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Chapter 8.   Heaps
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Chapter 8.   Heaps
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8.1   Heaps
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8.2   Building a heap
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8.3   The top-k problem
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8.4   Summary
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8.5   Exercises
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Chapter 9.   Graphs
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Chapter 9.   Graphs
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9.1   Graphs
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9.2   Basic graph operations
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9.3   Graph traversal
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9.4   Summary
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9.5   Exercises
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Chapter 10.   Searching
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Chapter 10.   Searching
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10.1   Binary search
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10.2   Finding an insertion point with binary search
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10.3   Finding boundaries with binary search
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10.4   Optimizing with hashing
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10.5   Search algorithms revisited
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10.6   Summary
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10.7   Exercises
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Chapter 11.   Sorting
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Chapter 11.   Sorting
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11.1   Sorting algorithms
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11.2   Selection sort
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11.3   Bubble sort
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11.4   Insertion sort
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11.5   Quick sort
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11.6   Merge sort
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11.7   Heap sort
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11.8   Bucket sort
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11.9   Counting sort
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11.10   Radix sort
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11.11   Summary
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11.12   Exercises
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Chapter 12.   Divide and conquer
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12.1   Divide and conquer
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12.2   Divide-and-conquer search
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12.3   Building a binary tree
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12.4   Tower of Hanoi
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12.5   Summary
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12.6   Exercises
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Chapter 13.   Backtracking
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Chapter 13.   Backtracking
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13.1   Backtracking algorithms
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13.2   Permutations problem
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13.3   Subset sum problem
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13.4   N-queens problem
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13.5   Summary
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13.6   Exercises
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Chapter 14.   Dynamic programming
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Chapter 14.   Dynamic programming
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14.1   Introduction to dynamic programming
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14.2   Properties of dynamic programming problems
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14.3   Solving dynamic programming problems
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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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14.7   Summary
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14.8   Exercises
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<h1 id="73-array-representation-of-a-binary-tree">7.3   Array representation of a binary tree<a class="headerlink" href="#73-array-representation-of-a-binary-tree" title="Permanent link"></a></h1>
<p>In a linked representation, a binary tree stores data in <code>TreeNode</code> nodes connected by pointers. The previous section introduced basic operations on binary trees in this form.</p>
<p>Can we represent a binary tree with an array instead? Yes.</p>
<h2 id="731-representing-a-perfect-binary-tree">7.3.1   Representing a perfect binary tree<a class="headerlink" href="#731-representing-a-perfect-binary-tree" title="Permanent link"></a></h2>
<p>Start with a simple case. Store every node of a perfect binary tree in an array in level order. Each node then corresponds to a unique array index.</p>
<p>Level-order traversal gives us a mapping between parent and child indices: <strong>if a node has index <span class="arithmatex">\(i\)</span>, its left child has index <span class="arithmatex">\(2i + 1\)</span> and its right child has index <span class="arithmatex">\(2i + 2\)</span></strong>. Figure 7-12 illustrates this relationship.</p>
<p><ha-svg-figure class="animation-figure" data-book-key="en/chapter_tree/array_representation_of_tree.assets/array_representation_binary_tree.png" data-dark-src="/assets/figure-svg/figures/b392d437519f272b1b6877e4.json" data-src="/assets/figure-svg/figures/812e6e2d195c9a115f8c75a2.json" style=";--figure-ratio:960.0/540.0"><object data="/en/chapter_tree/array_representation_of_tree.assets/array_representation_binary_tree.svg" data-theme="light" tabindex="-1" type="image/svg+xml">Array representation of a perfect binary tree</object><object data="/en/chapter_tree/array_representation_of_tree.assets/array_representation_binary_tree.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">Array representation of a perfect binary tree</object></ha-svg-figure></p>
<p align="center"> Figure 7-12   Array representation of a perfect binary tree </p>
<p><strong>The mapping formulas serve the same role as node references or pointers in a linked representation</strong>. Given any node in the array, we can use them to access its left or right child.</p>
<h2 id="732-representing-an-arbitrary-binary-tree">7.3.2   Representing an arbitrary binary tree<a class="headerlink" href="#732-representing-an-arbitrary-binary-tree" title="Permanent link"></a></h2>
<p>A perfect binary tree is a special case. Other binary trees often contain many missing nodes, <code>None</code>, at intermediate levels. Ordinary level-order traversal omits these positions, so its sequence alone cannot tell us their number or locations. <strong>Multiple tree structures can therefore produce the same level-order sequence</strong>.</p>
<p>As shown below, the array representation above no longer works for a non-perfect binary tree.</p>
<p><ha-svg-figure class="animation-figure" data-book-key="en/chapter_tree/array_representation_of_tree.assets/array_representation_without_empty.png" data-dark-src="/assets/figure-svg/figures/2d35f41eec6a811b5df1d477.json" data-src="/assets/figure-svg/figures/ea60507806a2a353335fe574.json" style=";--figure-ratio:960.0/540.0"><object data="/en/chapter_tree/array_representation_of_tree.assets/array_representation_without_empty.svg" data-theme="light" tabindex="-1" type="image/svg+xml">Multiple binary trees can share a level-order sequence</object><object data="/en/chapter_tree/array_representation_of_tree.assets/array_representation_without_empty.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">Multiple binary trees can share a level-order sequence</object></ha-svg-figure></p>
<p align="center"> Figure 7-13   Multiple binary trees can share a level-order sequence </p>
<p>To solve this, <strong>include every <code>None</code> position explicitly in the level-order sequence</strong>. The sequence then represents the tree uniquely, as shown below. Example code follows:</p>
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<div class="highlight"><pre><span></span><code><a href="#__codelineno-0-1" id="__codelineno-0-1" name="__codelineno-0-1"></a><span class="c1"># Array representation of a binary tree</span>
<a href="#__codelineno-0-2" id="__codelineno-0-2" name="__codelineno-0-2"></a><span class="c1"># Use None for empty positions</span>
<a href="#__codelineno-0-3" id="__codelineno-0-3" name="__codelineno-0-3"></a><span class="n">tree</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">15</span><span class="p">]</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-1-1" id="__codelineno-1-1" name="__codelineno-1-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-1-2" id="__codelineno-1-2" name="__codelineno-1-2"></a><span class="c1">// Use INT_MAX, the maximum int value, for empty positions</span>
<a href="#__codelineno-1-3" id="__codelineno-1-3" name="__codelineno-1-3"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">};</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-2-1" id="__codelineno-2-1" name="__codelineno-2-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-2-2" id="__codelineno-2-2" name="__codelineno-2-2"></a><span class="c1">// Use the wrapper class Integer so that null can mark empty positions</span>
<a href="#__codelineno-2-3" id="__codelineno-2-3" name="__codelineno-2-3"></a><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="w"> </span><span class="p">};</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-3-1" id="__codelineno-3-1" name="__codelineno-3-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-3-2" id="__codelineno-3-2" name="__codelineno-3-2"></a><span class="c1">// Use the nullable type int? so that null can mark empty positions</span>
<a href="#__codelineno-3-3" id="__codelineno-3-3" name="__codelineno-3-3"></a><span class="kt">int?</span><span class="p">[]</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">];</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-4-1" id="__codelineno-4-1" name="__codelineno-4-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-4-2" id="__codelineno-4-2" name="__codelineno-4-2"></a><span class="c1">// Use a slice of any so that nil can mark empty positions</span>
<a href="#__codelineno-4-3" id="__codelineno-4-3" name="__codelineno-4-3"></a><span class="nx">tree</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-5-1" id="__codelineno-5-1" name="__codelineno-5-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-5-2" id="__codelineno-5-2" name="__codelineno-5-2"></a><span class="c1">// Use the optional type Int? so that nil can mark empty positions</span>
<a href="#__codelineno-5-3" id="__codelineno-5-3" name="__codelineno-5-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">tree</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">?]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">]</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-6-1" id="__codelineno-6-1" name="__codelineno-6-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-6-2" id="__codelineno-6-2" name="__codelineno-6-2"></a><span class="c1">// Use null for empty positions</span>
<a href="#__codelineno-6-3" id="__codelineno-6-3" name="__codelineno-6-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">15</span><span class="p">];</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-7-1" id="__codelineno-7-1" name="__codelineno-7-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-7-2" id="__codelineno-7-2" name="__codelineno-7-2"></a><span class="c1">// Use null for empty positions</span>
<a href="#__codelineno-7-3" id="__codelineno-7-3" name="__codelineno-7-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">tree</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</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="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">15</span><span class="p">];</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-8-1" id="__codelineno-8-1" name="__codelineno-8-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-8-2" id="__codelineno-8-2" name="__codelineno-8-2"></a><span class="c1">// Use the nullable type int? so that null can mark empty positions</span>
<a href="#__codelineno-8-3" id="__codelineno-8-3" name="__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</span><span class="p">];</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-9-1" id="__codelineno-9-1" name="__codelineno-9-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-9-2" id="__codelineno-9-2" name="__codelineno-9-2"></a><span class="c1">// Use None for empty positions</span>
<a href="#__codelineno-9-3" id="__codelineno-9-3" name="__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nb">Some</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">4</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">6</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">7</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">8</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">9</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">12</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">15</span><span class="p">)];</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-10-1" id="__codelineno-10-1" name="__codelineno-10-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-10-2" id="__codelineno-10-2" name="__codelineno-10-2"></a><span class="c1">// Use the maximum int value for empty positions, so node values must not equal INT_MAX</span>
<a href="#__codelineno-10-3" id="__codelineno-10-3" name="__codelineno-10-3"></a><span class="kt">int</span><span class="w"> </span><span class="n">tree</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">};</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-11-1" id="__codelineno-11-1" name="__codelineno-11-1"></a><span class="cm">/* Array representation of a binary tree */</span>
<a href="#__codelineno-11-2" id="__codelineno-11-2" name="__codelineno-11-2"></a><span class="c1">// Use null for empty positions</span>
<a href="#__codelineno-11-3" id="__codelineno-11-3" name="__codelineno-11-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOf</span><span class="p">(</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</span><span class="w"> </span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a href="#__codelineno-12-1" id="__codelineno-12-1" name="__codelineno-12-1"></a><span class="c1">### Array representation of a binary tree ###</span>
<a href="#__codelineno-12-2" id="__codelineno-12-2" name="__codelineno-12-2"></a><span class="c1"># Use nil for empty positions</span>
<a href="#__codelineno-12-3" id="__codelineno-12-3" name="__codelineno-12-3"></a><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="o">]</span>
</code></pre></div>
</div>
</div>
</div>
<p><ha-svg-figure class="animation-figure" data-book-key="en/chapter_tree/array_representation_of_tree.assets/array_representation_with_empty.png" data-dark-src="/assets/figure-svg/figures/ff671a8377bed4aefcd361da.json" data-src="/assets/figure-svg/figures/d59f75336599c6424576064b.json" style=";--figure-ratio:960.0/540.0"><object data="/en/chapter_tree/array_representation_of_tree.assets/array_representation_with_empty.svg" data-theme="light" tabindex="-1" type="image/svg+xml">Array representation of an arbitrary binary tree</object><object data="/en/chapter_tree/array_representation_of_tree.assets/array_representation_with_empty.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">Array representation of an arbitrary binary tree</object></ha-svg-figure></p>
<p align="center"> Figure 7-14   Array representation of an arbitrary binary tree </p>
<p><strong>Complete binary trees are particularly well suited to array representation</strong>. By definition, missing positions occur only at the right end of the lowest level, <strong>so all <code>None</code> entries appear at the end of the level-order sequence</strong>.</p>
<p>We can therefore omit all <code>None</code> entries when storing a complete binary tree in an array. An example is shown below.</p>
<p><ha-svg-figure class="animation-figure" data-book-key="en/chapter_tree/array_representation_of_tree.assets/array_representation_complete_binary_tree.png" data-dark-src="/assets/figure-svg/figures/a070e69d1ad1772032577cca.json" data-src="/assets/figure-svg/figures/dc96b54b5128bb22f8e30e4a.json" style=";--figure-ratio:960.0/540.0"><object data="/en/chapter_tree/array_representation_of_tree.assets/array_representation_complete_binary_tree.svg" data-theme="light" tabindex="-1" type="image/svg+xml">Array representation of a complete binary tree</object><object data="/en/chapter_tree/array_representation_of_tree.assets/array_representation_complete_binary_tree.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">Array representation of a complete binary tree</object></ha-svg-figure></p>
<p align="center"> Figure 7-15   Array representation of a complete binary tree </p>
<p>The following code implements an array-based binary tree with these operations.</p>
<ul>
<li>Given a node, get its value, left or right child, and parent.</li>
<li>Obtain preorder, inorder, postorder, and level-order traversal sequences.</li>
</ul>
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<div class="highlight"><span class="filename">array_binary_tree.py</span><pre><span></span><code><a href="#__codelineno-13-1" id="__codelineno-13-1" name="__codelineno-13-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="p">:</span>
<a href="#__codelineno-13-2" id="__codelineno-13-2" name="__codelineno-13-2"></a><span class="w"> </span><span class="sd">"""Binary tree class using an array representation"""</span>
<a href="#__codelineno-13-3" id="__codelineno-13-3" name="__codelineno-13-3"></a>
<a href="#__codelineno-13-4" id="__codelineno-13-4" name="__codelineno-13-4"></a> <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]):</span>
<a href="#__codelineno-13-5" id="__codelineno-13-5" name="__codelineno-13-5"></a><span class="w"> </span><span class="sd">"""Constructor"""</span>
<a href="#__codelineno-13-6" id="__codelineno-13-6" name="__codelineno-13-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">_tree</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<a href="#__codelineno-13-7" id="__codelineno-13-7" name="__codelineno-13-7"></a>
<a href="#__codelineno-13-8" id="__codelineno-13-8" name="__codelineno-13-8"></a> <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<a href="#__codelineno-13-9" id="__codelineno-13-9" name="__codelineno-13-9"></a><span class="w"> </span><span class="sd">"""Length of the backing list"""</span>
<a href="#__codelineno-13-10" id="__codelineno-13-10" name="__codelineno-13-10"></a> <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_tree</span><span class="p">)</span>
<a href="#__codelineno-13-11" id="__codelineno-13-11" name="__codelineno-13-11"></a>
<a href="#__codelineno-13-12" id="__codelineno-13-12" name="__codelineno-13-12"></a> <span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a href="#__codelineno-13-13" id="__codelineno-13-13" name="__codelineno-13-13"></a><span class="w"> </span><span class="sd">"""Get the value of the node at index i"""</span>
<a href="#__codelineno-13-14" id="__codelineno-13-14" name="__codelineno-13-14"></a> <span class="c1"># If the index is out of bounds, return None to represent an empty position</span>
<a href="#__codelineno-13-15" id="__codelineno-13-15" name="__codelineno-13-15"></a> <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">():</span>
<a href="#__codelineno-13-16" id="__codelineno-13-16" name="__codelineno-13-16"></a> <span class="k">return</span> <span class="kc">None</span>
<a href="#__codelineno-13-17" id="__codelineno-13-17" name="__codelineno-13-17"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_tree</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a href="#__codelineno-13-18" id="__codelineno-13-18" name="__codelineno-13-18"></a>
<a href="#__codelineno-13-19" id="__codelineno-13-19" name="__codelineno-13-19"></a> <span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a href="#__codelineno-13-20" id="__codelineno-13-20" name="__codelineno-13-20"></a><span class="w"> </span><span class="sd">"""Get the left child index of the node at index i"""</span>
<a href="#__codelineno-13-21" id="__codelineno-13-21" name="__codelineno-13-21"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
<a href="#__codelineno-13-22" id="__codelineno-13-22" name="__codelineno-13-22"></a>
<a href="#__codelineno-13-23" id="__codelineno-13-23" name="__codelineno-13-23"></a> <span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a href="#__codelineno-13-24" id="__codelineno-13-24" name="__codelineno-13-24"></a><span class="w"> </span><span class="sd">"""Get the right child index of the node at index i"""</span>
<a href="#__codelineno-13-25" id="__codelineno-13-25" name="__codelineno-13-25"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
<a href="#__codelineno-13-26" id="__codelineno-13-26" name="__codelineno-13-26"></a>
<a href="#__codelineno-13-27" id="__codelineno-13-27" name="__codelineno-13-27"></a> <span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a href="#__codelineno-13-28" id="__codelineno-13-28" name="__codelineno-13-28"></a><span class="w"> </span><span class="sd">"""Get the parent index of the node at index i"""</span>
<a href="#__codelineno-13-29" id="__codelineno-13-29" name="__codelineno-13-29"></a> <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
