-23" name="__codelineno-54-23" href="#__codelineno-54-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
|
<a id="__codelineno-54-24" name="__codelineno-54-24" href="#__codelineno-54-24"></a><span class="p">}</span>
|
|
<a id="__codelineno-54-25" name="__codelineno-54-25" href="#__codelineno-54-25"></a>
|
|
<a id="__codelineno-54-26" name="__codelineno-54-26" href="#__codelineno-54-26"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
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|
<a id="__codelineno-54-27" name="__codelineno-54-27" href="#__codelineno-54-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-54-28" name="__codelineno-54-28" href="#__codelineno-54-28"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
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|
<a id="__codelineno-54-29" name="__codelineno-54-29" href="#__codelineno-54-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-54-30" name="__codelineno-54-30" href="#__codelineno-54-30"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-54-31" name="__codelineno-54-31" href="#__codelineno-54-31"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-54-32" name="__codelineno-54-32" href="#__codelineno-54-32"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-54-33" name="__codelineno-54-33" href="#__codelineno-54-33"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-54-34" name="__codelineno-54-34" href="#__codelineno-54-34"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-54-35" name="__codelineno-54-35" href="#__codelineno-54-35"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-54-36" name="__codelineno-54-36" href="#__codelineno-54-36"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-54-37" name="__codelineno-54-37" href="#__codelineno-54-37"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
|
|
<a id="__codelineno-54-38" name="__codelineno-54-38" href="#__codelineno-54-38"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-54-39" name="__codelineno-54-39" href="#__codelineno-54-39"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
|
|
<a id="__codelineno-54-40" name="__codelineno-54-40" href="#__codelineno-54-40"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">choice</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">right</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-54-41" name="__codelineno-54-41" href="#__codelineno-54-41"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-54-42" name="__codelineno-54-42" href="#__codelineno-54-42"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-54-43" name="__codelineno-54-43" href="#__codelineno-54-43"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-54-44" name="__codelineno-54-44" href="#__codelineno-54-44"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-54-45" name="__codelineno-54-45" href="#__codelineno-54-45"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_template.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* Check if the current state is a solution */</span>
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|
<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">IsSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="o">^</span><span class="mi">1</span><span class="p">].</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
|
|
<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="p">}</span>
|
|
<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a>
|
|
<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="cm">/* Record solution */</span>
|
|
<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="k">void</span><span class="w"> </span><span class="nf">RecordSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
|
|
<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="p">}</span>
|
|
<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a>
|
|
<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
|
|
<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">IsValid</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
|
|
<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a><span class="p">}</span>
|
|
<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a>
|
|
<a id="__codelineno-55-16" name="__codelineno-55-16" href="#__codelineno-55-16"></a><span class="cm">/* Update state */</span>
|
|
<a id="__codelineno-55-17" name="__codelineno-55-17" href="#__codelineno-55-17"></a><span class="k">void</span><span class="w"> </span><span class="nf">MakeChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-55-18" name="__codelineno-55-18" href="#__codelineno-55-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-55-19" name="__codelineno-55-19" href="#__codelineno-55-19"></a><span class="p">}</span>
|
|
<a id="__codelineno-55-20" name="__codelineno-55-20" href="#__codelineno-55-20"></a>
|
|
<a id="__codelineno-55-21" name="__codelineno-55-21" href="#__codelineno-55-21"></a><span class="cm">/* Restore state */</span>
|
|
<a id="__codelineno-55-22" name="__codelineno-55-22" href="#__codelineno-55-22"></a><span class="k">void</span><span class="w"> </span><span class="nf">UndoChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-55-23" name="__codelineno-55-23" href="#__codelineno-55-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
|
<a id="__codelineno-55-24" name="__codelineno-55-24" href="#__codelineno-55-24"></a><span class="p">}</span>
|
|
<a id="__codelineno-55-25" name="__codelineno-55-25" href="#__codelineno-55-25"></a>
|
|
<a id="__codelineno-55-26" name="__codelineno-55-26" href="#__codelineno-55-26"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
|
|
<a id="__codelineno-55-27" name="__codelineno-55-27" href="#__codelineno-55-27"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-55-28" name="__codelineno-55-28" href="#__codelineno-55-28"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-55-29" name="__codelineno-55-29" href="#__codelineno-55-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-55-30" name="__codelineno-55-30" href="#__codelineno-55-30"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-55-31" name="__codelineno-55-31" href="#__codelineno-55-31"></a><span class="w"> </span><span class="n">RecordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-55-32" name="__codelineno-55-32" href="#__codelineno-55-32"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-55-33" name="__codelineno-55-33" href="#__codelineno-55-33"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-55-34" name="__codelineno-55-34" href="#__codelineno-55-34"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-55-35" name="__codelineno-55-35" href="#__codelineno-55-35"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-55-36" name="__codelineno-55-36" href="#__codelineno-55-36"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-55-37" name="__codelineno-55-37" href="#__codelineno-55-37"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
|
|
<a id="__codelineno-55-38" name="__codelineno-55-38" href="#__codelineno-55-38"></a><span class="w"> </span><span class="n">MakeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-55-39" name="__codelineno-55-39" href="#__codelineno-55-39"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
|
|
<a id="__codelineno-55-40" name="__codelineno-55-40" href="#__codelineno-55-40"></a><span class="w"> </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="n">choice</span><span class="p">.</span><span class="n">left</span><span class="o">!</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">right</span><span class="o">!</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-55-41" name="__codelineno-55-41" href="#__codelineno-55-41"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-55-42" name="__codelineno-55-42" href="#__codelineno-55-42"></a><span class="w"> </span><span class="n">UndoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-55-43" name="__codelineno-55-43" href="#__codelineno-55-43"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-55-44" name="__codelineno-55-44" href="#__codelineno-55-44"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-55-45" name="__codelineno-55-45" href="#__codelineno-55-45"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_template.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* Check if the current state is a solution */</span>
|
|
<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">].</span><span class="nx">Val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
|
|
<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="p">}</span>
|
|
<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a>
|
|
<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="cm">/* Record solution */</span>
|
|
<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="o">...</span><span class="p">))</span>
|
|
<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="p">}</span>
|
|
<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a>
|
|
<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
|
|
<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span>
|
|
