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18
docs/chapter_searching/binary_search.md
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@@ -10,7 +10,7 @@ comments: true
给定一个长度为 $n$ 的数组 `nums` ，元素按从小到大的顺序排列，数组不包含重复元素。请查找并返回元素 `target` 在该数组中的索引。若数组不包含该元素，则返回 $-1$ 。
![二分查找示例数据](binary_search.assets/binary_search_example.png)
![二分查找示例数据](binary_search.assets/binary_search_example.png){ class="animation-figure" }
<p align="center"> 图 10-1 &nbsp; 二分查找示例数据 </p>
@@ -27,25 +27,25 @@ comments: true
若数组不包含目标元素，搜索区间最终会缩小为空。此时返回 $-1$ 。
=== "<1>"
![二分查找流程](binary_search.assets/binary_search_step1.png)
![二分查找流程](binary_search.assets/binary_search_step1.png){ class="animation-figure" }
=== "<2>"
![binary_search_step2](binary_search.assets/binary_search_step2.png)
![binary_search_step2](binary_search.assets/binary_search_step2.png){ class="animation-figure" }
=== "<3>"
![binary_search_step3](binary_search.assets/binary_search_step3.png)
![binary_search_step3](binary_search.assets/binary_search_step3.png){ class="animation-figure" }
=== "<4>"
![binary_search_step4](binary_search.assets/binary_search_step4.png)
![binary_search_step4](binary_search.assets/binary_search_step4.png){ class="animation-figure" }
=== "<5>"
![binary_search_step5](binary_search.assets/binary_search_step5.png)
![binary_search_step5](binary_search.assets/binary_search_step5.png){ class="animation-figure" }
=== "<6>"
![binary_search_step6](binary_search.assets/binary_search_step6.png)
![binary_search_step6](binary_search.assets/binary_search_step6.png){ class="animation-figure" }
=== "<7>"
![binary_search_step7](binary_search.assets/binary_search_step7.png)
![binary_search_step7](binary_search.assets/binary_search_step7.png){ class="animation-figure" }
<p align="center"> 图 10-2 &nbsp; 二分查找流程 </p>
@@ -627,7 +627,7 @@ comments: true
由于“双闭区间”表示中的左右边界都被定义为闭区间，因此指针 $i$ 和 $j$ 缩小区间操作也是对称的。这样更不容易出错，**因此一般建议采用“双闭区间”的写法**。
![两种区间定义](binary_search.assets/binary_search_ranges.png)
![两种区间定义](binary_search.assets/binary_search_ranges.png){ class="animation-figure" }
<p align="center"> 图 10-3 &nbsp; 两种区间定义 </p>

4
docs/chapter_searching/binary_search_edge.md
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@@ -211,7 +211,7 @@ comments: true
如图 10-7 所示，查找完成后，指针 $i$ 指向最左一个 `target + 1`（如果存在），而 $j$ 指向最右一个 `target` ，**因此返回 $j$ 即可**。
![将查找右边界转化为查找左边界](binary_search_edge.assets/binary_search_right_edge_by_left_edge.png)
![将查找右边界转化为查找左边界](binary_search_edge.assets/binary_search_right_edge_by_left_edge.png){ class="animation-figure" }
<p align="center"> 图 10-7 &nbsp; 将查找右边界转化为查找左边界 </p>
@@ -428,7 +428,7 @@ comments: true
- 查找最左一个 `target` ：可以转化为查找 `target - 0.5` ，并返回指针 $i$ 。
- 查找最右一个 `target` ：可以转化为查找 `target + 0.5` ，并返回指针 $j$ 。
![将查找边界转化为查找元素](binary_search_edge.assets/binary_search_edge_by_element.png)
![将查找边界转化为查找元素](binary_search_edge.assets/binary_search_edge_by_element.png){ class="animation-figure" }
<p align="center"> 图 10-8 &nbsp; 将查找边界转化为查找元素 </p>