<a href="#__codelineno-13-30" id="__codelineno-13-30" name="__codelineno-13-30"></a>
<a href="#__codelineno-13-31" id="__codelineno-13-31" name="__codelineno-13-31"></a> <span class="k">def</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
<a href="#__codelineno-13-32" id="__codelineno-13-32" name="__codelineno-13-32"></a><span class="w"> </span><span class="sd">"""Level-order traversal"""</span>
<a href="#__codelineno-13-33" id="__codelineno-13-33" name="__codelineno-13-33"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
<a href="#__codelineno-13-34" id="__codelineno-13-34" name="__codelineno-13-34"></a> <span class="c1"># Traverse the array directly</span>
<a href="#__codelineno-13-35" id="__codelineno-13-35" name="__codelineno-13-35"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
<a href="#__codelineno-13-36" id="__codelineno-13-36" name="__codelineno-13-36"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a href="#__codelineno-13-37" id="__codelineno-13-37" name="__codelineno-13-37"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<a href="#__codelineno-13-38" id="__codelineno-13-38" name="__codelineno-13-38"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
<a href="#__codelineno-13-39" id="__codelineno-13-39" name="__codelineno-13-39"></a>
<a href="#__codelineno-13-40" id="__codelineno-13-40" name="__codelineno-13-40"></a> <span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">order</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
<a href="#__codelineno-13-41" id="__codelineno-13-41" name="__codelineno-13-41"></a><span class="w"> </span><span class="sd">"""Depth-first traversal"""</span>
<a href="#__codelineno-13-42" id="__codelineno-13-42" name="__codelineno-13-42"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<a href="#__codelineno-13-43" id="__codelineno-13-43" name="__codelineno-13-43"></a> <span class="k">return</span>
<a href="#__codelineno-13-44" id="__codelineno-13-44" name="__codelineno-13-44"></a> <span class="c1"># Preorder traversal</span>
<a href="#__codelineno-13-45" id="__codelineno-13-45" name="__codelineno-13-45"></a> <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">"pre"</span><span class="p">:</span>
<a href="#__codelineno-13-46" id="__codelineno-13-46" name="__codelineno-13-46"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<a href="#__codelineno-13-47" id="__codelineno-13-47" name="__codelineno-13-47"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">order</span><span class="p">)</span>
<a href="#__codelineno-13-48" id="__codelineno-13-48" name="__codelineno-13-48"></a> <span class="c1"># Inorder traversal</span>
<a href="#__codelineno-13-49" id="__codelineno-13-49" name="__codelineno-13-49"></a> <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">"in"</span><span class="p">:</span>
<a href="#__codelineno-13-50" id="__codelineno-13-50" name="__codelineno-13-50"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<a href="#__codelineno-13-51" id="__codelineno-13-51" name="__codelineno-13-51"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">order</span><span class="p">)</span>
<a href="#__codelineno-13-52" id="__codelineno-13-52" name="__codelineno-13-52"></a> <span class="c1"># Postorder traversal</span>
<a href="#__codelineno-13-53" id="__codelineno-13-53" name="__codelineno-13-53"></a> <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">"post"</span><span class="p">:</span>
<a href="#__codelineno-13-54" id="__codelineno-13-54" name="__codelineno-13-54"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<a href="#__codelineno-13-55" id="__codelineno-13-55" name="__codelineno-13-55"></a>
<a href="#__codelineno-13-56" id="__codelineno-13-56" name="__codelineno-13-56"></a> <span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
<a href="#__codelineno-13-57" id="__codelineno-13-57" name="__codelineno-13-57"></a><span class="w"> </span><span class="sd">"""Preorder traversal"""</span>
<a href="#__codelineno-13-58" id="__codelineno-13-58" name="__codelineno-13-58"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
<a href="#__codelineno-13-59" id="__codelineno-13-59" name="__codelineno-13-59"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">"pre"</span><span class="p">)</span>
<a href="#__codelineno-13-60" id="__codelineno-13-60" name="__codelineno-13-60"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
<a href="#__codelineno-13-61" id="__codelineno-13-61" name="__codelineno-13-61"></a>
<a href="#__codelineno-13-62" id="__codelineno-13-62" name="__codelineno-13-62"></a> <span class="k">def</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
<a href="#__codelineno-13-63" id="__codelineno-13-63" name="__codelineno-13-63"></a><span class="w"> </span><span class="sd">"""Inorder traversal"""</span>
<a href="#__codelineno-13-64" id="__codelineno-13-64" name="__codelineno-13-64"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
<a href="#__codelineno-13-65" id="__codelineno-13-65" name="__codelineno-13-65"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">"in"</span><span class="p">)</span>
<a href="#__codelineno-13-66" id="__codelineno-13-66" name="__codelineno-13-66"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
<a href="#__codelineno-13-67" id="__codelineno-13-67" name="__codelineno-13-67"></a>
<a href="#__codelineno-13-68" id="__codelineno-13-68" name="__codelineno-13-68"></a> <span class="k">def</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
<a href="#__codelineno-13-69" id="__codelineno-13-69" name="__codelineno-13-69"></a><span class="w"> </span><span class="sd">"""Postorder traversal"""</span>
<a href="#__codelineno-13-70" id="__codelineno-13-70" name="__codelineno-13-70"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
<a href="#__codelineno-13-71" id="__codelineno-13-71" name="__codelineno-13-71"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">"post"</span><span class="p">)</span>
<a href="#__codelineno-13-72" id="__codelineno-13-72" name="__codelineno-13-72"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.cpp</span><pre><span></span><code><a href="#__codelineno-14-1" id="__codelineno-14-1" name="__codelineno-14-1"></a><span class="cm">/* Binary tree class using an array representation */</span>
<a href="#__codelineno-14-2" id="__codelineno-14-2" name="__codelineno-14-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-3" id="__codelineno-14-3" name="__codelineno-14-3"></a><span class="w"> </span><span class="k">public</span><span class="o">:</span>
<a href="#__codelineno-14-4" id="__codelineno-14-4" name="__codelineno-14-4"></a><span class="w"> </span><span class="cm">/* Constructor */</span>
<a href="#__codelineno-14-5" id="__codelineno-14-5" name="__codelineno-14-5"></a><span class="w"> </span><span class="n">ArrayBinaryTree</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-6" id="__codelineno-14-6" name="__codelineno-14-6"></a><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
<a href="#__codelineno-14-7" id="__codelineno-14-7" name="__codelineno-14-7"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-8" id="__codelineno-14-8" name="__codelineno-14-8"></a>
<a href="#__codelineno-14-9" id="__codelineno-14-9" name="__codelineno-14-9"></a><span class="w"> </span><span class="cm">/* Number of positions in the array */</span>
<a href="#__codelineno-14-10" id="__codelineno-14-10" name="__codelineno-14-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-11" id="__codelineno-14-11" name="__codelineno-14-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
<a href="#__codelineno-14-12" id="__codelineno-14-12" name="__codelineno-14-12"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-13" id="__codelineno-14-13" name="__codelineno-14-13"></a>
<a href="#__codelineno-14-14" id="__codelineno-14-14" name="__codelineno-14-14"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-14-15" id="__codelineno-14-15" name="__codelineno-14-15"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-16" id="__codelineno-14-16" name="__codelineno-14-16"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return INT_MAX to represent an empty position</span>
<a href="#__codelineno-14-17" id="__codelineno-14-17" name="__codelineno-14-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
<a href="#__codelineno-14-18" id="__codelineno-14-18" name="__codelineno-14-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
<a href="#__codelineno-14-19" id="__codelineno-14-19" name="__codelineno-14-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a href="#__codelineno-14-20" id="__codelineno-14-20" name="__codelineno-14-20"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-21" id="__codelineno-14-21" name="__codelineno-14-21"></a>
<a href="#__codelineno-14-22" id="__codelineno-14-22" name="__codelineno-14-22"></a><span class="w"> </span><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-14-23" id="__codelineno-14-23" name="__codelineno-14-23"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-24" id="__codelineno-14-24" name="__codelineno-14-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
<a href="#__codelineno-14-25" id="__codelineno-14-25" name="__codelineno-14-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-26" id="__codelineno-14-26" name="__codelineno-14-26"></a>
<a href="#__codelineno-14-27" id="__codelineno-14-27" name="__codelineno-14-27"></a><span class="w"> </span><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-14-28" id="__codelineno-14-28" name="__codelineno-14-28"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-29" id="__codelineno-14-29" name="__codelineno-14-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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>
<a href="#__codelineno-14-30" id="__codelineno-14-30" name="__codelineno-14-30"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-31" id="__codelineno-14-31" name="__codelineno-14-31"></a>
<a href="#__codelineno-14-32" id="__codelineno-14-32" name="__codelineno-14-32"></a><span class="w"> </span><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-14-33" id="__codelineno-14-33" name="__codelineno-14-33"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-34" id="__codelineno-14-34" name="__codelineno-14-34"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a href="#__codelineno-14-35" id="__codelineno-14-35" name="__codelineno-14-35"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-36" id="__codelineno-14-36" name="__codelineno-14-36"></a>
<a href="#__codelineno-14-37" id="__codelineno-14-37" name="__codelineno-14-37"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-14-38" id="__codelineno-14-38" name="__codelineno-14-38"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-39" id="__codelineno-14-39" name="__codelineno-14-39"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-14-40" id="__codelineno-14-40" name="__codelineno-14-40"></a><span class="w"> </span><span class="c1">// Traverse the array directly</span>
<a href="#__codelineno-14-41" id="__codelineno-14-41" name="__codelineno-14-41"></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">&lt;</span><span class="w"> </span><span class="n">size</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 href="#__codelineno-14-42" id="__codelineno-14-42" name="__codelineno-14-42"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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">INT_MAX</span><span class="p">)</span>
<a href="#__codelineno-14-43" id="__codelineno-14-43" name="__codelineno-14-43"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-14-44" id="__codelineno-14-44" name="__codelineno-14-44"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-45" id="__codelineno-14-45" name="__codelineno-14-45"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-14-46" id="__codelineno-14-46" name="__codelineno-14-46"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-47" id="__codelineno-14-47" name="__codelineno-14-47"></a>
<a href="#__codelineno-14-48" id="__codelineno-14-48" name="__codelineno-14-48"></a><span class="w"> </span><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-14-49" id="__codelineno-14-49" name="__codelineno-14-49"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-50" id="__codelineno-14-50" name="__codelineno-14-50"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-14-51" id="__codelineno-14-51" name="__codelineno-14-51"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-14-52" id="__codelineno-14-52" name="__codelineno-14-52"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-14-53" id="__codelineno-14-53" name="__codelineno-14-53"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-54" id="__codelineno-14-54" name="__codelineno-14-54"></a>
<a href="#__codelineno-14-55" id="__codelineno-14-55" name="__codelineno-14-55"></a><span class="w"> </span><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-14-56" id="__codelineno-14-56" name="__codelineno-14-56"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-57" id="__codelineno-14-57" name="__codelineno-14-57"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-14-58" id="__codelineno-14-58" name="__codelineno-14-58"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-14-59" id="__codelineno-14-59" name="__codelineno-14-59"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-14-60" id="__codelineno-14-60" name="__codelineno-14-60"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-61" id="__codelineno-14-61" name="__codelineno-14-61"></a>
<a href="#__codelineno-14-62" id="__codelineno-14-62" name="__codelineno-14-62"></a><span class="w"> </span><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-14-63" id="__codelineno-14-63" name="__codelineno-14-63"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-64" id="__codelineno-14-64" name="__codelineno-14-64"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-14-65" id="__codelineno-14-65" name="__codelineno-14-65"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-14-66" id="__codelineno-14-66" name="__codelineno-14-66"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-14-67" id="__codelineno-14-67" name="__codelineno-14-67"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-68" id="__codelineno-14-68" name="__codelineno-14-68"></a>
<a href="#__codelineno-14-69" id="__codelineno-14-69" name="__codelineno-14-69"></a><span class="w"> </span><span class="k">private</span><span class="o">:</span>
<a href="#__codelineno-14-70" id="__codelineno-14-70" name="__codelineno-14-70"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="p">;</span>
<a href="#__codelineno-14-71" id="__codelineno-14-71" name="__codelineno-14-71"></a>
<a href="#__codelineno-14-72" id="__codelineno-14-72" name="__codelineno-14-72"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-14-73" id="__codelineno-14-73" name="__codelineno-14-73"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-74" id="__codelineno-14-74" name="__codelineno-14-74"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-14-75" id="__codelineno-14-75" name="__codelineno-14-75"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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">INT_MAX</span><span class="p">)</span>
<a href="#__codelineno-14-76" id="__codelineno-14-76" name="__codelineno-14-76"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a href="#__codelineno-14-77" id="__codelineno-14-77" name="__codelineno-14-77"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-14-78" id="__codelineno-14-78" name="__codelineno-14-78"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"pre"</span><span class="p">)</span>
<a href="#__codelineno-14-79" id="__codelineno-14-79" name="__codelineno-14-79"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-14-80" id="__codelineno-14-80" name="__codelineno-14-80"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-14-81" id="__codelineno-14-81" name="__codelineno-14-81"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-14-82" id="__codelineno-14-82" name="__codelineno-14-82"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"in"</span><span class="p">)</span>
<a href="#__codelineno-14-83" id="__codelineno-14-83" name="__codelineno-14-83"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-14-84" id="__codelineno-14-84" name="__codelineno-14-84"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-14-85" id="__codelineno-14-85" name="__codelineno-14-85"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-14-86" id="__codelineno-14-86" name="__codelineno-14-86"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"post"</span><span class="p">)</span>
<a href="#__codelineno-14-87" id="__codelineno-14-87" name="__codelineno-14-87"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-14-88" id="__codelineno-14-88" name="__codelineno-14-88"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-89" id="__codelineno-14-89" name="__codelineno-14-89"></a><span class="p">};</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.java</span><pre><span></span><code><a href="#__codelineno-15-1" id="__codelineno-15-1" name="__codelineno-15-1"></a><span class="cm">/* Binary tree class using an array representation */</span>
<a href="#__codelineno-15-2" id="__codelineno-15-2" name="__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-3" id="__codelineno-15-3" name="__codelineno-15-3"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="p">;</span>
<a href="#__codelineno-15-4" id="__codelineno-15-4" name="__codelineno-15-4"></a>
<a href="#__codelineno-15-5" id="__codelineno-15-5" name="__codelineno-15-5"></a><span class="w"> </span><span class="cm">/* Constructor */</span>
<a href="#__codelineno-15-6" id="__codelineno-15-6" name="__codelineno-15-6"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayBinaryTree</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-7" id="__codelineno-15-7" name="__codelineno-15-7"></a><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
<a href="#__codelineno-15-8" id="__codelineno-15-8" name="__codelineno-15-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-9" id="__codelineno-15-9" name="__codelineno-15-9"></a>
<a href="#__codelineno-15-10" id="__codelineno-15-10" name="__codelineno-15-10"></a><span class="w"> </span><span class="cm">/* List size */</span>
<a href="#__codelineno-15-11" id="__codelineno-15-11" name="__codelineno-15-11"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-12" id="__codelineno-15-12" name="__codelineno-15-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
<a href="#__codelineno-15-13" id="__codelineno-15-13" name="__codelineno-15-13"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-14" id="__codelineno-15-14" name="__codelineno-15-14"></a>
<a href="#__codelineno-15-15" id="__codelineno-15-15" name="__codelineno-15-15"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-15-16" id="__codelineno-15-16" name="__codelineno-15-16"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-17" id="__codelineno-15-17" name="__codelineno-15-17"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return null to represent an empty position</span>
<a href="#__codelineno-15-18" id="__codelineno-15-18" name="__codelineno-15-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
<a href="#__codelineno-15-19" id="__codelineno-15-19" name="__codelineno-15-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a href="#__codelineno-15-20" id="__codelineno-15-20" name="__codelineno-15-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<a href="#__codelineno-15-21" id="__codelineno-15-21" name="__codelineno-15-21"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-22" id="__codelineno-15-22" name="__codelineno-15-22"></a>
<a href="#__codelineno-15-23" id="__codelineno-15-23" name="__codelineno-15-23"></a><span class="w"> </span><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-15-24" id="__codelineno-15-24" name="__codelineno-15-24"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-25" id="__codelineno-15-25" name="__codelineno-15-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
<a href="#__codelineno-15-26" id="__codelineno-15-26" name="__codelineno-15-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-27" id="__codelineno-15-27" name="__codelineno-15-27"></a>
<a href="#__codelineno-15-28" id="__codelineno-15-28" name="__codelineno-15-28"></a><span class="w"> </span><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-15-29" id="__codelineno-15-29" name="__codelineno-15-29"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-30" id="__codelineno-15-30" name="__codelineno-15-30"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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>
<a href="#__codelineno-15-31" id="__codelineno-15-31" name="__codelineno-15-31"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-32" id="__codelineno-15-32" name="__codelineno-15-32"></a>
<a href="#__codelineno-15-33" id="__codelineno-15-33" name="__codelineno-15-33"></a><span class="w"> </span><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-15-34" id="__codelineno-15-34" name="__codelineno-15-34"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-35" id="__codelineno-15-35" name="__codelineno-15-35"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a href="#__codelineno-15-36" id="__codelineno-15-36" name="__codelineno-15-36"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-37" id="__codelineno-15-37" name="__codelineno-15-37"></a>
<a href="#__codelineno-15-38" id="__codelineno-15-38" name="__codelineno-15-38"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-15-39" id="__codelineno-15-39" name="__codelineno-15-39"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-40" id="__codelineno-15-40" name="__codelineno-15-40"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a href="#__codelineno-15-41" id="__codelineno-15-41" name="__codelineno-15-41"></a><span class="w"> </span><span class="c1">// Traverse the array directly</span>