<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a><span class="p">}</span>
|
|
<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a>
|
|
<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="cm">/* Update state */</span>
|
|
<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a><span class="kd">func</span><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a><span class="p">}</span>
|
|
<a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a>
|
|
<a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a><span class="cm">/* Restore state */</span>
|
|
<a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a><span class="kd">func</span><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
|
<a id="__codelineno-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></a><span class="p">}</span>
|
|
<a id="__codelineno-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a>
|
|
<a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
|
|
<a id="__codelineno-56-27" name="__codelineno-56-27" href="#__codelineno-56-27"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrackIII</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-56-28" name="__codelineno-56-28" href="#__codelineno-56-28"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-56-29" name="__codelineno-56-29" href="#__codelineno-56-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-56-30" name="__codelineno-56-30" href="#__codelineno-56-30"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-56-31" name="__codelineno-56-31" href="#__codelineno-56-31"></a><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
|
|
<a id="__codelineno-56-32" name="__codelineno-56-32" href="#__codelineno-56-32"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-56-33" name="__codelineno-56-33" href="#__codelineno-56-33"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-56-34" name="__codelineno-56-34" href="#__codelineno-56-34"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="o">*</span><span class="nx">choices</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-56-35" name="__codelineno-56-35" href="#__codelineno-56-35"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-56-36" name="__codelineno-56-36" href="#__codelineno-56-36"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-56-37" name="__codelineno-56-37" href="#__codelineno-56-37"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
|
|
<a id="__codelineno-56-38" name="__codelineno-56-38" href="#__codelineno-56-38"></a><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-56-39" name="__codelineno-56-39" href="#__codelineno-56-39"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
|
|
<a id="__codelineno-56-40" name="__codelineno-56-40" href="#__codelineno-56-40"></a><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
|
<a id="__codelineno-56-41" name="__codelineno-56-41" href="#__codelineno-56-41"></a><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">temp</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
|
|
<a id="__codelineno-56-42" name="__codelineno-56-42" href="#__codelineno-56-42"></a><span class="w"> </span><span class="nx">backtrackIII</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="nx">temp</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
|
|
<a id="__codelineno-56-43" name="__codelineno-56-43" href="#__codelineno-56-43"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-56-44" name="__codelineno-56-44" href="#__codelineno-56-44"></a><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-56-45" name="__codelineno-56-45" href="#__codelineno-56-45"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-56-46" name="__codelineno-56-46" href="#__codelineno-56-46"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-56-47" name="__codelineno-56-47" href="#__codelineno-56-47"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_template.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* Check if the current state is a solution */</span>
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<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">])</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="bp">isEmpty</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="bp">last</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">7</span>
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|
<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="p">}</span>
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<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a>
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<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="cm">/* Record solution */</span>
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|
<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="kd">func</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="n">TreeNode</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
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|
<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
|
|
<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="p">}</span>
|
|
<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a>
|
|
<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
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|
<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="kd">func</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Bool</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">!.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span>
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|
<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="p">}</span>
|
|
<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a>
|
|
<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a><span class="cm">/* Update state */</span>
|
|
<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="kd">func</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="p">}</span>
|
|
<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a>
|
|
<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="cm">/* Restore state */</span>
|
|
<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="kd">func</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
|
|
<a id="__codelineno-57-24" name="__codelineno-57-24" href="#__codelineno-57-24"></a><span class="p">}</span>
|
|
<a id="__codelineno-57-25" name="__codelineno-57-25" href="#__codelineno-57-25"></a>
|
|
<a id="__codelineno-57-26" name="__codelineno-57-26" href="#__codelineno-57-26"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
|
|
<a id="__codelineno-57-27" name="__codelineno-57-27" href="#__codelineno-57-27"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[[</span><span class="n">TreeNode</span><span class="p">]])</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-57-28" name="__codelineno-57-28" href="#__codelineno-57-28"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
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|
<a id="__codelineno-57-29" name="__codelineno-57-29" href="#__codelineno-57-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-57-30" name="__codelineno-57-30" href="#__codelineno-57-30"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-57-31" name="__codelineno-57-31" href="#__codelineno-57-31"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-57-32" name="__codelineno-57-32" href="#__codelineno-57-32"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-57-33" name="__codelineno-57-33" href="#__codelineno-57-33"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-57-34" name="__codelineno-57-34" href="#__codelineno-57-34"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
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<a id="__codelineno-57-35" name="__codelineno-57-35" href="#__codelineno-57-35"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-57-36" name="__codelineno-57-36" href="#__codelineno-57-36"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
|
|
<a id="__codelineno-57-37" name="__codelineno-57-37" href="#__codelineno-57-37"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-57-38" name="__codelineno-57-38" href="#__codelineno-57-38"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
|
|
<a id="__codelineno-57-39" name="__codelineno-57-39" href="#__codelineno-57-39"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">choice</span><span class="p">.</span><span class="kr">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="kr">right</span><span class="p">].</span><span class="n">compactMap</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-57-40" name="__codelineno-57-40" href="#__codelineno-57-40"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-57-41" name="__codelineno-57-41" href="#__codelineno-57-41"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-57-42" name="__codelineno-57-42" href="#__codelineno-57-42"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-57-43" name="__codelineno-57-43" href="#__codelineno-57-43"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-57-44" name="__codelineno-57-44" href="#__codelineno-57-44"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_template.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* Check if the current state is a solution */</span>