<a href="#__codelineno-15-42" id="__codelineno-15-42" name="__codelineno-15-42"></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">&lt;</span><span class="w"> </span><span class="n">size</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 href="#__codelineno-15-43" id="__codelineno-15-43" name="__codelineno-15-43"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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="kc">null</span><span class="p">)</span>
<a href="#__codelineno-15-44" id="__codelineno-15-44" name="__codelineno-15-44"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-15-45" id="__codelineno-15-45" name="__codelineno-15-45"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-46" id="__codelineno-15-46" name="__codelineno-15-46"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-15-47" id="__codelineno-15-47" name="__codelineno-15-47"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-48" id="__codelineno-15-48" name="__codelineno-15-48"></a>
<a href="#__codelineno-15-49" id="__codelineno-15-49" name="__codelineno-15-49"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-15-50" id="__codelineno-15-50" name="__codelineno-15-50"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">Integer</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-51" id="__codelineno-15-51" name="__codelineno-15-51"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-15-52" id="__codelineno-15-52" name="__codelineno-15-52"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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="kc">null</span><span class="p">)</span>
<a href="#__codelineno-15-53" id="__codelineno-15-53" name="__codelineno-15-53"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a href="#__codelineno-15-54" id="__codelineno-15-54" name="__codelineno-15-54"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-15-55" id="__codelineno-15-55" name="__codelineno-15-55"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">"pre"</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
<a href="#__codelineno-15-56" id="__codelineno-15-56" name="__codelineno-15-56"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-15-57" id="__codelineno-15-57" name="__codelineno-15-57"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-15-58" id="__codelineno-15-58" name="__codelineno-15-58"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-15-59" id="__codelineno-15-59" name="__codelineno-15-59"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">"in"</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
<a href="#__codelineno-15-60" id="__codelineno-15-60" name="__codelineno-15-60"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-15-61" id="__codelineno-15-61" name="__codelineno-15-61"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-15-62" id="__codelineno-15-62" name="__codelineno-15-62"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-15-63" id="__codelineno-15-63" name="__codelineno-15-63"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">"post"</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
<a href="#__codelineno-15-64" id="__codelineno-15-64" name="__codelineno-15-64"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-15-65" id="__codelineno-15-65" name="__codelineno-15-65"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-66" id="__codelineno-15-66" name="__codelineno-15-66"></a>
<a href="#__codelineno-15-67" id="__codelineno-15-67" name="__codelineno-15-67"></a><span class="w"> </span><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-15-68" id="__codelineno-15-68" name="__codelineno-15-68"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-69" id="__codelineno-15-69" name="__codelineno-15-69"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a href="#__codelineno-15-70" id="__codelineno-15-70" name="__codelineno-15-70"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-15-71" id="__codelineno-15-71" name="__codelineno-15-71"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-15-72" id="__codelineno-15-72" name="__codelineno-15-72"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-73" id="__codelineno-15-73" name="__codelineno-15-73"></a>
<a href="#__codelineno-15-74" id="__codelineno-15-74" name="__codelineno-15-74"></a><span class="w"> </span><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-15-75" id="__codelineno-15-75" name="__codelineno-15-75"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-76" id="__codelineno-15-76" name="__codelineno-15-76"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a href="#__codelineno-15-77" id="__codelineno-15-77" name="__codelineno-15-77"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-15-78" id="__codelineno-15-78" name="__codelineno-15-78"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-15-79" id="__codelineno-15-79" name="__codelineno-15-79"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-80" id="__codelineno-15-80" name="__codelineno-15-80"></a>
<a href="#__codelineno-15-81" id="__codelineno-15-81" name="__codelineno-15-81"></a><span class="w"> </span><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-15-82" id="__codelineno-15-82" name="__codelineno-15-82"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-83" id="__codelineno-15-83" name="__codelineno-15-83"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a href="#__codelineno-15-84" id="__codelineno-15-84" name="__codelineno-15-84"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-15-85" id="__codelineno-15-85" name="__codelineno-15-85"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-15-86" id="__codelineno-15-86" name="__codelineno-15-86"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-87" id="__codelineno-15-87" name="__codelineno-15-87"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.cs</span><pre><span></span><code><a href="#__codelineno-16-1" id="__codelineno-16-1" name="__codelineno-16-1"></a><span class="cm">/* Binary tree class using an array representation */</span>
<a href="#__codelineno-16-2" id="__codelineno-16-2" name="__codelineno-16-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">ArrayBinaryTree</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int?</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-3" id="__codelineno-16-3" name="__codelineno-16-3"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int?</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
<a href="#__codelineno-16-4" id="__codelineno-16-4" name="__codelineno-16-4"></a>
<a href="#__codelineno-16-5" id="__codelineno-16-5" name="__codelineno-16-5"></a><span class="w"> </span><span class="cm">/* List size */</span>
<a href="#__codelineno-16-6" id="__codelineno-16-6" name="__codelineno-16-6"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-7" id="__codelineno-16-7" name="__codelineno-16-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
<a href="#__codelineno-16-8" id="__codelineno-16-8" name="__codelineno-16-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-9" id="__codelineno-16-9" name="__codelineno-16-9"></a>
<a href="#__codelineno-16-10" id="__codelineno-16-10" name="__codelineno-16-10"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-16-11" id="__codelineno-16-11" name="__codelineno-16-11"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">Val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-12" id="__codelineno-16-12" name="__codelineno-16-12"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return null to represent an empty position</span>
<a href="#__codelineno-16-13" id="__codelineno-16-13" name="__codelineno-16-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">Size</span><span class="p">())</span>
<a href="#__codelineno-16-14" id="__codelineno-16-14" name="__codelineno-16-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
<a href="#__codelineno-16-15" id="__codelineno-16-15" name="__codelineno-16-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a href="#__codelineno-16-16" id="__codelineno-16-16" name="__codelineno-16-16"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-17" id="__codelineno-16-17" name="__codelineno-16-17"></a>
<a href="#__codelineno-16-18" id="__codelineno-16-18" name="__codelineno-16-18"></a><span class="w"> </span><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-16-19" id="__codelineno-16-19" name="__codelineno-16-19"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-20" id="__codelineno-16-20" name="__codelineno-16-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
<a href="#__codelineno-16-21" id="__codelineno-16-21" name="__codelineno-16-21"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-22" id="__codelineno-16-22" name="__codelineno-16-22"></a>
<a href="#__codelineno-16-23" id="__codelineno-16-23" name="__codelineno-16-23"></a><span class="w"> </span><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-16-24" id="__codelineno-16-24" name="__codelineno-16-24"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-25" id="__codelineno-16-25" name="__codelineno-16-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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>
<a href="#__codelineno-16-26" id="__codelineno-16-26" name="__codelineno-16-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-27" id="__codelineno-16-27" name="__codelineno-16-27"></a>
<a href="#__codelineno-16-28" id="__codelineno-16-28" name="__codelineno-16-28"></a><span class="w"> </span><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-16-29" id="__codelineno-16-29" name="__codelineno-16-29"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">Parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-30" id="__codelineno-16-30" name="__codelineno-16-30"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a href="#__codelineno-16-31" id="__codelineno-16-31" name="__codelineno-16-31"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-32" id="__codelineno-16-32" name="__codelineno-16-32"></a>
<a href="#__codelineno-16-33" id="__codelineno-16-33" name="__codelineno-16-33"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-16-34" id="__codelineno-16-34" name="__codelineno-16-34"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">LevelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-35" id="__codelineno-16-35" name="__codelineno-16-35"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-16-36" id="__codelineno-16-36" name="__codelineno-16-36"></a><span class="w"> </span><span class="c1">// Traverse the array directly</span>
<a href="#__codelineno-16-37" id="__codelineno-16-37" name="__codelineno-16-37"></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">&lt;</span><span class="w"> </span><span class="n">Size</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 href="#__codelineno-16-38" id="__codelineno-16-38" name="__codelineno-16-38"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">Val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">HasValue</span><span class="p">)</span>
<a href="#__codelineno-16-39" id="__codelineno-16-39" name="__codelineno-16-39"></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">Val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
<a href="#__codelineno-16-40" id="__codelineno-16-40" name="__codelineno-16-40"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-41" id="__codelineno-16-41" name="__codelineno-16-41"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-16-42" id="__codelineno-16-42" name="__codelineno-16-42"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-43" id="__codelineno-16-43" name="__codelineno-16-43"></a>
<a href="#__codelineno-16-44" id="__codelineno-16-44" name="__codelineno-16-44"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-16-45" id="__codelineno-16-45" name="__codelineno-16-45"></a><span class="w"> </span><span class="k">void</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-46" id="__codelineno-16-46" name="__codelineno-16-46"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-16-47" id="__codelineno-16-47" name="__codelineno-16-47"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">Val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">HasValue</span><span class="p">)</span>
<a href="#__codelineno-16-48" id="__codelineno-16-48" name="__codelineno-16-48"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a href="#__codelineno-16-49" id="__codelineno-16-49" name="__codelineno-16-49"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-16-50" id="__codelineno-16-50" name="__codelineno-16-50"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"pre"</span><span class="p">)</span>
<a href="#__codelineno-16-51" id="__codelineno-16-51" name="__codelineno-16-51"></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">Val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
<a href="#__codelineno-16-52" id="__codelineno-16-52" name="__codelineno-16-52"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">Left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-16-53" id="__codelineno-16-53" name="__codelineno-16-53"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-16-54" id="__codelineno-16-54" name="__codelineno-16-54"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"in"</span><span class="p">)</span>
<a href="#__codelineno-16-55" id="__codelineno-16-55" name="__codelineno-16-55"></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">Val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
<a href="#__codelineno-16-56" id="__codelineno-16-56" name="__codelineno-16-56"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">Right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-16-57" id="__codelineno-16-57" name="__codelineno-16-57"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-16-58" id="__codelineno-16-58" name="__codelineno-16-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"post"</span><span class="p">)</span>
<a href="#__codelineno-16-59" id="__codelineno-16-59" name="__codelineno-16-59"></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">Val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
<a href="#__codelineno-16-60" id="__codelineno-16-60" name="__codelineno-16-60"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-61" id="__codelineno-16-61" name="__codelineno-16-61"></a>
<a href="#__codelineno-16-62" id="__codelineno-16-62" name="__codelineno-16-62"></a><span class="w"> </span><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-16-63" id="__codelineno-16-63" name="__codelineno-16-63"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">PreOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-64" id="__codelineno-16-64" name="__codelineno-16-64"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-16-65" id="__codelineno-16-65" name="__codelineno-16-65"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-16-66" id="__codelineno-16-66" name="__codelineno-16-66"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-16-67" id="__codelineno-16-67" name="__codelineno-16-67"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-68" id="__codelineno-16-68" name="__codelineno-16-68"></a>
<a href="#__codelineno-16-69" id="__codelineno-16-69" name="__codelineno-16-69"></a><span class="w"> </span><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-16-70" id="__codelineno-16-70" name="__codelineno-16-70"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">InOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-71" id="__codelineno-16-71" name="__codelineno-16-71"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-16-72" id="__codelineno-16-72" name="__codelineno-16-72"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-16-73" id="__codelineno-16-73" name="__codelineno-16-73"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-16-74" id="__codelineno-16-74" name="__codelineno-16-74"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-75" id="__codelineno-16-75" name="__codelineno-16-75"></a>
<a href="#__codelineno-16-76" id="__codelineno-16-76" name="__codelineno-16-76"></a><span class="w"> </span><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-16-77" id="__codelineno-16-77" name="__codelineno-16-77"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">PostOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-78" id="__codelineno-16-78" name="__codelineno-16-78"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-16-79" id="__codelineno-16-79" name="__codelineno-16-79"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-16-80" id="__codelineno-16-80" name="__codelineno-16-80"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-16-81" id="__codelineno-16-81" name="__codelineno-16-81"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-82" id="__codelineno-16-82" name="__codelineno-16-82"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.go</span><pre><span></span><code><a href="#__codelineno-17-1" id="__codelineno-17-1" name="__codelineno-17-1"></a><span class="cm">/* Binary tree type using an array representation */</span>
<a href="#__codelineno-17-2" id="__codelineno-17-2" name="__codelineno-17-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">arrayBinaryTree</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-3" id="__codelineno-17-3" name="__codelineno-17-3"></a><span class="w"> </span><span class="nx">tree</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
<a href="#__codelineno-17-4" id="__codelineno-17-4" name="__codelineno-17-4"></a><span class="p">}</span>
<a href="#__codelineno-17-5" id="__codelineno-17-5" name="__codelineno-17-5"></a>
<a href="#__codelineno-17-6" id="__codelineno-17-6" name="__codelineno-17-6"></a><span class="cm">/* Constructor */</span>
<a href="#__codelineno-17-7" id="__codelineno-17-7" name="__codelineno-17-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newArrayBinaryTree</span><span class="p">(</span><span class="nx">arr</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-8" id="__codelineno-17-8" name="__codelineno-17-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">arrayBinaryTree</span><span class="p">{</span>
<a href="#__codelineno-17-9" id="__codelineno-17-9" name="__codelineno-17-9"></a><span class="w"> </span><span class="nx">tree</span><span class="p">:</span><span class="w"> </span><span class="nx">arr</span><span class="p">,</span>
<a href="#__codelineno-17-10" id="__codelineno-17-10" name="__codelineno-17-10"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-11" id="__codelineno-17-11" name="__codelineno-17-11"></a><span class="p">}</span>
<a href="#__codelineno-17-12" id="__codelineno-17-12" name="__codelineno-17-12"></a>
<a href="#__codelineno-17-13" id="__codelineno-17-13" name="__codelineno-17-13"></a><span class="cm">/* Length of the backing slice */</span>
<a href="#__codelineno-17-14" id="__codelineno-17-14" name="__codelineno-17-14"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-15" id="__codelineno-17-15" name="__codelineno-17-15"></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="nx">abt</span><span class="p">.</span><span class="nx">tree</span><span class="p">)</span>
<a href="#__codelineno-17-16" id="__codelineno-17-16" name="__codelineno-17-16"></a><span class="p">}</span>
<a href="#__codelineno-17-17" id="__codelineno-17-17" name="__codelineno-17-17"></a>
<a href="#__codelineno-17-18" id="__codelineno-17-18" name="__codelineno-17-18"></a><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-17-19" id="__codelineno-17-19" name="__codelineno-17-19"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-20" id="__codelineno-17-20" name="__codelineno-17-20"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return nil to represent an empty position</span>
<a href="#__codelineno-17-21" id="__codelineno-17-21" name="__codelineno-17-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-22" id="__codelineno-17-22" name="__codelineno-17-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
<a href="#__codelineno-17-23" id="__codelineno-17-23" name="__codelineno-17-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-24" id="__codelineno-17-24" name="__codelineno-17-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">tree</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
<a href="#__codelineno-17-25" id="__codelineno-17-25" name="__codelineno-17-25"></a><span class="p">}</span>
<a href="#__codelineno-17-26" id="__codelineno-17-26" name="__codelineno-17-26"></a>
<a href="#__codelineno-17-27" id="__codelineno-17-27" name="__codelineno-17-27"></a><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-17-28" id="__codelineno-17-28" name="__codelineno-17-28"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-29" id="__codelineno-17-29" name="__codelineno-17-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a href="#__codelineno-17-30" id="__codelineno-17-30" name="__codelineno-17-30"></a><span class="p">}</span>
<a href="#__codelineno-17-31" id="__codelineno-17-31" name="__codelineno-17-31"></a>
<a href="#__codelineno-17-32" id="__codelineno-17-32" name="__codelineno-17-32"></a><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-17-33" id="__codelineno-17-33" name="__codelineno-17-33"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-34" id="__codelineno-17-34" name="__codelineno-17-34"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
<a href="#__codelineno-17-35" id="__codelineno-17-35" name="__codelineno-17-35"></a><span class="p">}</span>
<a href="#__codelineno-17-36" id="__codelineno-17-36" name="__codelineno-17-36"></a>
<a href="#__codelineno-17-37" id="__codelineno-17-37" name="__codelineno-17-37"></a><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-17-38" id="__codelineno-17-38" name="__codelineno-17-38"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-39" id="__codelineno-17-39" name="__codelineno-17-39"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
<a href="#__codelineno-17-40" id="__codelineno-17-40" name="__codelineno-17-40"></a><span class="p">}</span>
<a href="#__codelineno-17-41" id="__codelineno-17-41" name="__codelineno-17-41"></a>
<a href="#__codelineno-17-42" id="__codelineno-17-42" name="__codelineno-17-42"></a><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-17-43" id="__codelineno-17-43" name="__codelineno-17-43"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-44" id="__codelineno-17-44" name="__codelineno-17-44"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
<a href="#__codelineno-17-45" id="__codelineno-17-45" name="__codelineno-17-45"></a><span class="w"> </span><span class="c1">// Traverse the array directly</span>
<a href="#__codelineno-17-46" id="__codelineno-17-46" name="__codelineno-17-46"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">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="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-47" id="__codelineno-17-47" name="__codelineno-17-47"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</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 href="#__codelineno-17-48" id="__codelineno-17-48" name="__codelineno-17-48"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
<a href="#__codelineno-17-49" id="__codelineno-17-49" name="__codelineno-17-49"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-50" id="__codelineno-17-50" name="__codelineno-17-50"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-51" id="__codelineno-17-51" name="__codelineno-17-51"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
<a href="#__codelineno-17-52" id="__codelineno-17-52" name="__codelineno-17-52"></a><span class="p">}</span>
<a href="#__codelineno-17-53" id="__codelineno-17-53" name="__codelineno-17-53"></a>
<a href="#__codelineno-17-54" id="__codelineno-17-54" name="__codelineno-17-54"></a><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-17-55" id="__codelineno-17-55" name="__codelineno-17-55"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">order</span><span class="w"> </span><span class="kt">string</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="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-56" id="__codelineno-17-56" name="__codelineno-17-56"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-17-57" id="__codelineno-17-57" name="__codelineno-17-57"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</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 href="#__codelineno-17-58" id="__codelineno-17-58" name="__codelineno-17-58"></a><span class="w"> </span><span class="k">return</span>
<a href="#__codelineno-17-59" id="__codelineno-17-59" name="__codelineno-17-59"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-60" id="__codelineno-17-60" name="__codelineno-17-60"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-17-61" id="__codelineno-17-61" name="__codelineno-17-61"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"pre"</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-62" id="__codelineno-17-62" name="__codelineno-17-62"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="o">=</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">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
<a href="#__codelineno-17-63" id="__codelineno-17-63" name="__codelineno-17-63"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-64" id="__codelineno-17-64" name="__codelineno-17-64"></a><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="nx">abt</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
<a href="#__codelineno-17-65" id="__codelineno-17-65" name="__codelineno-17-65"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-17-66" id="__codelineno-17-66" name="__codelineno-17-66"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"in"</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-67" id="__codelineno-17-67" name="__codelineno-17-67"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="o">=</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">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
<a href="#__codelineno-17-68" id="__codelineno-17-68" name="__codelineno-17-68"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-69" id="__codelineno-17-69" name="__codelineno-17-69"></a><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="nx">abt</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
<a href="#__codelineno-17-70" id="__codelineno-17-70" name="__codelineno-17-70"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-17-71" id="__codelineno-17-71" name="__codelineno-17-71"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"post"</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-72" id="__codelineno-17-72" name="__codelineno-17-72"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="o">=</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">abt</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
<a href="#__codelineno-17-73" id="__codelineno-17-73" name="__codelineno-17-73"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-74" id="__codelineno-17-74" name="__codelineno-17-74"></a><span class="p">}</span>
<a href="#__codelineno-17-75" id="__codelineno-17-75" name="__codelineno-17-75"></a>
<a href="#__codelineno-17-76" id="__codelineno-17-76" name="__codelineno-17-76"></a><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-17-77" id="__codelineno-17-77" name="__codelineno-17-77"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-78" id="__codelineno-17-78" name="__codelineno-17-78"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
<a href="#__codelineno-17-79" id="__codelineno-17-79" name="__codelineno-17-79"></a><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
<a href="#__codelineno-17-80" id="__codelineno-17-80" name="__codelineno-17-80"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
<a href="#__codelineno-17-81" id="__codelineno-17-81" name="__codelineno-17-81"></a><span class="p">}</span>
<a href="#__codelineno-17-82" id="__codelineno-17-82" name="__codelineno-17-82"></a>
<a href="#__codelineno-17-83" id="__codelineno-17-83" name="__codelineno-17-83"></a><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-17-84" id="__codelineno-17-84" name="__codelineno-17-84"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-85" id="__codelineno-17-85" name="__codelineno-17-85"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
<a href="#__codelineno-17-86" id="__codelineno-17-86" name="__codelineno-17-86"></a><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
<a href="#__codelineno-17-87" id="__codelineno-17-87" name="__codelineno-17-87"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
<a href="#__codelineno-17-88" id="__codelineno-17-88" name="__codelineno-17-88"></a><span class="p">}</span>
<a href="#__codelineno-17-89" id="__codelineno-17-89" name="__codelineno-17-89"></a>
<a href="#__codelineno-17-90" id="__codelineno-17-90" name="__codelineno-17-90"></a><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-17-91" id="__codelineno-17-91" name="__codelineno-17-91"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">abt</span><span class="w"> </span><span class="o">*</span><span class="nx">arrayBinaryTree</span><span class="p">)</span><span class="w"> </span><span class="nx">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-92" id="__codelineno-17-92" name="__codelineno-17-92"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
<a href="#__codelineno-17-93" id="__codelineno-17-93" name="__codelineno-17-93"></a><span class="w"> </span><span class="nx">abt</span><span class="p">.</span><span class="nx">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">res</span><span class="p">)</span>
<a href="#__codelineno-17-94" id="__codelineno-17-94" name="__codelineno-17-94"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
<a href="#__codelineno-17-95" id="__codelineno-17-95" name="__codelineno-17-95"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.swift</span><pre><span></span><code><a href="#__codelineno-18-1" id="__codelineno-18-1" name="__codelineno-18-1"></a><span class="cm">/* Binary tree class using an array representation */</span>
<a href="#__codelineno-18-2" id="__codelineno-18-2" name="__codelineno-18-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-3" id="__codelineno-18-3" name="__codelineno-18-3"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">tree</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">?]</span>
<a href="#__codelineno-18-4" id="__codelineno-18-4" name="__codelineno-18-4"></a>
<a href="#__codelineno-18-5" id="__codelineno-18-5" name="__codelineno-18-5"></a><span class="w"> </span><span class="cm">/* Constructor */</span>
<a href="#__codelineno-18-6" id="__codelineno-18-6" name="__codelineno-18-6"></a><span class="w"> </span><span class="kd">init</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">?])</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-7" id="__codelineno-18-7" name="__codelineno-18-7"></a><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">arr</span>
<a href="#__codelineno-18-8" id="__codelineno-18-8" name="__codelineno-18-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-9" id="__codelineno-18-9" name="__codelineno-18-9"></a>
<a href="#__codelineno-18-10" id="__codelineno-18-10" name="__codelineno-18-10"></a><span class="w"> </span><span class="cm">/* Length of the backing array */</span>
<a href="#__codelineno-18-11" id="__codelineno-18-11" name="__codelineno-18-11"></a><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-12" id="__codelineno-18-12" name="__codelineno-18-12"></a><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="bp">count</span>
<a href="#__codelineno-18-13" id="__codelineno-18-13" name="__codelineno-18-13"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-14" id="__codelineno-18-14" name="__codelineno-18-14"></a>
<a href="#__codelineno-18-15" id="__codelineno-18-15" name="__codelineno-18-15"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-18-16" id="__codelineno-18-16" name="__codelineno-18-16"></a><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-17" id="__codelineno-18-17" name="__codelineno-18-17"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return nil to represent an empty position</span>
<a href="#__codelineno-18-18" id="__codelineno-18-18" name="__codelineno-18-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-19" id="__codelineno-18-19" name="__codelineno-18-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
<a href="#__codelineno-18-20" id="__codelineno-18-20" name="__codelineno-18-20"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-21" id="__codelineno-18-21" name="__codelineno-18-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a href="#__codelineno-18-22" id="__codelineno-18-22" name="__codelineno-18-22"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-23" id="__codelineno-18-23" name="__codelineno-18-23"></a>
<a href="#__codelineno-18-24" id="__codelineno-18-24" name="__codelineno-18-24"></a><span class="w"> </span><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-18-25" id="__codelineno-18-25" name="__codelineno-18-25"></a><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-26" id="__codelineno-18-26" name="__codelineno-18-26"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span>
<a href="#__codelineno-18-27" id="__codelineno-18-27" name="__codelineno-18-27"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-28" id="__codelineno-18-28" name="__codelineno-18-28"></a>
<a href="#__codelineno-18-29" id="__codelineno-18-29" name="__codelineno-18-29"></a><span class="w"> </span><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-18-30" id="__codelineno-18-30" name="__codelineno-18-30"></a><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-31" id="__codelineno-18-31" name="__codelineno-18-31"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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>
<a href="#__codelineno-18-32" id="__codelineno-18-32" name="__codelineno-18-32"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-33" id="__codelineno-18-33" name="__codelineno-18-33"></a>
<a href="#__codelineno-18-34" id="__codelineno-18-34" name="__codelineno-18-34"></a><span class="w"> </span><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-18-35" id="__codelineno-18-35" name="__codelineno-18-35"></a><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-36" id="__codelineno-18-36" name="__codelineno-18-36"></a><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
<a href="#__codelineno-18-37" id="__codelineno-18-37" name="__codelineno-18-37"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-38" id="__codelineno-18-38" name="__codelineno-18-38"></a>
<a href="#__codelineno-18-39" id="__codelineno-18-39" name="__codelineno-18-39"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-18-40" id="__codelineno-18-40" name="__codelineno-18-40"></a><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-41" id="__codelineno-18-41" name="__codelineno-18-41"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
<a href="#__codelineno-18-42" id="__codelineno-18-42" name="__codelineno-18-42"></a><span class="w"> </span><span class="c1">// Traverse the array directly</span>
<a href="#__codelineno-18-43" id="__codelineno-18-43" name="__codelineno-18-43"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-44" id="__codelineno-18-44" name="__codelineno-18-44"></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="nv">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-45" id="__codelineno-18-45" name="__codelineno-18-45"></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">val</span><span class="p">)</span>
<a href="#__codelineno-18-46" id="__codelineno-18-46" name="__codelineno-18-46"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-47" id="__codelineno-18-47" name="__codelineno-18-47"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-48" id="__codelineno-18-48" name="__codelineno-18-48"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-18-49" id="__codelineno-18-49" name="__codelineno-18-49"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-50" id="__codelineno-18-50" name="__codelineno-18-50"></a>
<a href="#__codelineno-18-51" id="__codelineno-18-51" name="__codelineno-18-51"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-18-52" id="__codelineno-18-52" name="__codelineno-18-52"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="nb">String</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="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-53" id="__codelineno-18-53" name="__codelineno-18-53"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-18-54" id="__codelineno-18-54" name="__codelineno-18-54"></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">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-55" id="__codelineno-18-55" name="__codelineno-18-55"></a><span class="w"> </span><span class="k">return</span>
<a href="#__codelineno-18-56" id="__codelineno-18-56" name="__codelineno-18-56"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-57" id="__codelineno-18-57" name="__codelineno-18-57"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-18-58" id="__codelineno-18-58" name="__codelineno-18-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="s">"pre"</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-59" id="__codelineno-18-59" name="__codelineno-18-59"></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">val</span><span class="p">)</span>
<a href="#__codelineno-18-60" id="__codelineno-18-60" name="__codelineno-18-60"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-61" id="__codelineno-18-61" name="__codelineno-18-61"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kr">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="n">order</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">&amp;</span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-18-62" id="__codelineno-18-62" name="__codelineno-18-62"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-18-63" id="__codelineno-18-63" name="__codelineno-18-63"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="s">"in"</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-64" id="__codelineno-18-64" name="__codelineno-18-64"></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">val</span><span class="p">)</span>
<a href="#__codelineno-18-65" id="__codelineno-18-65" name="__codelineno-18-65"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-66" id="__codelineno-18-66" name="__codelineno-18-66"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kr">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="n">order</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">&amp;</span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-18-67" id="__codelineno-18-67" name="__codelineno-18-67"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-18-68" id="__codelineno-18-68" name="__codelineno-18-68"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="s">"post"</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-69" id="__codelineno-18-69" name="__codelineno-18-69"></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">val</span><span class="p">)</span>
<a href="#__codelineno-18-70" id="__codelineno-18-70" name="__codelineno-18-70"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-71" id="__codelineno-18-71" name="__codelineno-18-71"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-72" id="__codelineno-18-72" name="__codelineno-18-72"></a>
<a href="#__codelineno-18-73" id="__codelineno-18-73" name="__codelineno-18-73"></a><span class="w"> </span><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-18-74" id="__codelineno-18-74" name="__codelineno-18-74"></a><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-75" id="__codelineno-18-75" name="__codelineno-18-75"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
<a href="#__codelineno-18-76" id="__codelineno-18-76" name="__codelineno-18-76"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="s">"pre"</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">&amp;</span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-18-77" id="__codelineno-18-77" name="__codelineno-18-77"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-18-78" id="__codelineno-18-78" name="__codelineno-18-78"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-79" id="__codelineno-18-79" name="__codelineno-18-79"></a>
<a href="#__codelineno-18-80" id="__codelineno-18-80" name="__codelineno-18-80"></a><span class="w"> </span><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-18-81" id="__codelineno-18-81" name="__codelineno-18-81"></a><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-82" id="__codelineno-18-82" name="__codelineno-18-82"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
<a href="#__codelineno-18-83" id="__codelineno-18-83" name="__codelineno-18-83"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="s">"in"</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">&amp;</span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-18-84" id="__codelineno-18-84" name="__codelineno-18-84"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-18-85" id="__codelineno-18-85" name="__codelineno-18-85"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-86" id="__codelineno-18-86" name="__codelineno-18-86"></a>
<a href="#__codelineno-18-87" id="__codelineno-18-87" name="__codelineno-18-87"></a><span class="w"> </span><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-18-88" id="__codelineno-18-88" name="__codelineno-18-88"></a><span class="w"> </span><span class="kd">func</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-89" id="__codelineno-18-89" name="__codelineno-18-89"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
<a href="#__codelineno-18-90" id="__codelineno-18-90" name="__codelineno-18-90"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="s">"post"</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">&amp;</span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-18-91" id="__codelineno-18-91" name="__codelineno-18-91"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-18-92" id="__codelineno-18-92" name="__codelineno-18-92"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-93" id="__codelineno-18-93" name="__codelineno-18-93"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.js</span><pre><span></span><code><a href="#__codelineno-19-1" id="__codelineno-19-1" name="__codelineno-19-1"></a><span class="cm">/* Binary tree class using an array representation */</span>
<a href="#__codelineno-19-2" id="__codelineno-19-2" name="__codelineno-19-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-3" id="__codelineno-19-3" name="__codelineno-19-3"></a><span class="w"> </span><span class="n">#tree</span><span class="p">;</span>
<a href="#__codelineno-19-4" id="__codelineno-19-4" name="__codelineno-19-4"></a>
<a href="#__codelineno-19-5" id="__codelineno-19-5" name="__codelineno-19-5"></a><span class="w"> </span><span class="cm">/* Constructor */</span>
<a href="#__codelineno-19-6" id="__codelineno-19-6" name="__codelineno-19-6"></a><span class="w"> </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-7" id="__codelineno-19-7" name="__codelineno-19-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
<a href="#__codelineno-19-8" id="__codelineno-19-8" name="__codelineno-19-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-9" id="__codelineno-19-9" name="__codelineno-19-9"></a>
<a href="#__codelineno-19-10" id="__codelineno-19-10" name="__codelineno-19-10"></a><span class="w"> </span><span class="cm">/* Array length */</span>
<a href="#__codelineno-19-11" id="__codelineno-19-11" name="__codelineno-19-11"></a><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-12" id="__codelineno-19-12" name="__codelineno-19-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
<a href="#__codelineno-19-13" id="__codelineno-19-13" name="__codelineno-19-13"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-14" id="__codelineno-19-14" name="__codelineno-19-14"></a>
<a href="#__codelineno-19-15" id="__codelineno-19-15" name="__codelineno-19-15"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-19-16" id="__codelineno-19-16" name="__codelineno-19-16"></a><span class="w"> </span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-17" id="__codelineno-19-17" name="__codelineno-19-17"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return null to indicate an empty position</span>