|
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<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">state</span><span class="p">[</span><span class="nx">state</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="o">?</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">;</span>
|
|
<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="p">}</span>
|
|
<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a>
|
|
<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="cm">/* Record solution */</span>
|
|
<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
|
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<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="p">}</span>
|
|
<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a>
|
|
<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
|
|
<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span>
|
|
<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="p">}</span>
|
|
<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a>
|
|
<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="cm">/* Update state */</span>
|
|
<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="w"> </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a><span class="p">}</span>
|
|
<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a>
|
|
<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="cm">/* Restore state */</span>
|
|
<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="w"> </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
|
<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a><span class="p">}</span>
|
|
<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a>
|
|
<a id="__codelineno-58-26" name="__codelineno-58-26" href="#__codelineno-58-26"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
|
|
<a id="__codelineno-58-27" name="__codelineno-58-27" href="#__codelineno-58-27"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-58-28" name="__codelineno-58-28" href="#__codelineno-58-28"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-58-29" name="__codelineno-58-29" href="#__codelineno-58-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-58-30" name="__codelineno-58-30" href="#__codelineno-58-30"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-58-31" name="__codelineno-58-31" href="#__codelineno-58-31"></a><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-58-32" name="__codelineno-58-32" href="#__codelineno-58-32"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-58-33" name="__codelineno-58-33" href="#__codelineno-58-33"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-58-34" name="__codelineno-58-34" href="#__codelineno-58-34"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-58-35" name="__codelineno-58-35" href="#__codelineno-58-35"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-58-36" name="__codelineno-58-36" href="#__codelineno-58-36"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-58-37" name="__codelineno-58-37" href="#__codelineno-58-37"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
|
|
<a id="__codelineno-58-38" name="__codelineno-58-38" href="#__codelineno-58-38"></a><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-58-39" name="__codelineno-58-39" href="#__codelineno-58-39"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
|
|
<a id="__codelineno-58-40" name="__codelineno-58-40" href="#__codelineno-58-40"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="nx">choice</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">right</span><span class="p">],</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-58-41" name="__codelineno-58-41" href="#__codelineno-58-41"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-58-42" name="__codelineno-58-42" href="#__codelineno-58-42"></a><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">);</span>
|
|
<a id="__codelineno-58-43" name="__codelineno-58-43" href="#__codelineno-58-43"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-58-44" name="__codelineno-58-44" href="#__codelineno-58-44"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-58-45" name="__codelineno-58-45" href="#__codelineno-58-45"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_template.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* Check if the current state is a solution */</span>
|
|
<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">state</span><span class="p">[</span><span class="nx">state</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="o">?</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">7</span><span class="p">;</span>
|
|
<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="p">}</span>
|
|
<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a>
|
|
<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="cm">/* Record solution */</span>
|
|
<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[][])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">([...</span><span class="nx">state</span><span class="p">]);</span>
|
|
<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="p">}</span>
|
|
<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a>
|
|
<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
|
|
<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span><span class="w"> </span><span class="nx">choice</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span>
|
|
<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a><span class="p">}</span>
|
|
<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a>
|
|
<a id="__codelineno-59-16" name="__codelineno-59-16" href="#__codelineno-59-16"></a><span class="cm">/* Update state */</span>
|
|
<a id="__codelineno-59-17" name="__codelineno-59-17" href="#__codelineno-59-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span><span class="w"> </span><span class="nx">choice</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="w"> </span><span class="nx">state</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-59-19" name="__codelineno-59-19" href="#__codelineno-59-19"></a><span class="p">}</span>
|
|
<a id="__codelineno-59-20" name="__codelineno-59-20" href="#__codelineno-59-20"></a>
|
|
<a id="__codelineno-59-21" name="__codelineno-59-21" href="#__codelineno-59-21"></a><span class="cm">/* Restore state */</span>
|
|
<a id="__codelineno-59-22" name="__codelineno-59-22" href="#__codelineno-59-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-59-23" name="__codelineno-59-23" href="#__codelineno-59-23"></a><span class="w"> </span><span class="nx">state</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
|
<a id="__codelineno-59-24" name="__codelineno-59-24" href="#__codelineno-59-24"></a><span class="p">}</span>
|
|
<a id="__codelineno-59-25" name="__codelineno-59-25" href="#__codelineno-59-25"></a>
|
|
<a id="__codelineno-59-26" name="__codelineno-59-26" href="#__codelineno-59-26"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
|
|
<a id="__codelineno-59-27" name="__codelineno-59-27" href="#__codelineno-59-27"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span>
|
|
<a id="__codelineno-59-28" name="__codelineno-59-28" href="#__codelineno-59-28"></a><span class="w"> </span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span>
|
|
<a id="__codelineno-59-29" name="__codelineno-59-29" href="#__codelineno-59-29"></a><span class="w"> </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[],</span>
|
|
<a id="__codelineno-59-30" name="__codelineno-59-30" href="#__codelineno-59-30"></a><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">[][]</span>
|
|
<a id="__codelineno-59-31" name="__codelineno-59-31" href="#__codelineno-59-31"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-59-32" name="__codelineno-59-32" href="#__codelineno-59-32"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-59-33" name="__codelineno-59-33" href="#__codelineno-59-33"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-59-34" name="__codelineno-59-34" href="#__codelineno-59-34"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-59-35" name="__codelineno-59-35" href="#__codelineno-59-35"></a><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-59-36" name="__codelineno-59-36" href="#__codelineno-59-36"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-59-37" name="__codelineno-59-37" href="#__codelineno-59-37"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-59-38" name="__codelineno-59-38" href="#__codelineno-59-38"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-59-39" name="__codelineno-59-39" href="#__codelineno-59-39"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-59-40" name="__codelineno-59-40" href="#__codelineno-59-40"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-59-41" name="__codelineno-59-41" href="#__codelineno-59-41"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
|
|