<a href="#__codelineno-19-18" id="__codelineno-19-18" name="__codelineno-19-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">())</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a href="#__codelineno-19-19" id="__codelineno-19-19" name="__codelineno-19-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
<a href="#__codelineno-19-20" id="__codelineno-19-20" name="__codelineno-19-20"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-21" id="__codelineno-19-21" name="__codelineno-19-21"></a>
<a href="#__codelineno-19-22" id="__codelineno-19-22" name="__codelineno-19-22"></a><span class="w"> </span><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-19-23" id="__codelineno-19-23" name="__codelineno-19-23"></a><span class="w"> </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-24" id="__codelineno-19-24" name="__codelineno-19-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a href="#__codelineno-19-25" id="__codelineno-19-25" name="__codelineno-19-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-26" id="__codelineno-19-26" name="__codelineno-19-26"></a>
<a href="#__codelineno-19-27" id="__codelineno-19-27" name="__codelineno-19-27"></a><span class="w"> </span><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-19-28" id="__codelineno-19-28" name="__codelineno-19-28"></a><span class="w"> </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-29" id="__codelineno-19-29" name="__codelineno-19-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
<a href="#__codelineno-19-30" id="__codelineno-19-30" name="__codelineno-19-30"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-31" id="__codelineno-19-31" name="__codelineno-19-31"></a>
<a href="#__codelineno-19-32" id="__codelineno-19-32" name="__codelineno-19-32"></a><span class="w"> </span><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-19-33" id="__codelineno-19-33" name="__codelineno-19-33"></a><span class="w"> </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-34" id="__codelineno-19-34" name="__codelineno-19-34"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Floor division</span>
<a href="#__codelineno-19-35" id="__codelineno-19-35" name="__codelineno-19-35"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-36" id="__codelineno-19-36" name="__codelineno-19-36"></a>
<a href="#__codelineno-19-37" id="__codelineno-19-37" name="__codelineno-19-37"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-19-38" id="__codelineno-19-38" name="__codelineno-19-38"></a><span class="w"> </span><span class="nx">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-39" id="__codelineno-19-39" name="__codelineno-19-39"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-19-40" id="__codelineno-19-40" name="__codelineno-19-40"></a><span class="w"> </span><span class="c1">// Traverse the array directly</span>
<a href="#__codelineno-19-41" id="__codelineno-19-41" name="__codelineno-19-41"></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">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-42" id="__codelineno-19-42" name="__codelineno-19-42"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</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="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
<a href="#__codelineno-19-43" id="__codelineno-19-43" name="__codelineno-19-43"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-44" id="__codelineno-19-44" name="__codelineno-19-44"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
<a href="#__codelineno-19-45" id="__codelineno-19-45" name="__codelineno-19-45"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-46" id="__codelineno-19-46" name="__codelineno-19-46"></a>
<a href="#__codelineno-19-47" id="__codelineno-19-47" name="__codelineno-19-47"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-19-48" id="__codelineno-19-48" name="__codelineno-19-48"></a><span class="w"> </span><span class="n">#dfs</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">order</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 href="#__codelineno-19-49" id="__codelineno-19-49" name="__codelineno-19-49"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-19-50" id="__codelineno-19-50" name="__codelineno-19-50"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</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="k">return</span><span class="p">;</span>
<a href="#__codelineno-19-51" id="__codelineno-19-51" name="__codelineno-19-51"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-19-52" id="__codelineno-19-52" name="__codelineno-19-52"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">'pre'</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
<a href="#__codelineno-19-53" id="__codelineno-19-53" name="__codelineno-19-53"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-19-54" id="__codelineno-19-54" name="__codelineno-19-54"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-19-55" id="__codelineno-19-55" name="__codelineno-19-55"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">'in'</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
<a href="#__codelineno-19-56" id="__codelineno-19-56" name="__codelineno-19-56"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-19-57" id="__codelineno-19-57" name="__codelineno-19-57"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-19-58" id="__codelineno-19-58" name="__codelineno-19-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">'post'</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
<a href="#__codelineno-19-59" id="__codelineno-19-59" name="__codelineno-19-59"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-60" id="__codelineno-19-60" name="__codelineno-19-60"></a>
<a href="#__codelineno-19-61" id="__codelineno-19-61" name="__codelineno-19-61"></a><span class="w"> </span><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-19-62" id="__codelineno-19-62" name="__codelineno-19-62"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-63" id="__codelineno-19-63" name="__codelineno-19-63"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-19-64" id="__codelineno-19-64" name="__codelineno-19-64"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">'pre'</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-19-65" id="__codelineno-19-65" name="__codelineno-19-65"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
<a href="#__codelineno-19-66" id="__codelineno-19-66" name="__codelineno-19-66"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-67" id="__codelineno-19-67" name="__codelineno-19-67"></a>
<a href="#__codelineno-19-68" id="__codelineno-19-68" name="__codelineno-19-68"></a><span class="w"> </span><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-19-69" id="__codelineno-19-69" name="__codelineno-19-69"></a><span class="w"> </span><span class="nx">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-70" id="__codelineno-19-70" name="__codelineno-19-70"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-19-71" id="__codelineno-19-71" name="__codelineno-19-71"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">'in'</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-19-72" id="__codelineno-19-72" name="__codelineno-19-72"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
<a href="#__codelineno-19-73" id="__codelineno-19-73" name="__codelineno-19-73"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-74" id="__codelineno-19-74" name="__codelineno-19-74"></a>
<a href="#__codelineno-19-75" id="__codelineno-19-75" name="__codelineno-19-75"></a><span class="w"> </span><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-19-76" id="__codelineno-19-76" name="__codelineno-19-76"></a><span class="w"> </span><span class="nx">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-77" id="__codelineno-19-77" name="__codelineno-19-77"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-19-78" id="__codelineno-19-78" name="__codelineno-19-78"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">'post'</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-19-79" id="__codelineno-19-79" name="__codelineno-19-79"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
<a href="#__codelineno-19-80" id="__codelineno-19-80" name="__codelineno-19-80"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-81" id="__codelineno-19-81" name="__codelineno-19-81"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.ts</span><pre><span></span><code><a href="#__codelineno-20-1" id="__codelineno-20-1" name="__codelineno-20-1"></a><span class="cm">/* Binary tree class using an array representation */</span>
<a href="#__codelineno-20-2" id="__codelineno-20-2" name="__codelineno-20-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-3" id="__codelineno-20-3" name="__codelineno-20-3"></a><span class="w"> </span><span class="n">#tree</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[];</span>
<a href="#__codelineno-20-4" id="__codelineno-20-4" name="__codelineno-20-4"></a>
<a href="#__codelineno-20-5" id="__codelineno-20-5" name="__codelineno-20-5"></a><span class="w"> </span><span class="cm">/* Constructor */</span>
<a href="#__codelineno-20-6" id="__codelineno-20-6" name="__codelineno-20-6"></a><span class="w"> </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">arr</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</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 href="#__codelineno-20-7" id="__codelineno-20-7" name="__codelineno-20-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">arr</span><span class="p">;</span>
<a href="#__codelineno-20-8" id="__codelineno-20-8" name="__codelineno-20-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-9" id="__codelineno-20-9" name="__codelineno-20-9"></a>
<a href="#__codelineno-20-10" id="__codelineno-20-10" name="__codelineno-20-10"></a><span class="w"> </span><span class="cm">/* Array length, including empty positions */</span>
<a href="#__codelineno-20-11" id="__codelineno-20-11" name="__codelineno-20-11"></a><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-12" id="__codelineno-20-12" name="__codelineno-20-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
<a href="#__codelineno-20-13" id="__codelineno-20-13" name="__codelineno-20-13"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-14" id="__codelineno-20-14" name="__codelineno-20-14"></a>
<a href="#__codelineno-20-15" id="__codelineno-20-15" name="__codelineno-20-15"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-20-16" id="__codelineno-20-16" name="__codelineno-20-16"></a><span class="w"> </span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-17" id="__codelineno-20-17" name="__codelineno-20-17"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return null to indicate an empty position</span>
<a href="#__codelineno-20-18" id="__codelineno-20-18" name="__codelineno-20-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">())</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a href="#__codelineno-20-19" id="__codelineno-20-19" name="__codelineno-20-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#tree</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
<a href="#__codelineno-20-20" id="__codelineno-20-20" name="__codelineno-20-20"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-21" id="__codelineno-20-21" name="__codelineno-20-21"></a>
<a href="#__codelineno-20-22" id="__codelineno-20-22" name="__codelineno-20-22"></a><span class="w"> </span><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-20-23" id="__codelineno-20-23" name="__codelineno-20-23"></a><span class="w"> </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-24" id="__codelineno-20-24" name="__codelineno-20-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a href="#__codelineno-20-25" id="__codelineno-20-25" name="__codelineno-20-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-26" id="__codelineno-20-26" name="__codelineno-20-26"></a>
<a href="#__codelineno-20-27" id="__codelineno-20-27" name="__codelineno-20-27"></a><span class="w"> </span><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-20-28" id="__codelineno-20-28" name="__codelineno-20-28"></a><span class="w"> </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-29" id="__codelineno-20-29" name="__codelineno-20-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
<a href="#__codelineno-20-30" id="__codelineno-20-30" name="__codelineno-20-30"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-31" id="__codelineno-20-31" name="__codelineno-20-31"></a>
<a href="#__codelineno-20-32" id="__codelineno-20-32" name="__codelineno-20-32"></a><span class="w"> </span><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-20-33" id="__codelineno-20-33" name="__codelineno-20-33"></a><span class="w"> </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-34" id="__codelineno-20-34" name="__codelineno-20-34"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Floor division</span>
<a href="#__codelineno-20-35" id="__codelineno-20-35" name="__codelineno-20-35"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-36" id="__codelineno-20-36" name="__codelineno-20-36"></a>
<a href="#__codelineno-20-37" id="__codelineno-20-37" name="__codelineno-20-37"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-20-38" id="__codelineno-20-38" name="__codelineno-20-38"></a><span class="w"> </span><span class="nx">levelOrder</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-39" id="__codelineno-20-39" name="__codelineno-20-39"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-20-40" id="__codelineno-20-40" name="__codelineno-20-40"></a><span class="w"> </span><span class="c1">// Traverse the array directly</span>
<a href="#__codelineno-20-41" id="__codelineno-20-41" name="__codelineno-20-41"></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">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">();</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-42" id="__codelineno-20-42" name="__codelineno-20-42"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</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="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
<a href="#__codelineno-20-43" id="__codelineno-20-43" name="__codelineno-20-43"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-44" id="__codelineno-20-44" name="__codelineno-20-44"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
<a href="#__codelineno-20-45" id="__codelineno-20-45" name="__codelineno-20-45"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-46" id="__codelineno-20-46" name="__codelineno-20-46"></a>
<a href="#__codelineno-20-47" id="__codelineno-20-47" name="__codelineno-20-47"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-20-48" id="__codelineno-20-48" name="__codelineno-20-48"></a><span class="w"> </span><span class="n">#dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">order</span><span class="o">:</span><span class="w"> </span><span class="kt">Order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</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 href="#__codelineno-20-49" id="__codelineno-20-49" name="__codelineno-20-49"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-20-50" id="__codelineno-20-50" name="__codelineno-20-50"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">)</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="k">return</span><span class="p">;</span>
<a href="#__codelineno-20-51" id="__codelineno-20-51" name="__codelineno-20-51"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-20-52" id="__codelineno-20-52" name="__codelineno-20-52"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">'pre'</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
<a href="#__codelineno-20-53" id="__codelineno-20-53" name="__codelineno-20-53"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-20-54" id="__codelineno-20-54" name="__codelineno-20-54"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-20-55" id="__codelineno-20-55" name="__codelineno-20-55"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">'in'</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
<a href="#__codelineno-20-56" id="__codelineno-20-56" name="__codelineno-20-56"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">order</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-20-57" id="__codelineno-20-57" name="__codelineno-20-57"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-20-58" id="__codelineno-20-58" name="__codelineno-20-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">order</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="s1">'post'</span><span class="p">)</span><span class="w"> </span><span class="nx">res</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
<a href="#__codelineno-20-59" id="__codelineno-20-59" name="__codelineno-20-59"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-60" id="__codelineno-20-60" name="__codelineno-20-60"></a>
<a href="#__codelineno-20-61" id="__codelineno-20-61" name="__codelineno-20-61"></a><span class="w"> </span><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-20-62" id="__codelineno-20-62" name="__codelineno-20-62"></a><span class="w"> </span><span class="nx">preOrder</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</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 href="#__codelineno-20-63" id="__codelineno-20-63" name="__codelineno-20-63"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-20-64" id="__codelineno-20-64" name="__codelineno-20-64"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">'pre'</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-20-65" id="__codelineno-20-65" name="__codelineno-20-65"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
<a href="#__codelineno-20-66" id="__codelineno-20-66" name="__codelineno-20-66"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-67" id="__codelineno-20-67" name="__codelineno-20-67"></a>
<a href="#__codelineno-20-68" id="__codelineno-20-68" name="__codelineno-20-68"></a><span class="w"> </span><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-20-69" id="__codelineno-20-69" name="__codelineno-20-69"></a><span class="w"> </span><span class="nx">inOrder</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</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 href="#__codelineno-20-70" id="__codelineno-20-70" name="__codelineno-20-70"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-20-71" id="__codelineno-20-71" name="__codelineno-20-71"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">'in'</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-20-72" id="__codelineno-20-72" name="__codelineno-20-72"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
<a href="#__codelineno-20-73" id="__codelineno-20-73" name="__codelineno-20-73"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-74" id="__codelineno-20-74" name="__codelineno-20-74"></a>
<a href="#__codelineno-20-75" id="__codelineno-20-75" name="__codelineno-20-75"></a><span class="w"> </span><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-20-76" id="__codelineno-20-76" name="__codelineno-20-76"></a><span class="w"> </span><span class="nx">postOrder</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</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 href="#__codelineno-20-77" id="__codelineno-20-77" name="__codelineno-20-77"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-20-78" id="__codelineno-20-78" name="__codelineno-20-78"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">#dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="s1">'post'</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
<a href="#__codelineno-20-79" id="__codelineno-20-79" name="__codelineno-20-79"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
<a href="#__codelineno-20-80" id="__codelineno-20-80" name="__codelineno-20-80"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-81" id="__codelineno-20-81" name="__codelineno-20-81"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.dart</span><pre><span></span><code><a href="#__codelineno-21-1" id="__codelineno-21-1" name="__codelineno-21-1"></a><span class="cm">/* Binary tree class using an array representation */</span>
<a href="#__codelineno-21-2" id="__codelineno-21-2" name="__codelineno-21-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-3" id="__codelineno-21-3" name="__codelineno-21-3"></a><span class="w"> </span><span class="kd">late</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">_tree</span><span class="p">;</span>
<a href="#__codelineno-21-4" id="__codelineno-21-4" name="__codelineno-21-4"></a>
<a href="#__codelineno-21-5" id="__codelineno-21-5" name="__codelineno-21-5"></a><span class="w"> </span><span class="cm">/* Constructor */</span>
<a href="#__codelineno-21-6" id="__codelineno-21-6" name="__codelineno-21-6"></a><span class="w"> </span><span class="n">ArrayBinaryTree</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">_tree</span><span class="p">);</span>
<a href="#__codelineno-21-7" id="__codelineno-21-7" name="__codelineno-21-7"></a>
<a href="#__codelineno-21-8" id="__codelineno-21-8" name="__codelineno-21-8"></a><span class="w"> </span><span class="cm">/* Array length, including empty positions */</span>
<a href="#__codelineno-21-9" id="__codelineno-21-9" name="__codelineno-21-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-10" id="__codelineno-21-10" name="__codelineno-21-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">_tree</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
<a href="#__codelineno-21-11" id="__codelineno-21-11" name="__codelineno-21-11"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-12" id="__codelineno-21-12" name="__codelineno-21-12"></a>
<a href="#__codelineno-21-13" id="__codelineno-21-13" name="__codelineno-21-13"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-21-14" id="__codelineno-21-14" name="__codelineno-21-14"></a><span class="w"> </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-15" id="__codelineno-21-15" name="__codelineno-21-15"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return null to indicate an empty position</span>
<a href="#__codelineno-21-16" id="__codelineno-21-16" name="__codelineno-21-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-17" id="__codelineno-21-17" name="__codelineno-21-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a href="#__codelineno-21-18" id="__codelineno-21-18" name="__codelineno-21-18"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-19" id="__codelineno-21-19" name="__codelineno-21-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">_tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a href="#__codelineno-21-20" id="__codelineno-21-20" name="__codelineno-21-20"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-21" id="__codelineno-21-21" name="__codelineno-21-21"></a>
<a href="#__codelineno-21-22" id="__codelineno-21-22" name="__codelineno-21-22"></a><span class="w"> </span><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-21-23" id="__codelineno-21-23" name="__codelineno-21-23"></a><span class="w"> </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-24" id="__codelineno-21-24" name="__codelineno-21-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a href="#__codelineno-21-25" id="__codelineno-21-25" name="__codelineno-21-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-26" id="__codelineno-21-26" name="__codelineno-21-26"></a>
<a href="#__codelineno-21-27" id="__codelineno-21-27" name="__codelineno-21-27"></a><span class="w"> </span><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-21-28" id="__codelineno-21-28" name="__codelineno-21-28"></a><span class="w"> </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-29" id="__codelineno-21-29" name="__codelineno-21-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
<a href="#__codelineno-21-30" id="__codelineno-21-30" name="__codelineno-21-30"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-31" id="__codelineno-21-31" name="__codelineno-21-31"></a>
<a href="#__codelineno-21-32" id="__codelineno-21-32" name="__codelineno-21-32"></a><span class="w"> </span><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-21-33" id="__codelineno-21-33" name="__codelineno-21-33"></a><span class="w"> </span><span class="kt">int</span><span class="o">?</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-34" id="__codelineno-21-34" name="__codelineno-21-34"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
<a href="#__codelineno-21-35" id="__codelineno-21-35" name="__codelineno-21-35"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-36" id="__codelineno-21-36" name="__codelineno-21-36"></a>
<a href="#__codelineno-21-37" id="__codelineno-21-37" name="__codelineno-21-37"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-21-38" id="__codelineno-21-38" name="__codelineno-21-38"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-39" id="__codelineno-21-39" name="__codelineno-21-39"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-21-40" id="__codelineno-21-40" name="__codelineno-21-40"></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="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</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 href="#__codelineno-21-41" id="__codelineno-21-41" name="__codelineno-21-41"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-42" id="__codelineno-21-42" name="__codelineno-21-42"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">);</span>
<a href="#__codelineno-21-43" id="__codelineno-21-43" name="__codelineno-21-43"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-44" id="__codelineno-21-44" name="__codelineno-21-44"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-45" id="__codelineno-21-45" name="__codelineno-21-45"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-21-46" id="__codelineno-21-46" name="__codelineno-21-46"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-47" id="__codelineno-21-47" name="__codelineno-21-47"></a>
<a href="#__codelineno-21-48" id="__codelineno-21-48" name="__codelineno-21-48"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-21-49" id="__codelineno-21-49" name="__codelineno-21-49"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-50" id="__codelineno-21-50" name="__codelineno-21-50"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-21-51" id="__codelineno-21-51" name="__codelineno-21-51"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-52" id="__codelineno-21-52" name="__codelineno-21-52"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a href="#__codelineno-21-53" id="__codelineno-21-53" name="__codelineno-21-53"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-54" id="__codelineno-21-54" name="__codelineno-21-54"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-21-55" id="__codelineno-21-55" name="__codelineno-21-55"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s1">'pre'</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-56" id="__codelineno-21-56" name="__codelineno-21-56"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-21-57" id="__codelineno-21-57" name="__codelineno-21-57"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-58" id="__codelineno-21-58" name="__codelineno-21-58"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-21-59" id="__codelineno-21-59" name="__codelineno-21-59"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-21-60" id="__codelineno-21-60" name="__codelineno-21-60"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s1">'in'</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-61" id="__codelineno-21-61" name="__codelineno-21-61"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-21-62" id="__codelineno-21-62" name="__codelineno-21-62"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-63" id="__codelineno-21-63" name="__codelineno-21-63"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">!</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-21-64" id="__codelineno-21-64" name="__codelineno-21-64"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-21-65" id="__codelineno-21-65" name="__codelineno-21-65"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s1">'post'</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-66" id="__codelineno-21-66" name="__codelineno-21-66"></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">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
<a href="#__codelineno-21-67" id="__codelineno-21-67" name="__codelineno-21-67"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-68" id="__codelineno-21-68" name="__codelineno-21-68"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-69" id="__codelineno-21-69" name="__codelineno-21-69"></a>
<a href="#__codelineno-21-70" id="__codelineno-21-70" name="__codelineno-21-70"></a><span class="w"> </span><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-21-71" id="__codelineno-21-71" name="__codelineno-21-71"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-72" id="__codelineno-21-72" name="__codelineno-21-72"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-21-73" id="__codelineno-21-73" name="__codelineno-21-73"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s1">'pre'</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-21-74" id="__codelineno-21-74" name="__codelineno-21-74"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-21-75" id="__codelineno-21-75" name="__codelineno-21-75"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-76" id="__codelineno-21-76" name="__codelineno-21-76"></a>
<a href="#__codelineno-21-77" id="__codelineno-21-77" name="__codelineno-21-77"></a><span class="w"> </span><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-21-78" id="__codelineno-21-78" name="__codelineno-21-78"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-79" id="__codelineno-21-79" name="__codelineno-21-79"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-21-80" id="__codelineno-21-80" name="__codelineno-21-80"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s1">'in'</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-21-81" id="__codelineno-21-81" name="__codelineno-21-81"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-21-82" id="__codelineno-21-82" name="__codelineno-21-82"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-83" id="__codelineno-21-83" name="__codelineno-21-83"></a>
<a href="#__codelineno-21-84" id="__codelineno-21-84" name="__codelineno-21-84"></a><span class="w"> </span><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-21-85" id="__codelineno-21-85" name="__codelineno-21-85"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-86" id="__codelineno-21-86" name="__codelineno-21-86"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a href="#__codelineno-21-87" id="__codelineno-21-87" name="__codelineno-21-87"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s1">'post'</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-21-88" id="__codelineno-21-88" name="__codelineno-21-88"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-21-89" id="__codelineno-21-89" name="__codelineno-21-89"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-90" id="__codelineno-21-90" name="__codelineno-21-90"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.rs</span><pre><span></span><code><a href="#__codelineno-22-1" id="__codelineno-22-1" name="__codelineno-22-1"></a><span class="cm">/* Binary tree type using an array representation */</span>
<a href="#__codelineno-22-2" id="__codelineno-22-2" name="__codelineno-22-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-3" id="__codelineno-22-3" name="__codelineno-22-3"></a><span class="w"> </span><span class="n">tree</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">,</span>
<a href="#__codelineno-22-4" id="__codelineno-22-4" name="__codelineno-22-4"></a><span class="p">}</span>
<a href="#__codelineno-22-5" id="__codelineno-22-5" name="__codelineno-22-5"></a>
<a href="#__codelineno-22-6" id="__codelineno-22-6" name="__codelineno-22-6"></a><span class="k">impl</span><span class="w"> </span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-7" id="__codelineno-22-7" name="__codelineno-22-7"></a><span class="w"> </span><span class="cm">/* Constructor */</span>
<a href="#__codelineno-22-8" id="__codelineno-22-8" name="__codelineno-22-8"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-9" id="__codelineno-22-9" name="__codelineno-22-9"></a><span class="w"> </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">tree</span><span class="p">:</span><span class="w"> </span><span class="nc">arr</span><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-10" id="__codelineno-22-10" name="__codelineno-22-10"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-11" id="__codelineno-22-11" name="__codelineno-22-11"></a>
<a href="#__codelineno-22-12" id="__codelineno-22-12" name="__codelineno-22-12"></a><span class="w"> </span><span class="cm">/* Number of positions in the array */</span>
<a href="#__codelineno-22-13" id="__codelineno-22-13" name="__codelineno-22-13"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-14" id="__codelineno-22-14" name="__codelineno-22-14"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">tree</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span>
<a href="#__codelineno-22-15" id="__codelineno-22-15" name="__codelineno-22-15"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-16" id="__codelineno-22-16" name="__codelineno-22-16"></a>
<a href="#__codelineno-22-17" id="__codelineno-22-17" name="__codelineno-22-17"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-22-18" id="__codelineno-22-18" name="__codelineno-22-18"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-19" id="__codelineno-22-19" name="__codelineno-22-19"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return None to represent an empty position</span>
<a href="#__codelineno-22-20" id="__codelineno-22-20" name="__codelineno-22-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-21" id="__codelineno-22-21" name="__codelineno-22-21"></a><span class="w"> </span><span class="nb">None</span>
<a href="#__codelineno-22-22" id="__codelineno-22-22" name="__codelineno-22-22"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-23" id="__codelineno-22-23" name="__codelineno-22-23"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span>
<a href="#__codelineno-22-24" id="__codelineno-22-24" name="__codelineno-22-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-25" id="__codelineno-22-25" name="__codelineno-22-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-26" id="__codelineno-22-26" name="__codelineno-22-26"></a>
<a href="#__codelineno-22-27" id="__codelineno-22-27" name="__codelineno-22-27"></a><span class="w"> </span><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-22-28" id="__codelineno-22-28" name="__codelineno-22-28"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-29" id="__codelineno-22-29" name="__codelineno-22-29"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span>
<a href="#__codelineno-22-30" id="__codelineno-22-30" name="__codelineno-22-30"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-31" id="__codelineno-22-31" name="__codelineno-22-31"></a>
<a href="#__codelineno-22-32" id="__codelineno-22-32" name="__codelineno-22-32"></a><span class="w"> </span><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-22-33" id="__codelineno-22-33" name="__codelineno-22-33"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-34" id="__codelineno-22-34" name="__codelineno-22-34"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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>
<a href="#__codelineno-22-35" id="__codelineno-22-35" name="__codelineno-22-35"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-36" id="__codelineno-22-36" name="__codelineno-22-36"></a>
<a href="#__codelineno-22-37" id="__codelineno-22-37" name="__codelineno-22-37"></a><span class="w"> </span><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-22-38" id="__codelineno-22-38" name="__codelineno-22-38"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-39" id="__codelineno-22-39" name="__codelineno-22-39"></a><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
<a href="#__codelineno-22-40" id="__codelineno-22-40" name="__codelineno-22-40"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-41" id="__codelineno-22-41" name="__codelineno-22-41"></a>
<a href="#__codelineno-22-42" id="__codelineno-22-42" name="__codelineno-22-42"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-22-43" id="__codelineno-22-43" name="__codelineno-22-43"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-44" id="__codelineno-22-44" name="__codelineno-22-44"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">tree</span><span class="p">.</span><span class="n">iter</span><span class="p">().</span><span class="n">filter_map</span><span class="p">(</span><span class="o">|&amp;</span><span class="n">x</span><span class="o">|</span><span class="w"> </span><span class="n">x</span><span class="p">).</span><span class="n">collect</span><span class="p">()</span>
<a href="#__codelineno-22-45" id="__codelineno-22-45" name="__codelineno-22-45"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-46" id="__codelineno-22-46" name="__codelineno-22-46"></a>
<a href="#__codelineno-22-47" id="__codelineno-22-47" name="__codelineno-22-47"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-22-48" id="__codelineno-22-48" name="__codelineno-22-48"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="o">'</span><span class="nb">static</span><span class="w"> </span><span class="kt">str</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">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-49" id="__codelineno-22-49" name="__codelineno-22-49"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-50" id="__codelineno-22-50" name="__codelineno-22-50"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a href="#__codelineno-22-51" id="__codelineno-22-51" name="__codelineno-22-51"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-52" id="__codelineno-22-52" name="__codelineno-22-52"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">unwrap</span><span class="p">();</span>
<a href="#__codelineno-22-53" id="__codelineno-22-53" name="__codelineno-22-53"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-22-54" id="__codelineno-22-54" name="__codelineno-22-54"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"pre"</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-55" id="__codelineno-22-55" name="__codelineno-22-55"></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">val</span><span class="p">);</span>
<a href="#__codelineno-22-56" id="__codelineno-22-56" name="__codelineno-22-56"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-57" id="__codelineno-22-57" name="__codelineno-22-57"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-22-58" id="__codelineno-22-58" name="__codelineno-22-58"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-22-59" id="__codelineno-22-59" name="__codelineno-22-59"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"in"</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-60" id="__codelineno-22-60" name="__codelineno-22-60"></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">val</span><span class="p">);</span>
<a href="#__codelineno-22-61" id="__codelineno-22-61" name="__codelineno-22-61"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-62" id="__codelineno-22-62" name="__codelineno-22-62"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-22-63" id="__codelineno-22-63" name="__codelineno-22-63"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-22-64" id="__codelineno-22-64" name="__codelineno-22-64"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"post"</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-65" id="__codelineno-22-65" name="__codelineno-22-65"></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">val</span><span class="p">);</span>
<a href="#__codelineno-22-66" id="__codelineno-22-66" name="__codelineno-22-66"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-67" id="__codelineno-22-67" name="__codelineno-22-67"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-68" id="__codelineno-22-68" name="__codelineno-22-68"></a>
<a href="#__codelineno-22-69" id="__codelineno-22-69" name="__codelineno-22-69"></a><span class="w"> </span><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-22-70" id="__codelineno-22-70" name="__codelineno-22-70"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-71" id="__codelineno-22-71" name="__codelineno-22-71"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a href="#__codelineno-22-72" id="__codelineno-22-72" name="__codelineno-22-72"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-22-73" id="__codelineno-22-73" name="__codelineno-22-73"></a><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-22-74" id="__codelineno-22-74" name="__codelineno-22-74"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-75" id="__codelineno-22-75" name="__codelineno-22-75"></a>
<a href="#__codelineno-22-76" id="__codelineno-22-76" name="__codelineno-22-76"></a><span class="w"> </span><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-22-77" id="__codelineno-22-77" name="__codelineno-22-77"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-78" id="__codelineno-22-78" name="__codelineno-22-78"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a href="#__codelineno-22-79" id="__codelineno-22-79" name="__codelineno-22-79"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-22-80" id="__codelineno-22-80" name="__codelineno-22-80"></a><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-22-81" id="__codelineno-22-81" name="__codelineno-22-81"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-82" id="__codelineno-22-82" name="__codelineno-22-82"></a>
<a href="#__codelineno-22-83" id="__codelineno-22-83" name="__codelineno-22-83"></a><span class="w"> </span><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-22-84" id="__codelineno-22-84" name="__codelineno-22-84"></a><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-85" id="__codelineno-22-85" name="__codelineno-22-85"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a href="#__codelineno-22-86" id="__codelineno-22-86" name="__codelineno-22-86"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a href="#__codelineno-22-87" id="__codelineno-22-87" name="__codelineno-22-87"></a><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-22-88" id="__codelineno-22-88" name="__codelineno-22-88"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-89" id="__codelineno-22-89" name="__codelineno-22-89"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.c</span><pre><span></span><code><a href="#__codelineno-23-1" id="__codelineno-23-1" name="__codelineno-23-1"></a><span class="cm">/* Binary tree structure represented by an array */</span>
<a href="#__codelineno-23-2" id="__codelineno-23-2" name="__codelineno-23-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-3" id="__codelineno-23-3" name="__codelineno-23-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tree</span><span class="p">;</span>
<a href="#__codelineno-23-4" id="__codelineno-23-4" name="__codelineno-23-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
<a href="#__codelineno-23-5" id="__codelineno-23-5" name="__codelineno-23-5"></a><span class="p">}</span><span class="w"> </span><span class="n">ArrayBinaryTree</span><span class="p">;</span>
<a href="#__codelineno-23-6" id="__codelineno-23-6" name="__codelineno-23-6"></a>
<a href="#__codelineno-23-7" id="__codelineno-23-7" name="__codelineno-23-7"></a><span class="cm">/* Constructor */</span>
<a href="#__codelineno-23-8" id="__codelineno-23-8" name="__codelineno-23-8"></a><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="nf">newArrayBinaryTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">arrSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-9" id="__codelineno-23-9" name="__codelineno-23-9"></a><span class="w"> </span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="p">));</span>