<a id="__codelineno-59-42" name="__codelineno-59-42" href="#__codelineno-59-42"></a><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-59-43" name="__codelineno-59-43" href="#__codelineno-59-43"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
|
|
<a id="__codelineno-59-44" name="__codelineno-59-44" href="#__codelineno-59-44"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="nx">choice</span><span class="p">.</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">right</span><span class="p">],</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
|
|
<a id="__codelineno-59-45" name="__codelineno-59-45" href="#__codelineno-59-45"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-59-46" name="__codelineno-59-46" href="#__codelineno-59-46"></a><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">);</span>
|
|
<a id="__codelineno-59-47" name="__codelineno-59-47" href="#__codelineno-59-47"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-59-48" name="__codelineno-59-48" href="#__codelineno-59-48"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-59-49" name="__codelineno-59-49" href="#__codelineno-59-49"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_template.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* Check if the current state is a solution */</span>
|
|
<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">isNotEmpty</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">last</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">;</span>
|
|
<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="p">}</span>
|
|
<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a>
|
|
<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="cm">/* Record solution */</span>
|
|
<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="kt">void</span><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">List</span><span class="p">.</span><span class="n">from</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
|
|
<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="p">}</span>
|
|
<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a>
|
|
<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
|
|
<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isValid</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
|
|
<a id="__codelineno-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a><span class="p">}</span>
|
|
<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></a>
|
|
<a id="__codelineno-60-16" name="__codelineno-60-16" href="#__codelineno-60-16"></a><span class="cm">/* Update state */</span>
|
|
<a id="__codelineno-60-17" name="__codelineno-60-17" href="#__codelineno-60-17"></a><span class="kt">void</span><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-60-18" name="__codelineno-60-18" href="#__codelineno-60-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">choice</span><span class="o">!</span><span class="p">);</span>
|
|
<a id="__codelineno-60-19" name="__codelineno-60-19" href="#__codelineno-60-19"></a><span class="p">}</span>
|
|
<a id="__codelineno-60-20" name="__codelineno-60-20" href="#__codelineno-60-20"></a>
|
|
<a id="__codelineno-60-21" name="__codelineno-60-21" href="#__codelineno-60-21"></a><span class="cm">/* Restore state */</span>
|
|
<a id="__codelineno-60-22" name="__codelineno-60-22" href="#__codelineno-60-22"></a><span class="kt">void</span><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-60-23" name="__codelineno-60-23" href="#__codelineno-60-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
|
|
<a id="__codelineno-60-24" name="__codelineno-60-24" href="#__codelineno-60-24"></a><span class="p">}</span>
|
|
<a id="__codelineno-60-25" name="__codelineno-60-25" href="#__codelineno-60-25"></a>
|
|
<a id="__codelineno-60-26" name="__codelineno-60-26" href="#__codelineno-60-26"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
|
|
<a id="__codelineno-60-27" name="__codelineno-60-27" href="#__codelineno-60-27"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
|
|
<a id="__codelineno-60-28" name="__codelineno-60-28" href="#__codelineno-60-28"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span>
|
|
<a id="__codelineno-60-29" name="__codelineno-60-29" href="#__codelineno-60-29"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">?></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span>
|
|
<a id="__codelineno-60-30" name="__codelineno-60-30" href="#__codelineno-60-30"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
|
|
<a id="__codelineno-60-31" name="__codelineno-60-31" href="#__codelineno-60-31"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-60-32" name="__codelineno-60-32" href="#__codelineno-60-32"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-60-33" name="__codelineno-60-33" href="#__codelineno-60-33"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-60-34" name="__codelineno-60-34" href="#__codelineno-60-34"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-60-35" name="__codelineno-60-35" href="#__codelineno-60-35"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-60-36" name="__codelineno-60-36" href="#__codelineno-60-36"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-60-37" name="__codelineno-60-37" href="#__codelineno-60-37"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-60-38" name="__codelineno-60-38" href="#__codelineno-60-38"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-60-39" name="__codelineno-60-39" href="#__codelineno-60-39"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-60-40" name="__codelineno-60-40" href="#__codelineno-60-40"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-60-41" name="__codelineno-60-41" href="#__codelineno-60-41"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
|
|
<a id="__codelineno-60-42" name="__codelineno-60-42" href="#__codelineno-60-42"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-60-43" name="__codelineno-60-43" href="#__codelineno-60-43"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
|
|
<a id="__codelineno-60-44" name="__codelineno-60-44" href="#__codelineno-60-44"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="n">choice</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">right</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-60-45" name="__codelineno-60-45" href="#__codelineno-60-45"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-60-46" name="__codelineno-60-46" href="#__codelineno-60-46"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-60-47" name="__codelineno-60-47" href="#__codelineno-60-47"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-60-48" name="__codelineno-60-48" href="#__codelineno-60-48"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-60-49" name="__codelineno-60-49" href="#__codelineno-60-49"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">preorder_traversal_iii_template.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* Check if the current state is a solution */</span>
|
|
<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">last</span><span class="p">().</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
|
|
<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="p">}</span>
|
|
<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a>
|
|
<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="cm">/* Record solution */</span>
|
|
<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="k">fn</span><span class="w"> </span><span class="nf">record_solution</span><span class="p">(</span>
|
|
<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
|
|
<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
|
<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
|
<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="p">}</span>
|
|
<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a>
|
|
<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
|
|
<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="k">fn</span><span class="w"> </span><span class="nf">is_valid</span><span class="p">(</span><span class="n">_</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
|
|
<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a><span class="p">}</span>
|
|
<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a>
|
|
<a id="__codelineno-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a><span class="cm">/* Update state */</span>
|
|
<a id="__codelineno-61-20" name="__codelineno-61-20" href="#__codelineno-61-20"></a><span class="k">fn</span><span class="w"> </span><span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="nc">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-61-21" name="__codelineno-61-21" href="#__codelineno-61-21"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-61-22" name="__codelineno-61-22" href="#__codelineno-61-22"></a><span class="p">}</span>
|
|
<a id="__codelineno-61-23" name="__codelineno-61-23" href="#__codelineno-61-23"></a>
|
|
<a id="__codelineno-61-24" name="__codelineno-61-24" href="#__codelineno-61-24"></a><span class="cm">/* Restore state */</span>
|
|