<a href="#__codelineno-23-10" id="__codelineno-23-10" name="__codelineno-23-10"></a><span class="w"> </span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</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="n">arrSize</span><span class="p">);</span>
<a href="#__codelineno-23-11" id="__codelineno-23-11" name="__codelineno-23-11"></a><span class="w"> </span><span class="n">memcpy</span><span class="p">(</span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">tree</span><span class="p">,</span><span class="w"> </span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</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="n">arrSize</span><span class="p">);</span>
<a href="#__codelineno-23-12" id="__codelineno-23-12" name="__codelineno-23-12"></a><span class="w"> </span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrSize</span><span class="p">;</span>
<a href="#__codelineno-23-13" id="__codelineno-23-13" name="__codelineno-23-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">abt</span><span class="p">;</span>
<a href="#__codelineno-23-14" id="__codelineno-23-14" name="__codelineno-23-14"></a><span class="p">}</span>
<a href="#__codelineno-23-15" id="__codelineno-23-15" name="__codelineno-23-15"></a>
<a href="#__codelineno-23-16" id="__codelineno-23-16" name="__codelineno-23-16"></a><span class="cm">/* Destructor */</span>
<a href="#__codelineno-23-17" id="__codelineno-23-17" name="__codelineno-23-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delArrayBinaryTree</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-18" id="__codelineno-23-18" name="__codelineno-23-18"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">tree</span><span class="p">);</span>
<a href="#__codelineno-23-19" id="__codelineno-23-19" name="__codelineno-23-19"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">abt</span><span class="p">);</span>
<a href="#__codelineno-23-20" id="__codelineno-23-20" name="__codelineno-23-20"></a><span class="p">}</span>
<a href="#__codelineno-23-21" id="__codelineno-23-21" name="__codelineno-23-21"></a>
<a href="#__codelineno-23-22" id="__codelineno-23-22" name="__codelineno-23-22"></a><span class="cm">/* Array length */</span>
<a href="#__codelineno-23-23" id="__codelineno-23-23" name="__codelineno-23-23"></a><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-24" id="__codelineno-23-24" name="__codelineno-23-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">;</span>
<a href="#__codelineno-23-25" id="__codelineno-23-25" name="__codelineno-23-25"></a><span class="p">}</span>
<a href="#__codelineno-23-26" id="__codelineno-23-26" name="__codelineno-23-26"></a>
<a href="#__codelineno-23-27" id="__codelineno-23-27" name="__codelineno-23-27"></a><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-23-28" id="__codelineno-23-28" name="__codelineno-23-28"></a><span class="kt">int</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-29" id="__codelineno-23-29" name="__codelineno-23-29"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return INT_MAX to represent an empty position</span>
<a href="#__codelineno-23-30" id="__codelineno-23-30" name="__codelineno-23-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">))</span>
<a href="#__codelineno-23-31" id="__codelineno-23-31" name="__codelineno-23-31"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
<a href="#__codelineno-23-32" id="__codelineno-23-32" name="__codelineno-23-32"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">abt</span><span class="o">-&gt;</span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a href="#__codelineno-23-33" id="__codelineno-23-33" name="__codelineno-23-33"></a><span class="p">}</span>
<a href="#__codelineno-23-34" id="__codelineno-23-34" name="__codelineno-23-34"></a>
<a href="#__codelineno-23-35" id="__codelineno-23-35" name="__codelineno-23-35"></a><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-23-36" id="__codelineno-23-36" name="__codelineno-23-36"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">levelOrder</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-37" id="__codelineno-23-37" name="__codelineno-23-37"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</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="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">));</span>
<a href="#__codelineno-23-38" id="__codelineno-23-38" name="__codelineno-23-38"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a href="#__codelineno-23-39" id="__codelineno-23-39" name="__codelineno-23-39"></a><span class="w"> </span><span class="c1">// Traverse the array directly</span>
<a href="#__codelineno-23-40" id="__codelineno-23-40" name="__codelineno-23-40"></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">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">abt</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 href="#__codelineno-23-41" id="__codelineno-23-41" name="__codelineno-23-41"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </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">INT_MAX</span><span class="p">)</span>
<a href="#__codelineno-23-42" id="__codelineno-23-42" name="__codelineno-23-42"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">index</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a href="#__codelineno-23-43" id="__codelineno-23-43" name="__codelineno-23-43"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-23-44" id="__codelineno-23-44" name="__codelineno-23-44"></a><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
<a href="#__codelineno-23-45" id="__codelineno-23-45" name="__codelineno-23-45"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-23-46" id="__codelineno-23-46" name="__codelineno-23-46"></a><span class="p">}</span>
<a href="#__codelineno-23-47" id="__codelineno-23-47" name="__codelineno-23-47"></a>
<a href="#__codelineno-23-48" id="__codelineno-23-48" name="__codelineno-23-48"></a><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-23-49" id="__codelineno-23-49" name="__codelineno-23-49"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="kt">int</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="o">*</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-50" id="__codelineno-23-50" name="__codelineno-23-50"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-23-51" id="__codelineno-23-51" name="__codelineno-23-51"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </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">INT_MAX</span><span class="p">)</span>
<a href="#__codelineno-23-52" id="__codelineno-23-52" name="__codelineno-23-52"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a href="#__codelineno-23-53" id="__codelineno-23-53" name="__codelineno-23-53"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-23-54" id="__codelineno-23-54" name="__codelineno-23-54"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">strcmp</span><span class="p">(</span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a href="#__codelineno-23-55" id="__codelineno-23-55" name="__codelineno-23-55"></a><span class="w"> </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">index</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a href="#__codelineno-23-56" id="__codelineno-23-56" name="__codelineno-23-56"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</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">index</span><span class="p">);</span>
<a href="#__codelineno-23-57" id="__codelineno-23-57" name="__codelineno-23-57"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-23-58" id="__codelineno-23-58" name="__codelineno-23-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">strcmp</span><span class="p">(</span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a href="#__codelineno-23-59" id="__codelineno-23-59" name="__codelineno-23-59"></a><span class="w"> </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">index</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a href="#__codelineno-23-60" id="__codelineno-23-60" name="__codelineno-23-60"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</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">index</span><span class="p">);</span>
<a href="#__codelineno-23-61" id="__codelineno-23-61" name="__codelineno-23-61"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-23-62" id="__codelineno-23-62" name="__codelineno-23-62"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">strcmp</span><span class="p">(</span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a href="#__codelineno-23-63" id="__codelineno-23-63" name="__codelineno-23-63"></a><span class="w"> </span><span class="n">res</span><span class="p">[(</span><span class="o">*</span><span class="n">index</span><span class="p">)</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a href="#__codelineno-23-64" id="__codelineno-23-64" name="__codelineno-23-64"></a><span class="p">}</span>
<a href="#__codelineno-23-65" id="__codelineno-23-65" name="__codelineno-23-65"></a>
<a href="#__codelineno-23-66" id="__codelineno-23-66" name="__codelineno-23-66"></a><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-23-67" id="__codelineno-23-67" name="__codelineno-23-67"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">preOrder</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-68" id="__codelineno-23-68" name="__codelineno-23-68"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</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="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">));</span>
<a href="#__codelineno-23-69" id="__codelineno-23-69" name="__codelineno-23-69"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a href="#__codelineno-23-70" id="__codelineno-23-70" name="__codelineno-23-70"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">index</span><span class="p">);</span>
<a href="#__codelineno-23-71" id="__codelineno-23-71" name="__codelineno-23-71"></a><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
<a href="#__codelineno-23-72" id="__codelineno-23-72" name="__codelineno-23-72"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-23-73" id="__codelineno-23-73" name="__codelineno-23-73"></a><span class="p">}</span>
<a href="#__codelineno-23-74" id="__codelineno-23-74" name="__codelineno-23-74"></a>
<a href="#__codelineno-23-75" id="__codelineno-23-75" name="__codelineno-23-75"></a><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-23-76" id="__codelineno-23-76" name="__codelineno-23-76"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">inOrder</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-77" id="__codelineno-23-77" name="__codelineno-23-77"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</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="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">));</span>
<a href="#__codelineno-23-78" id="__codelineno-23-78" name="__codelineno-23-78"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a href="#__codelineno-23-79" id="__codelineno-23-79" name="__codelineno-23-79"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">index</span><span class="p">);</span>
<a href="#__codelineno-23-80" id="__codelineno-23-80" name="__codelineno-23-80"></a><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
<a href="#__codelineno-23-81" id="__codelineno-23-81" name="__codelineno-23-81"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-23-82" id="__codelineno-23-82" name="__codelineno-23-82"></a><span class="p">}</span>
<a href="#__codelineno-23-83" id="__codelineno-23-83" name="__codelineno-23-83"></a>
<a href="#__codelineno-23-84" id="__codelineno-23-84" name="__codelineno-23-84"></a><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-23-85" id="__codelineno-23-85" name="__codelineno-23-85"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">postOrder</span><span class="p">(</span><span class="n">ArrayBinaryTree</span><span class="w"> </span><span class="o">*</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-86" id="__codelineno-23-86" name="__codelineno-23-86"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</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="n">size</span><span class="p">(</span><span class="n">abt</span><span class="p">));</span>
<a href="#__codelineno-23-87" id="__codelineno-23-87" name="__codelineno-23-87"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a href="#__codelineno-23-88" id="__codelineno-23-88" name="__codelineno-23-88"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">abt</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">index</span><span class="p">);</span>
<a href="#__codelineno-23-89" id="__codelineno-23-89" name="__codelineno-23-89"></a><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
<a href="#__codelineno-23-90" id="__codelineno-23-90" name="__codelineno-23-90"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-23-91" id="__codelineno-23-91" name="__codelineno-23-91"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.kt</span><pre><span></span><code><a href="#__codelineno-24-1" id="__codelineno-24-1" name="__codelineno-24-1"></a><span class="cm">/* Binary tree class using an array representation */</span>
<a href="#__codelineno-24-2" id="__codelineno-24-2" name="__codelineno-24-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="p">(</span><span class="kd">val</span><span class="w"> </span><span class="nv">tree</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-3" id="__codelineno-24-3" name="__codelineno-24-3"></a><span class="w"> </span><span class="cm">/* List size */</span>
<a href="#__codelineno-24-4" id="__codelineno-24-4" name="__codelineno-24-4"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">size</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-5" id="__codelineno-24-5" name="__codelineno-24-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">size</span>
<a href="#__codelineno-24-6" id="__codelineno-24-6" name="__codelineno-24-6"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-7" id="__codelineno-24-7" name="__codelineno-24-7"></a>
<a href="#__codelineno-24-8" id="__codelineno-24-8" name="__codelineno-24-8"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
<a href="#__codelineno-24-9" id="__codelineno-24-9" name="__codelineno-24-9"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">_val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int?</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-10" id="__codelineno-24-10" name="__codelineno-24-10"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return null to represent an empty position</span>
<a href="#__codelineno-24-11" id="__codelineno-24-11" name="__codelineno-24-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
<a href="#__codelineno-24-12" id="__codelineno-24-12" name="__codelineno-24-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a href="#__codelineno-24-13" id="__codelineno-24-13" name="__codelineno-24-13"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-14" id="__codelineno-24-14" name="__codelineno-24-14"></a>
<a href="#__codelineno-24-15" id="__codelineno-24-15" name="__codelineno-24-15"></a><span class="w"> </span><span class="cm">/* Get the left child index of the node at index i */</span>
<a href="#__codelineno-24-16" id="__codelineno-24-16" name="__codelineno-24-16"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-17" id="__codelineno-24-17" name="__codelineno-24-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
<a href="#__codelineno-24-18" id="__codelineno-24-18" name="__codelineno-24-18"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-19" id="__codelineno-24-19" name="__codelineno-24-19"></a>
<a href="#__codelineno-24-20" id="__codelineno-24-20" name="__codelineno-24-20"></a><span class="w"> </span><span class="cm">/* Get the right child index of the node at index i */</span>
<a href="#__codelineno-24-21" id="__codelineno-24-21" name="__codelineno-24-21"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-22" id="__codelineno-24-22" name="__codelineno-24-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span>
<a href="#__codelineno-24-23" id="__codelineno-24-23" name="__codelineno-24-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-24" id="__codelineno-24-24" name="__codelineno-24-24"></a>
<a href="#__codelineno-24-25" id="__codelineno-24-25" name="__codelineno-24-25"></a><span class="w"> </span><span class="cm">/* Get the parent index of the node at index i */</span>
<a href="#__codelineno-24-26" id="__codelineno-24-26" name="__codelineno-24-26"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-27" id="__codelineno-24-27" name="__codelineno-24-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span>
<a href="#__codelineno-24-28" id="__codelineno-24-28" name="__codelineno-24-28"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-29" id="__codelineno-24-29" name="__codelineno-24-29"></a>
<a href="#__codelineno-24-30" id="__codelineno-24-30" name="__codelineno-24-30"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
<a href="#__codelineno-24-31" id="__codelineno-24-31" name="__codelineno-24-31"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-32" id="__codelineno-24-32" name="__codelineno-24-32"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
<a href="#__codelineno-24-33" id="__codelineno-24-33" name="__codelineno-24-33"></a><span class="w"> </span><span class="c1">// Traverse the array directly</span>
<a href="#__codelineno-24-34" id="__codelineno-24-34" name="__codelineno-24-34"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o">&lt;</span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-35" id="__codelineno-24-35" name="__codelineno-24-35"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</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="kc">null</span><span class="p">)</span>
<a href="#__codelineno-24-36" id="__codelineno-24-36" name="__codelineno-24-36"></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">_val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<a href="#__codelineno-24-37" id="__codelineno-24-37" name="__codelineno-24-37"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-38" id="__codelineno-24-38" name="__codelineno-24-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-24-39" id="__codelineno-24-39" name="__codelineno-24-39"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-40" id="__codelineno-24-40" name="__codelineno-24-40"></a>
<a href="#__codelineno-24-41" id="__codelineno-24-41" name="__codelineno-24-41"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
<a href="#__codelineno-24-42" id="__codelineno-24-42" name="__codelineno-24-42"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">:</span><span class="w"> </span><span class="kt">String</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">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-43" id="__codelineno-24-43" name="__codelineno-24-43"></a><span class="w"> </span><span class="c1">// Return if this position is empty</span>
<a href="#__codelineno-24-44" id="__codelineno-24-44" name="__codelineno-24-44"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</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="kc">null</span><span class="p">)</span>
<a href="#__codelineno-24-45" id="__codelineno-24-45" name="__codelineno-24-45"></a><span class="w"> </span><span class="k">return</span>
<a href="#__codelineno-24-46" id="__codelineno-24-46" name="__codelineno-24-46"></a><span class="w"> </span><span class="c1">// Preorder traversal</span>
<a href="#__codelineno-24-47" id="__codelineno-24-47" name="__codelineno-24-47"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">"pre"</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a href="#__codelineno-24-48" id="__codelineno-24-48" name="__codelineno-24-48"></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">_val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<a href="#__codelineno-24-49" id="__codelineno-24-49" name="__codelineno-24-49"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-24-50" id="__codelineno-24-50" name="__codelineno-24-50"></a><span class="w"> </span><span class="c1">// Inorder traversal</span>
<a href="#__codelineno-24-51" id="__codelineno-24-51" name="__codelineno-24-51"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">"in"</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a href="#__codelineno-24-52" id="__codelineno-24-52" name="__codelineno-24-52"></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">_val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<a href="#__codelineno-24-53" id="__codelineno-24-53" name="__codelineno-24-53"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-24-54" id="__codelineno-24-54" name="__codelineno-24-54"></a><span class="w"> </span><span class="c1">// Postorder traversal</span>
<a href="#__codelineno-24-55" id="__codelineno-24-55" name="__codelineno-24-55"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">"post"</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a href="#__codelineno-24-56" id="__codelineno-24-56" name="__codelineno-24-56"></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">_val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<a href="#__codelineno-24-57" id="__codelineno-24-57" name="__codelineno-24-57"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-58" id="__codelineno-24-58" name="__codelineno-24-58"></a>
<a href="#__codelineno-24-59" id="__codelineno-24-59" name="__codelineno-24-59"></a><span class="w"> </span><span class="cm">/* Preorder traversal */</span>
<a href="#__codelineno-24-60" id="__codelineno-24-60" name="__codelineno-24-60"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-61" id="__codelineno-24-61" name="__codelineno-24-61"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