<a id="__codelineno-61-25" name="__codelineno-61-25" href="#__codelineno-61-25"></a><span class="k">fn</span><span class="w"> </span><span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="n">_</span><span class="p">:</span><span class="w"> </span><span class="nc">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-61-26" name="__codelineno-61-26" href="#__codelineno-61-26"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
|
<a id="__codelineno-61-27" name="__codelineno-61-27" href="#__codelineno-61-27"></a><span class="p">}</span>
|
|
<a id="__codelineno-61-28" name="__codelineno-61-28" href="#__codelineno-61-28"></a>
|
|
<a id="__codelineno-61-29" name="__codelineno-61-29" href="#__codelineno-61-29"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
|
|
<a id="__codelineno-61-30" name="__codelineno-61-30" href="#__codelineno-61-30"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
|
|
<a id="__codelineno-61-31" name="__codelineno-61-31" href="#__codelineno-61-31"></a><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span>
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|
<a id="__codelineno-61-32" name="__codelineno-61-32" href="#__codelineno-61-32"></a><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Option</span><span class="o"><&</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
|
|
<a id="__codelineno-61-33" name="__codelineno-61-33" href="#__codelineno-61-33"></a><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>>></span><span class="p">,</span>
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|
<a id="__codelineno-61-34" name="__codelineno-61-34" href="#__codelineno-61-34"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-61-35" name="__codelineno-61-35" href="#__codelineno-61-35"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
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|
<a id="__codelineno-61-36" name="__codelineno-61-36" href="#__codelineno-61-36"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-61-37" name="__codelineno-61-37" href="#__codelineno-61-37"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-61-38" name="__codelineno-61-38" href="#__codelineno-61-38"></a><span class="w"> </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-61-39" name="__codelineno-61-39" href="#__codelineno-61-39"></a><span class="w"> </span><span class="p">}</span>
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|
<a id="__codelineno-61-40" name="__codelineno-61-40" href="#__codelineno-61-40"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
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|
<a id="__codelineno-61-41" name="__codelineno-61-41" href="#__codelineno-61-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="o">&</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">iter</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-61-42" name="__codelineno-61-42" href="#__codelineno-61-42"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
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|
<a id="__codelineno-61-43" name="__codelineno-61-43" href="#__codelineno-61-43"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-61-44" name="__codelineno-61-44" href="#__codelineno-61-44"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
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<a id="__codelineno-61-45" name="__codelineno-61-45" href="#__codelineno-61-45"></a><span class="w"> </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">clone</span><span class="p">());</span>
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<a id="__codelineno-61-46" name="__codelineno-61-46" href="#__codelineno-61-46"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
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|
<a id="__codelineno-61-47" name="__codelineno-61-47" href="#__codelineno-61-47"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span>
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<a id="__codelineno-61-48" name="__codelineno-61-48" href="#__codelineno-61-48"></a><span class="w"> </span><span class="n">state</span><span class="p">,</span>
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|
<a id="__codelineno-61-49" name="__codelineno-61-49" href="#__codelineno-61-49"></a><span class="w"> </span><span class="o">&</span><span class="fm">vec!</span><span class="p">[</span>
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<a id="__codelineno-61-50" name="__codelineno-61-50" href="#__codelineno-61-50"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span>
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<a id="__codelineno-61-51" name="__codelineno-61-51" href="#__codelineno-61-51"></a><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span>
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<a id="__codelineno-61-52" name="__codelineno-61-52" href="#__codelineno-61-52"></a><span class="w"> </span><span class="p">],</span>
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|
<a id="__codelineno-61-53" name="__codelineno-61-53" href="#__codelineno-61-53"></a><span class="w"> </span><span class="n">res</span><span class="p">,</span>
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|
<a id="__codelineno-61-54" name="__codelineno-61-54" href="#__codelineno-61-54"></a><span class="w"> </span><span class="p">);</span>
|
|
<a id="__codelineno-61-55" name="__codelineno-61-55" href="#__codelineno-61-55"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-61-56" name="__codelineno-61-56" href="#__codelineno-61-56"></a><span class="w"> </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">clone</span><span class="p">());</span>
|
|
<a id="__codelineno-61-57" name="__codelineno-61-57" href="#__codelineno-61-57"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-61-58" name="__codelineno-61-58" href="#__codelineno-61-58"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-61-59" name="__codelineno-61-59" href="#__codelineno-61-59"></a><span class="p">}</span>
|
|
</code></pre></div>
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|
</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* Check if the current state is a solution */</span>
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<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">pathSize</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">pathSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
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<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="p">}</span>
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|
<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a>
|
|
<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="cm">/* Record solution */</span>
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|
<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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|
<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">pathSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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|
<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">resSize</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
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|
<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w"> </span><span class="n">resSize</span><span class="o">++</span><span class="p">;</span>
|
|
<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></a><span class="p">}</span>
|
|
<a id="__codelineno-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></a>
|
|
<a id="__codelineno-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
|
|
<a id="__codelineno-62-15" name="__codelineno-62-15" href="#__codelineno-62-15"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-62-16" name="__codelineno-62-16" href="#__codelineno-62-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
|
|
<a id="__codelineno-62-17" name="__codelineno-62-17" href="#__codelineno-62-17"></a><span class="p">}</span>
|
|
<a id="__codelineno-62-18" name="__codelineno-62-18" href="#__codelineno-62-18"></a>
|
|
<a id="__codelineno-62-19" name="__codelineno-62-19" href="#__codelineno-62-19"></a><span class="cm">/* Update state */</span>
|
|
<a id="__codelineno-62-20" name="__codelineno-62-20" href="#__codelineno-62-20"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-62-21" name="__codelineno-62-21" href="#__codelineno-62-21"></a><span class="w"> </span><span class="n">path</span><span class="p">[</span><span class="n">pathSize</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choice</span><span class="p">;</span>
|
|
<a id="__codelineno-62-22" name="__codelineno-62-22" href="#__codelineno-62-22"></a><span class="p">}</span>
|
|
<a id="__codelineno-62-23" name="__codelineno-62-23" href="#__codelineno-62-23"></a>
|
|
<a id="__codelineno-62-24" name="__codelineno-62-24" href="#__codelineno-62-24"></a><span class="cm">/* Restore state */</span>
|
|
<a id="__codelineno-62-25" name="__codelineno-62-25" href="#__codelineno-62-25"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-62-26" name="__codelineno-62-26" href="#__codelineno-62-26"></a><span class="w"> </span><span class="n">pathSize</span><span class="o">--</span><span class="p">;</span>