<a href="#__codelineno-24-62" id="__codelineno-24-62" name="__codelineno-24-62"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-24-63" id="__codelineno-24-63" name="__codelineno-24-63"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-24-64" id="__codelineno-24-64" name="__codelineno-24-64"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-65" id="__codelineno-24-65" name="__codelineno-24-65"></a>
<a href="#__codelineno-24-66" id="__codelineno-24-66" name="__codelineno-24-66"></a><span class="w"> </span><span class="cm">/* Inorder traversal */</span>
<a href="#__codelineno-24-67" id="__codelineno-24-67" name="__codelineno-24-67"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-68" id="__codelineno-24-68" name="__codelineno-24-68"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
<a href="#__codelineno-24-69" id="__codelineno-24-69" name="__codelineno-24-69"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-24-70" id="__codelineno-24-70" name="__codelineno-24-70"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-24-71" id="__codelineno-24-71" name="__codelineno-24-71"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-72" id="__codelineno-24-72" name="__codelineno-24-72"></a>
<a href="#__codelineno-24-73" id="__codelineno-24-73" name="__codelineno-24-73"></a><span class="w"> </span><span class="cm">/* Postorder traversal */</span>
<a href="#__codelineno-24-74" id="__codelineno-24-74" name="__codelineno-24-74"></a><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">():</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-75" id="__codelineno-24-75" name="__codelineno-24-75"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
<a href="#__codelineno-24-76" id="__codelineno-24-76" name="__codelineno-24-76"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
<a href="#__codelineno-24-77" id="__codelineno-24-77" name="__codelineno-24-77"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a href="#__codelineno-24-78" id="__codelineno-24-78" name="__codelineno-24-78"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-79" id="__codelineno-24-79" name="__codelineno-24-79"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a href="#__codelineno-25-1" id="__codelineno-25-1" name="__codelineno-25-1"></a><span class="c1">### Binary tree class using an array representation ###</span>
<a href="#__codelineno-25-2" id="__codelineno-25-2" name="__codelineno-25-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span>
<a href="#__codelineno-25-3" id="__codelineno-25-3" name="__codelineno-25-3"></a><span class="w"> </span><span class="c1">### Constructor ###</span>
<a href="#__codelineno-25-4" id="__codelineno-25-4" name="__codelineno-25-4"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<a href="#__codelineno-25-5" id="__codelineno-25-5" name="__codelineno-25-5"></a><span class="w"> </span><span class="vi">@tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">.</span><span class="n">to_a</span>
<a href="#__codelineno-25-6" id="__codelineno-25-6" name="__codelineno-25-6"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-7" id="__codelineno-25-7" name="__codelineno-25-7"></a>
<a href="#__codelineno-25-8" id="__codelineno-25-8" name="__codelineno-25-8"></a><span class="w"> </span><span class="c1">### Length of the array representation ###</span>
<a href="#__codelineno-25-9" id="__codelineno-25-9" name="__codelineno-25-9"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
<a href="#__codelineno-25-10" id="__codelineno-25-10" name="__codelineno-25-10"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">.</span><span class="n">length</span>
<a href="#__codelineno-25-11" id="__codelineno-25-11" name="__codelineno-25-11"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-12" id="__codelineno-25-12" name="__codelineno-25-12"></a>
<a href="#__codelineno-25-13" id="__codelineno-25-13" name="__codelineno-25-13"></a><span class="w"> </span><span class="c1">### Get the value of the node at index i ###</span>
<a href="#__codelineno-25-14" id="__codelineno-25-14" name="__codelineno-25-14"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a href="#__codelineno-25-15" id="__codelineno-25-15" name="__codelineno-25-15"></a><span class="w"> </span><span class="c1"># If the index is out of bounds, return nil to indicate an empty position</span>
<a href="#__codelineno-25-16" id="__codelineno-25-16" name="__codelineno-25-16"></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="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
<a href="#__codelineno-25-17" id="__codelineno-25-17" name="__codelineno-25-17"></a>
<a href="#__codelineno-25-18" id="__codelineno-25-18" name="__codelineno-25-18"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a href="#__codelineno-25-19" id="__codelineno-25-19" name="__codelineno-25-19"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-20" id="__codelineno-25-20" name="__codelineno-25-20"></a>
<a href="#__codelineno-25-21" id="__codelineno-25-21" name="__codelineno-25-21"></a><span class="w"> </span><span class="c1">### Get the left child index of the node at index i ###</span>
<a href="#__codelineno-25-22" id="__codelineno-25-22" name="__codelineno-25-22"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a href="#__codelineno-25-23" id="__codelineno-25-23" name="__codelineno-25-23"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span>
<a href="#__codelineno-25-24" id="__codelineno-25-24" name="__codelineno-25-24"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-25" id="__codelineno-25-25" name="__codelineno-25-25"></a>
<a href="#__codelineno-25-26" id="__codelineno-25-26" name="__codelineno-25-26"></a><span class="w"> </span><span class="c1">### Get the right child index of the node at index i ###</span>
<a href="#__codelineno-25-27" id="__codelineno-25-27" name="__codelineno-25-27"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a href="#__codelineno-25-28" id="__codelineno-25-28" name="__codelineno-25-28"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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>
<a href="#__codelineno-25-29" id="__codelineno-25-29" name="__codelineno-25-29"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-30" id="__codelineno-25-30" name="__codelineno-25-30"></a>
<a href="#__codelineno-25-31" id="__codelineno-25-31" name="__codelineno-25-31"></a><span class="w"> </span><span class="c1">### Get the parent index of the node at index i ###</span>
<a href="#__codelineno-25-32" id="__codelineno-25-32" name="__codelineno-25-32"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a href="#__codelineno-25-33" id="__codelineno-25-33" name="__codelineno-25-33"></a><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
<a href="#__codelineno-25-34" id="__codelineno-25-34" name="__codelineno-25-34"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-35" id="__codelineno-25-35" name="__codelineno-25-35"></a>
<a href="#__codelineno-25-36" id="__codelineno-25-36" name="__codelineno-25-36"></a><span class="w"> </span><span class="c1">### Level-order traversal ###</span>
<a href="#__codelineno-25-37" id="__codelineno-25-37" name="__codelineno-25-37"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span>
<a href="#__codelineno-25-38" id="__codelineno-25-38" name="__codelineno-25-38"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a href="#__codelineno-25-39" id="__codelineno-25-39" name="__codelineno-25-39"></a>
<a href="#__codelineno-25-40" id="__codelineno-25-40" name="__codelineno-25-40"></a><span class="w"> </span><span class="c1"># Traverse the array directly</span>
<a href="#__codelineno-25-41" id="__codelineno-25-41" name="__codelineno-25-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
<a href="#__codelineno-25-42" id="__codelineno-25-42" name="__codelineno-25-42"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a href="#__codelineno-25-43" id="__codelineno-25-43" name="__codelineno-25-43"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-44" id="__codelineno-25-44" name="__codelineno-25-44"></a>
<a href="#__codelineno-25-45" id="__codelineno-25-45" name="__codelineno-25-45"></a><span class="w"> </span><span class="vi">@res</span>
<a href="#__codelineno-25-46" id="__codelineno-25-46" name="__codelineno-25-46"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-47" id="__codelineno-25-47" name="__codelineno-25-47"></a>
<a href="#__codelineno-25-48" id="__codelineno-25-48" name="__codelineno-25-48"></a><span class="w"> </span><span class="c1">### Depth-first traversal ###</span>
<a href="#__codelineno-25-49" id="__codelineno-25-49" name="__codelineno-25-49"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a href="#__codelineno-25-50" id="__codelineno-25-50" name="__codelineno-25-50"></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="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a href="#__codelineno-25-51" id="__codelineno-25-51" name="__codelineno-25-51"></a><span class="w"> </span><span class="c1"># Preorder traversal</span>
<a href="#__codelineno-25-52" id="__codelineno-25-52" name="__codelineno-25-52"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:pre</span>
<a href="#__codelineno-25-53" id="__codelineno-25-53" name="__codelineno-25-53"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a href="#__codelineno-25-54" id="__codelineno-25-54" name="__codelineno-25-54"></a><span class="w"> </span><span class="c1"># Inorder traversal</span>
<a href="#__codelineno-25-55" id="__codelineno-25-55" name="__codelineno-25-55"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:in</span>
<a href="#__codelineno-25-56" id="__codelineno-25-56" name="__codelineno-25-56"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a href="#__codelineno-25-57" id="__codelineno-25-57" name="__codelineno-25-57"></a><span class="w"> </span><span class="c1"># Postorder traversal</span>
<a href="#__codelineno-25-58" id="__codelineno-25-58" name="__codelineno-25-58"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:post</span>
<a href="#__codelineno-25-59" id="__codelineno-25-59" name="__codelineno-25-59"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-60" id="__codelineno-25-60" name="__codelineno-25-60"></a>
<a href="#__codelineno-25-61" id="__codelineno-25-61" name="__codelineno-25-61"></a><span class="w"> </span><span class="c1">### Preorder traversal ###</span>
<a href="#__codelineno-25-62" id="__codelineno-25-62" name="__codelineno-25-62"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span>
<a href="#__codelineno-25-63" id="__codelineno-25-63" name="__codelineno-25-63"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a href="#__codelineno-25-64" id="__codelineno-25-64" name="__codelineno-25-64"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:pre</span><span class="p">)</span>
<a href="#__codelineno-25-65" id="__codelineno-25-65" name="__codelineno-25-65"></a><span class="w"> </span><span class="vi">@res</span>
<a href="#__codelineno-25-66" id="__codelineno-25-66" name="__codelineno-25-66"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-67" id="__codelineno-25-67" name="__codelineno-25-67"></a>
<a href="#__codelineno-25-68" id="__codelineno-25-68" name="__codelineno-25-68"></a><span class="w"> </span><span class="c1">### Inorder traversal ###</span>
<a href="#__codelineno-25-69" id="__codelineno-25-69" name="__codelineno-25-69"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span>
<a href="#__codelineno-25-70" id="__codelineno-25-70" name="__codelineno-25-70"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a href="#__codelineno-25-71" id="__codelineno-25-71" name="__codelineno-25-71"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:in</span><span class="p">)</span>
<a href="#__codelineno-25-72" id="__codelineno-25-72" name="__codelineno-25-72"></a><span class="w"> </span><span class="vi">@res</span>
<a href="#__codelineno-25-73" id="__codelineno-25-73" name="__codelineno-25-73"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-74" id="__codelineno-25-74" name="__codelineno-25-74"></a>
<a href="#__codelineno-25-75" id="__codelineno-25-75" name="__codelineno-25-75"></a><span class="w"> </span><span class="c1">### Postorder traversal ###</span>
<a href="#__codelineno-25-76" id="__codelineno-25-76" name="__codelineno-25-76"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span>
<a href="#__codelineno-25-77" id="__codelineno-25-77" name="__codelineno-25-77"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a href="#__codelineno-25-78" id="__codelineno-25-78" name="__codelineno-25-78"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:post</span><span class="p">)</span>
<a href="#__codelineno-25-79" id="__codelineno-25-79" name="__codelineno-25-79"></a><span class="w"> </span><span class="vi">@res</span>
<a href="#__codelineno-25-80" id="__codelineno-25-80" name="__codelineno-25-80"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-81" id="__codelineno-25-81" name="__codelineno-25-81"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
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<summary>Visualize execution</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22Binary%20tree%20node%20class%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%20%3D%20None%0A%0Aclass%20ArrayBinaryTree%3A%0A%20%20%20%20%22%22%22Binary%20tree%20class%20using%20an%20array%20representation%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20arr%3A%20list%5Bint%20%7C%20None%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22Constructor%22%22%22%0A%20%20%20%20%20%20%20%20self._tree%20%3D%20list%28arr%29%0A%0A%20%20%20%20def%20size%28self%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22Length%20of%20the%20backing%20list%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self._tree%29%0A%0A%20%20%20%20def%20val%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22Get%20the%20value%20of%20the%20node%20at%20index%20i%22%22%22%0A%20%20%20%20%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20self.size%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%20%20%20%20return%20self._tree%5Bi%5D%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20%22%22%22Get%20the%20left%20child%20index%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20%22%22%22Get%20the%20right%20child%20index%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20%22%22%22Get%20the%20parent%20index%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%0A%0A%20%20%20%20def%20level_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22Level-order%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20%23%20Traverse%20the%20array%20directly%0A%20%20%20%20%20%20%20%20for%20i%20in%20range%28self.size%28%29%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20self.val%28i%29%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20dfs%28self,%20i%3A%20int,%20order%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22Depth-first%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20if%20self.val%28i%29%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%23%20Preorder%20traversal%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%22pre%22%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20self.dfs%28self.left%28i%29,%20order%29%0A%20%20%20%20%20%20%20%20%23%20Inorder%20traversal%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%22in%22%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20self.dfs%28self.right%28i%29,%20order%29%0A%20%20%20%20%20%20%20%20%23%20Postorder%20traversal%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%22post%22%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%0A%20%20%20%20def%20pre_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22Preorder%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280,%20order%3D%22pre%22%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20in_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22Inorder%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280,%20order%3D%22in%22%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20post_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22Postorder%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280,%20order%3D%22post%22%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%22%22%22Driver%20code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20Initialize%20the%20binary%20tree%0A%20%20%20%20arr%20%3D%20%5B1,%202,%203,%204,%20None,%206,%20None%5D%0A%20%20%20%20abt%20%3D%20ArrayBinaryTree%28arr%29%0A%0A%20%20%20%20%23%20Access%20a%20node%0A%20%20%20%20i%20%3D%201%0A%20%20%20%20l,%20r,%20p%20%3D%20abt.left%28i%29,%20abt.right%28i%29,%20abt.parent%28i%29%0A%0A%20%20%20%20%23%20Traverse%20the%20tree%0A%20%20%20%20res%20%3D%20abt.level_order%28%29%0A%20%20%20%20res%20%3D%20abt.pre_order%28%29%0A%20%20%20%20res%20%3D%20abt.in_order%28%29%0A%20%20%20%20res%20%3D%20abt.post_order%28%29&amp;codeDivHeight=472&amp;codeDivWidth=350&amp;cumulative=false&amp;curInstr=5&amp;heapPrimitives=nevernest&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false" title="Visualize execution"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22Binary%20tree%20node%20class%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%29%3A%0A%20%20%20%20%20%20%20%20self.val%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%20%3D%20None%0A%0Aclass%20ArrayBinaryTree%3A%0A%20%20%20%20%22%22%22Binary%20tree%20class%20using%20an%20array%20representation%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20arr%3A%20list%5Bint%20%7C%20None%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22Constructor%22%22%22%0A%20%20%20%20%20%20%20%20self._tree%20%3D%20list%28arr%29%0A%0A%20%20%20%20def%20size%28self%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22Length%20of%20the%20backing%20list%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self._tree%29%0A%0A%20%20%20%20def%20val%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22Get%20the%20value%20of%20the%20node%20at%20index%20i%22%22%22%0A%20%20%20%20%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20self.size%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%20%20%20%20return%20self._tree%5Bi%5D%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20%22%22%22Get%20the%20left%20child%20index%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20%22%22%22Get%20the%20right%20child%20index%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%20%7C%20None%3A%0A%20%20%20%20%20%20%20%20%22%22%22Get%20the%20parent%20index%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%0A%0A%20%20%20%20def%20level_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22Level-order%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20%23%20Traverse%20the%20array%20directly%0A%20%20%20%20%20%20%20%20for%20i%20in%20range%28self.size%28%29%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20self.val%28i%29%20is%20not%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20dfs%28self,%20i%3A%20int,%20order%3A%20str%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22Depth-first%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20if%20self.val%28i%29%20is%20None%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%0A%20%20%20%20%20%20%20%20%23%20Preorder%20traversal%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%22pre%22%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20self.dfs%28self.left%28i%29,%20order%29%0A%20%20%20%20%20%20%20%20%23%20Inorder%20traversal%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%22in%22%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%20%20%20%20%20%20%20%20self.dfs%28self.right%28i%29,%20order%29%0A%20%20%20%20%20%20%20%20%23%20Postorder%20traversal%0A%20%20%20%20%20%20%20%20if%20order%20%3D%3D%20%22post%22%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.res.append%28self.val%28i%29%29%0A%0A%20%20%20%20def%20pre_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22Preorder%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280,%20order%3D%22pre%22%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20in_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22Inorder%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280,%20order%3D%22in%22%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%20%20%20%20def%20post_order%28self%29%20-%3E%20list%5Bint%5D%3A%0A%20%20%20%20%20%20%20%20%22%22%22Postorder%20traversal%22%22%22%0A%20%20%20%20%20%20%20%20self.res%20%3D%20%5B%5D%0A%20%20%20%20%20%20%20%20self.dfs%280,%20order%3D%22post%22%29%0A%20%20%20%20%20%20%20%20return%20self.res%0A%0A%22%22%22Driver%20code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20Initialize%20the%20binary%20tree%0A%20%20%20%20arr%20%3D%20%5B1,%202,%203,%204,%20None,%206,%20None%5D%0A%20%20%20%20abt%20%3D%20ArrayBinaryTree%28arr%29%0A%0A%20%20%20%20%23%20Access%20a%20node%0A%20%20%20%20i%20%3D%201%0A%20%20%20%20l,%20r,%20p%20%3D%20abt.left%28i%29,%20abt.right%28i%29,%20abt.parent%28i%29%0A%0A%20%20%20%20%23%20Traverse%20the%20tree%0A%20%20%20%20res%20%3D%20abt.level_order%28%29%0A%20%20%20%20res%20%3D%20abt.pre_order%28%29%0A%20%20%20%20res%20%3D%20abt.in_order%28%29%0A%20%20%20%20res%20%3D%20abt.post_order%28%29&amp;codeDivHeight=800&amp;codeDivWidth=600&amp;cumulative=false&amp;curInstr=5&amp;heapPrimitives=nevernest&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false" rel="noopener noreferrer" target="_blank">View full screen &gt;</a></div></p>
</details>
<h2 id="733-strengths-and-limitations">7.3.3   Strengths and limitations<a class="headerlink" href="#733-strengths-and-limitations" title="Permanent link"></a></h2>
<p>Array representation offers the following advantages.</p>
<ul>
<li>Contiguous memory is cache-friendly, making access and traversal fast.</li>
<li>No pointers need to be stored, saving space.</li>
<li>Nodes can be accessed randomly by index.</li>
</ul>
<p>However, it also has limitations.</p>
<ul>
<li>Arrays require contiguous memory, making them unsuitable for extremely large trees.</li>
<li>Adding and removing nodes requires array insertion and deletion operations, which are inefficient.</li>
<li>If the tree has many missing nodes, actual node data occupies only a small fraction of the array, wasting space.</li>
</ul>
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