|
|
<a id="__codelineno-62-27" name="__codelineno-62-27" href="#__codelineno-62-27"></a><span class="p">}</span>
|
|
<a id="__codelineno-62-28" name="__codelineno-62-28" href="#__codelineno-62-28"></a>
|
|
<a id="__codelineno-62-29" name="__codelineno-62-29" href="#__codelineno-62-29"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
|
|
<a id="__codelineno-62-30" name="__codelineno-62-30" href="#__codelineno-62-30"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-62-31" name="__codelineno-62-31" href="#__codelineno-62-31"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
|
|
<a id="__codelineno-62-32" name="__codelineno-62-32" href="#__codelineno-62-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-62-33" name="__codelineno-62-33" href="#__codelineno-62-33"></a><span class="w"> </span><span class="c1">// Record solution</span>
|
|
<a id="__codelineno-62-34" name="__codelineno-62-34" href="#__codelineno-62-34"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">();</span>
|
|
<a id="__codelineno-62-35" name="__codelineno-62-35" href="#__codelineno-62-35"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-62-36" name="__codelineno-62-36" href="#__codelineno-62-36"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
|
|
<a id="__codelineno-62-37" name="__codelineno-62-37" href="#__codelineno-62-37"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-62-38" name="__codelineno-62-38" href="#__codelineno-62-38"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
|
<a id="__codelineno-62-39" name="__codelineno-62-39" href="#__codelineno-62-39"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-62-40" name="__codelineno-62-40" href="#__codelineno-62-40"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-62-41" name="__codelineno-62-41" href="#__codelineno-62-41"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
|
|
<a id="__codelineno-62-42" name="__codelineno-62-42" href="#__codelineno-62-42"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
|
|
<a id="__codelineno-62-43" name="__codelineno-62-43" href="#__codelineno-62-43"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
|
|
<a id="__codelineno-62-44" name="__codelineno-62-44" href="#__codelineno-62-44"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">nextChoices</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="n">choice</span><span class="o">-></span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="o">-></span><span class="n">right</span><span class="p">};</span>
|
|
<a id="__codelineno-62-45" name="__codelineno-62-45" href="#__codelineno-62-45"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">nextChoices</span><span class="p">);</span>
|
|
<a id="__codelineno-62-46" name="__codelineno-62-46" href="#__codelineno-62-46"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-62-47" name="__codelineno-62-47" href="#__codelineno-62-47"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">();</span>
|
|
<a id="__codelineno-62-48" name="__codelineno-62-48" href="#__codelineno-62-48"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-62-49" name="__codelineno-62-49" href="#__codelineno-62-49"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-62-50" name="__codelineno-62-50" href="#__codelineno-62-50"></a><span class="p">}</span>
|
|
</code></pre></div>
|
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* Check if the current state is a solution */</span>
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<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">TreeNode?></span><span class="p">):</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">isNotEmpty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="o">[</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]?.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span>
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<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="p">}</span>
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<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a>
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<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="cm">/* Record solution */</span>
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<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">TreeNode?></span><span class="o">?</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">MutableList</span><span class="o"><</span><span class="n">TreeNode?></span><span class="o">?></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">state</span><span class="o">!!</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
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<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="p">}</span>
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<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a>
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<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="cm">/* Check if the choice is valid under the current state */</span>
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<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">TreeNode?></span><span class="o">?</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="m">3</span>
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<a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a><span class="p">}</span>
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<a id="__codelineno-63-15" name="__codelineno-63-15" href="#__codelineno-63-15"></a>
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<a id="__codelineno-63-16" name="__codelineno-63-16" href="#__codelineno-63-16"></a><span class="cm">/* Update state */</span>
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<a id="__codelineno-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">TreeNode?></span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-18" name="__codelineno-63-18" href="#__codelineno-63-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-63-19" name="__codelineno-63-19" href="#__codelineno-63-19"></a><span class="p">}</span>
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<a id="__codelineno-63-20" name="__codelineno-63-20" href="#__codelineno-63-20"></a>
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<a id="__codelineno-63-21" name="__codelineno-63-21" href="#__codelineno-63-21"></a><span class="cm">/* Restore state */</span>
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<a id="__codelineno-63-22" name="__codelineno-63-22" href="#__codelineno-63-22"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">TreeNode?></span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-23" name="__codelineno-63-23" href="#__codelineno-63-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">removeLast</span><span class="p">()</span>
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<a id="__codelineno-63-24" name="__codelineno-63-24" href="#__codelineno-63-24"></a><span class="p">}</span>
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<a id="__codelineno-63-25" name="__codelineno-63-25" href="#__codelineno-63-25"></a>
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<a id="__codelineno-63-26" name="__codelineno-63-26" href="#__codelineno-63-26"></a><span class="cm">/* Backtracking algorithm: Example 3 */</span>
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<a id="__codelineno-63-27" name="__codelineno-63-27" href="#__codelineno-63-27"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
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<a id="__codelineno-63-28" name="__codelineno-63-28" href="#__codelineno-63-28"></a><span class="w"> </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">TreeNode?></span><span class="p">,</span>
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<a id="__codelineno-63-29" name="__codelineno-63-29" href="#__codelineno-63-29"></a><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">TreeNode?></span><span class="p">,</span>
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<a id="__codelineno-63-30" name="__codelineno-63-30" href="#__codelineno-63-30"></a><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">MutableList</span><span class="o"><</span><span class="n">TreeNode?></span><span class="o">?></span>
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<a id="__codelineno-63-31" name="__codelineno-63-31" href="#__codelineno-63-31"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-32" name="__codelineno-63-32" href="#__codelineno-63-32"></a><span class="w"> </span><span class="c1">// Check if it is a solution</span>
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<a id="__codelineno-63-33" name="__codelineno-63-33" href="#__codelineno-63-33"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-34" name="__codelineno-63-34" href="#__codelineno-63-34"></a><span class="w"> </span><span class="c1">// Record solution</span>
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<a id="__codelineno-63-35" name="__codelineno-63-35" href="#__codelineno-63-35"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-63-36" name="__codelineno-63-36" href="#__codelineno-63-36"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-63-37" name="__codelineno-63-37" href="#__codelineno-63-37"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
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<a id="__codelineno-63-38" name="__codelineno-63-38" href="#__codelineno-63-38"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-39" name="__codelineno-63-39" href="#__codelineno-63-39"></a><span class="w"> </span><span class="c1">// Pruning: check if the choice is valid</span>
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<a id="__codelineno-63-40" name="__codelineno-63-40" href="#__codelineno-63-40"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-41" name="__codelineno-63-41" href="#__codelineno-63-41"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
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<a id="__codelineno-63-42" name="__codelineno-63-42" href="#__codelineno-63-42"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-63-43" name="__codelineno-63-43" href="#__codelineno-63-43"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
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<a id="__codelineno-63-44" name="__codelineno-63-44" href="#__codelineno-63-44"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">mutableListOf</span><span class="p">(</span><span class="n">choice</span><span class="o">!!</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">right</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-63-45" name="__codelineno-63-45" href="#__codelineno-63-45"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
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<a id="__codelineno-63-46" name="__codelineno-63-46" href="#__codelineno-63-46"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-63-47" name="__codelineno-63-47" href="#__codelineno-63-47"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-63-48" name="__codelineno-63-48" href="#__codelineno-63-48"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-63-49" name="__codelineno-63-49" href="#__codelineno-63-49"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">### Check if current state is solution ###</span>
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<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_solution?</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
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<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="o">.</span><span class="n">empty?</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">last</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span>
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<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="k">end</span>
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<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a>
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<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="c1">### Record solution ###</span>
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<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">dup</span>
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<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="k">end</span>
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<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a>
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<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="c1">### Check if choice is valid in current state ###</span>
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<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_valid?</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span>
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<a id="__codelineno-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></a><span class="k">end</span>
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<a id="__codelineno-64-15" name="__codelineno-64-15" href="#__codelineno-64-15"></a>
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<a id="__codelineno-64-16" name="__codelineno-64-16" href="#__codelineno-64-16"></a><span class="c1">### Update state ###</span>
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<a id="__codelineno-64-17" name="__codelineno-64-17" href="#__codelineno-64-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-64-18" name="__codelineno-64-18" href="#__codelineno-64-18"></a><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">choice</span>
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<a id="__codelineno-64-19" name="__codelineno-64-19" href="#__codelineno-64-19"></a><span class="k">end</span>
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|
<a id="__codelineno-64-20" name="__codelineno-64-20" href="#__codelineno-64-20"></a>
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<a id="__codelineno-64-21" name="__codelineno-64-21" href="#__codelineno-64-21"></a><span class="c1">### Restore state ###</span>
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<a id="__codelineno-64-22" name="__codelineno-64-22" href="#__codelineno-64-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-64-23" name="__codelineno-64-23" href="#__codelineno-64-23"></a><span class="w"> </span><span class="n">state</span><span class="o">.</span><span class="n">pop</span>
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<a id="__codelineno-64-24" name="__codelineno-64-24" href="#__codelineno-64-24"></a><span class="k">end</span>
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|
<a id="__codelineno-64-25" name="__codelineno-64-25" href="#__codelineno-64-25"></a>
|
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<a id="__codelineno-64-26" name="__codelineno-64-26" href="#__codelineno-64-26"></a><span class="c1">### Backtracking: example 3 ###</span>
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<a id="__codelineno-64-27" name="__codelineno-64-27" href="#__codelineno-64-27"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-64-28" name="__codelineno-64-28" href="#__codelineno-64-28"></a><span class="w"> </span><span class="c1"># Check if it is a solution</span>
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<a id="__codelineno-64-29" name="__codelineno-64-29" href="#__codelineno-64-29"></a><span class="w"> </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution?</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
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<a id="__codelineno-64-30" name="__codelineno-64-30" href="#__codelineno-64-30"></a>
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<a id="__codelineno-64-31" name="__codelineno-64-31" href="#__codelineno-64-31"></a><span class="w"> </span><span class="c1"># Traverse all choices</span>
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<a id="__codelineno-64-32" name="__codelineno-64-32" href="#__codelineno-64-32"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span>
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<a id="__codelineno-64-33" name="__codelineno-64-33" href="#__codelineno-64-33"></a><span class="w"> </span><span class="c1"># Pruning: check if the choice is valid</span>
|
|
<a id="__codelineno-64-34" name="__codelineno-64-34" href="#__codelineno-64-34"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid?</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-64-35" name="__codelineno-64-35" href="#__codelineno-64-35"></a><span class="w"> </span><span class="c1"># Attempt: make choice, update state</span>
|
|
<a id="__codelineno-64-36" name="__codelineno-64-36" href="#__codelineno-64-36"></a><span class="w"> </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-64-37" name="__codelineno-64-37" href="#__codelineno-64-37"></a><span class="w"> </span><span class="c1"># Proceed to the next round of selection</span>
|
|
<a id="__codelineno-64-38" name="__codelineno-64-38" href="#__codelineno-64-38"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">[</span><span class="n">choice</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="o">.</span><span class="n">right</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
|
|
<a id="__codelineno-64-39" name="__codelineno-64-39" href="#__codelineno-64-39"></a><span class="w"> </span><span class="c1"># Backtrack: undo choice, restore to previous state</span>
|
|
<a id="__codelineno-64-40" name="__codelineno-64-40" href="#__codelineno-64-40"></a><span class="w"> </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
|
|
<a id="__codelineno-64-41" name="__codelineno-64-41" href="#__codelineno-64-41"></a><span class="w"> </span><span class="k">end</span>
|
|
<a id="__codelineno-64-42" name="__codelineno-64-42" href="#__codelineno-64-42"></a><span class="w"> </span><span class="k">end</span>
|
|
<a id="__codelineno-64-43" name="__codelineno-64-43" href="#__codelineno-64-43"></a><span class="k">end</span>
|
|
</code></pre></div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<p>As per the problem statement, we should continue searching after finding a node with value <span class="arithmatex">\(7\)</span>. <strong>Therefore, we need to remove the <code>return</code> statement after recording the solution</strong>. The following figure compares the search process with and without the <code>return</code> statement.</p>
|
|
<p><a class="glightbox" href="../backtracking_algorithm.assets/backtrack_remove_return_or_not.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Comparison of search process with and without return statement" class="animation-figure" src="../backtracking_algorithm.assets/backtrack_remove_return_or_not.png" /></a></p>
|
|
<p align="center"> Figure 13-4 Comparison of search process with and without return statement </p>
|
|
|
|
<p>Compared to code based on preorder traversal, code based on the backtracking algorithm framework appears more verbose, but has better generality. In fact, <strong>many backtracking problems can be solved within this framework</strong>. We only need to define <code>state</code> and <code>choices</code> for the specific problem and implement each method in the framework.</p>
|
|
<h2 id="1314-common-terminology">13.1.4 Common Terminology<a class="headerlink" href="#1314-common-terminology" title="Permanent link">¶</a></h2>
|
|
<p>To analyze algorithmic problems more clearly, we summarize the meanings of common terminology used in backtracking algorithms and provide corresponding examples from Example 3, as shown in the following table.</p>
|
|
<p align="center"> Table 13-1 Common Backtracking Algorithm Terminology </p>
|
|
|
|
<div class="center-table">
|
|
<table>
|
|
<thead>
|
|
<tr>
|
|
<th>Term</th>
|
|
<th>Definition</th>
|
|
<th>Example 3</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>Solution (solution)</td>
|
|
<td>A solution is an answer that satisfies the specific conditions of a problem; there may be one or more solutions</td>
|
|
<td>All paths from root to nodes with value <span class="arithmatex">\(7\)</span> that satisfy the constraint</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Constraint (constraint)</td>
|
|
<td>A constraint is a condition in the problem that limits the feasibility of solutions, typically used for pruning</td>
|
|
<td>Paths do not contain nodes with value <span class="arithmatex">\(3\)</span></td>
|
|
</tr>
|
|
<tr>
|
|
<td>State (state)</td>
|
|
<td>State represents the situation of a problem at a certain moment, including the choices already made</td>
|
|
<td>The currently visited node path, i.e., the <code>path</code> list of nodes</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Attempt (attempt)</td>
|
|
<td>An attempt is the process of exploring the solution space according to available choices, including making choices, updating state, and checking if it is a solution</td>
|
|
<td>Recursively visit left (right) child nodes, add nodes to <code>path</code>, check if node value is <span class="arithmatex">\(7\)</span></td>
|
|
</tr>
|
|
<tr>
|
|
<td>Backtrack (backtracking)</td>
|
|
<td>Backtracking refers to undoing previous choices and returning to a previous state when encountering a state that does not satisfy constraints</td>
|
|
<td>Stop searching when passing over leaf nodes, ending node visits, or encountering nodes with value <span class="arithmatex">\(3\)</span>; function returns</td>
|
|
</tr>
|
|
<tr>
|
|
<td>Pruning (pruning)</td>
|
|
<td>Pruning is a method of avoiding meaningless search paths according to problem characteristics and constraints, which can improve search efficiency</td>
|
|
<td>When encountering a node with value <span class="arithmatex">\(3\)</span>, do not continue searching</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
<div class="admonition tip">
|
|
<p class="admonition-title">Tip</p>
|
|
<p>The concepts of problem, solution, state, etc. are universal and are involved in divide-and-conquer, backtracking, dynamic programming, greedy and other algorithms.</p>
|
|
</div>
|
|
<h2 id="1315-advantages-and-limitations">13.1.5 Advantages and Limitations<a class="headerlink" href="#1315-advantages-and-limitations" title="Permanent link">¶</a></h2>
|
|
<p>The backtracking algorithm is essentially a depth-first search algorithm that tries all possible solutions until it finds one that satisfies the conditions. The advantage of this approach is that it can find all possible solutions, and with reasonable pruning operations, it achieves high efficiency.</p>
|
|
<p>However, when dealing with large-scale or complex problems, <strong>the running efficiency of the backtracking algorithm may be unacceptable</strong>.</p>
|
|
<ul>
|
|
<li><strong>Time</strong>: The backtracking algorithm usually needs to traverse all possibilities in the solution space, and the time complexity can reach exponential or factorial order.</li>
|
|
<li><strong>Space</strong>: During recursive calls, the current state needs to be saved (such as paths, auxiliary variables used for pruning, etc.), and when the depth is large, the space requirement can become very large.</li>
|
|
</ul>
|
|
<p>Nevertheless, <strong>the backtracking algorithm is still the best solution for certain search problems and constraint satisfaction problems</strong>. For these problems, since we cannot predict which choices will generate valid solutions, we must traverse all possible choices. In this case, <strong>the key is how to optimize efficiency</strong>. There are two common efficiency optimization methods.</p>
|
|
<ul>
|
|
<li><strong>Pruning</strong>: Avoid searching paths that are guaranteed not to produce solutions, thereby saving time and space.</li>
|
|
<li><strong>Heuristic search</strong>: Introduce certain strategies or estimation values during the search process to prioritize searching paths that are most likely to produce valid solutions.</li>
|
|
</ul>
|
|
<h2 id="1316-typical-backtracking-examples">13.1.6 Typical Backtracking Examples<a class="headerlink" href="#1316-typical-backtracking-examples" title="Permanent link">¶</a></h2>
|
|
<p>The backtracking algorithm can be used to solve many search problems, constraint satisfaction problems, and combinatorial optimization problems.</p>
|
|
<p><strong>Search problems</strong>: The goal of these problems is to find solutions that satisfy specific conditions.</p>
|
|
<ul>
|
|
<li>Permutation problem: Given a set, find all possible permutations and combinations.</li>
|
|
<li>Subset sum problem: Given a set and a target sum, find all subsets in the set whose elements sum to the target.</li>
|
|
<li>Tower of Hanoi: Given three pegs and a series of disks of different sizes, move all disks from one peg to another, moving only one disk at a time, and never placing a larger disk on a smaller disk.</li>
|
|
</ul>
|
|
<p><strong>Constraint satisfaction problems</strong>: The goal of these problems is to find solutions that satisfy all constraints.</p>
|
|
<ul>
|
|
<li>N-Queens: Place <span class="arithmatex">\(n\)</span> queens on an <span class="arithmatex">\(n \times n\)</span> chessboard such that they do not attack each other.</li>
|
|
<li>Sudoku: Fill numbers <span class="arithmatex">\(1\)</span> to <span class="arithmatex">\(9\)</span> in a <span class="arithmatex">\(9 \times 9\)</span> grid such that each row, column, and <span class="arithmatex">\(3 \times 3\)</span> subgrid contains no repeated digits.</li>
|
|
<li>Graph coloring: Given an undirected graph, color each vertex with the minimum number of colors such that adjacent vertices have different colors.</li>
|
|
</ul>
|
|
<p><strong>Combinatorial optimization problems</strong>: The goal of these problems is to find an optimal solution that satisfies certain conditions in a combinatorial space.</p>
|
|
<ul>
|
|
<li>0-1 Knapsack: Given a set of items and a knapsack, each item has a value and weight. Under the knapsack capacity constraint, select items to maximize total value.</li>
|
|
<li>Traveling Salesman Problem: Starting from a point in a graph, visit all other points exactly once and return to the starting point, finding the shortest path.</li>
|
|
<li>Maximum Clique: Given an undirected graph, find the largest complete subgraph, i.e., a subgraph where any two vertices are connected by an edge.</li>
|
|
</ul>
|
|
<p>Note that for many combinatorial optimization problems, backtracking is not the optimal solution.</p>
|
|
<ul>
|
|
<li>The 0-1 Knapsack problem is usually solved using dynamic programming to achieve higher time efficiency.</li>
|
|
<li>The Traveling Salesman Problem is a famous NP-Hard problem; common solutions include genetic algorithms and ant colony algorithms.</li>
|
|
<li>The Maximum Clique problem is a classical problem in graph theory and can be solved using heuristic algorithms such as greedy algorithms.</li>
|
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</ul>
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