20
docs/chapter_searching/binary_search_insertion.md
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@@ -12,7 +12,7 @@ comments: true
给定一个长度为 $n$ 的有序数组 `nums` 和一个元素 `target` ，数组不存在重复元素。现将 `target` 插入到数组 `nums` 中，并保持其有序性。若数组中已存在元素 `target` ，则插入到其左方。请返回插入后 `target` 在数组中的索引。
![二分查找插入点示例数据](binary_search_insertion.assets/binary_search_insertion_example.png)
![二分查找插入点示例数据](binary_search_insertion.assets/binary_search_insertion_example.png){ class="animation-figure" }
<p align="center"> 图 10-4 &nbsp; 二分查找插入点示例数据 </p>
@@ -285,7 +285,7 @@ comments: true
1. 执行二分查找，得到任意一个 `target` 的索引，记为 $k$ 。
2. 从索引 $k$ 开始，向左进行线性遍历，当找到最左边的 `target` 时返回。
![线性查找重复元素的插入点](binary_search_insertion.assets/binary_search_insertion_naive.png)
![线性查找重复元素的插入点](binary_search_insertion.assets/binary_search_insertion_naive.png){ class="animation-figure" }
<p align="center"> 图 10-5 &nbsp; 线性查找重复元素的插入点 </p>
@@ -299,28 +299,28 @@ comments: true
循环完成后，$i$ 指向最左边的 `target` ，$j$ 指向首个小于 `target` 的元素，**因此索引 $i$ 就是插入点**。
=== "<1>"
![二分查找重复元素的插入点的步骤](binary_search_insertion.assets/binary_search_insertion_step1.png)
![二分查找重复元素的插入点的步骤](binary_search_insertion.assets/binary_search_insertion_step1.png){ class="animation-figure" }
=== "<2>"
![binary_search_insertion_step2](binary_search_insertion.assets/binary_search_insertion_step2.png)
![binary_search_insertion_step2](binary_search_insertion.assets/binary_search_insertion_step2.png){ class="animation-figure" }
=== "<3>"
![binary_search_insertion_step3](binary_search_insertion.assets/binary_search_insertion_step3.png)
![binary_search_insertion_step3](binary_search_insertion.assets/binary_search_insertion_step3.png){ class="animation-figure" }
=== "<4>"
![binary_search_insertion_step4](binary_search_insertion.assets/binary_search_insertion_step4.png)
![binary_search_insertion_step4](binary_search_insertion.assets/binary_search_insertion_step4.png){ class="animation-figure" }
=== "<5>"
![binary_search_insertion_step5](binary_search_insertion.assets/binary_search_insertion_step5.png)
![binary_search_insertion_step5](binary_search_insertion.assets/binary_search_insertion_step5.png){ class="animation-figure" }
=== "<6>"
![binary_search_insertion_step6](binary_search_insertion.assets/binary_search_insertion_step6.png)
![binary_search_insertion_step6](binary_search_insertion.assets/binary_search_insertion_step6.png){ class="animation-figure" }
=== "<7>"
![binary_search_insertion_step7](binary_search_insertion.assets/binary_search_insertion_step7.png)
![binary_search_insertion_step7](binary_search_insertion.assets/binary_search_insertion_step7.png){ class="animation-figure" }
=== "<8>"
![binary_search_insertion_step8](binary_search_insertion.assets/binary_search_insertion_step8.png)
![binary_search_insertion_step8](binary_search_insertion.assets/binary_search_insertion_step8.png){ class="animation-figure" }
<p align="center"> 图 10-6 &nbsp; 二分查找重复元素的插入点的步骤 </p>

2
docs/chapter_searching/index.md
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@@ -7,7 +7,7 @@ icon: material/text-search
<div class="center-table" markdown>
![搜索](../assets/covers/chapter_searching.jpg){ width="600" }
![搜索](../assets/covers/chapter_searching.jpg){ class="cover-image" }
</div>

8
docs/chapter_searching/replace_linear_by_hashing.md
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@@ -14,7 +14,7 @@ comments: true
考虑直接遍历所有可能的组合。如图 10-9 所示，我们开启一个两层循环，在每轮中判断两个整数的和是否为 `target` ，若是则返回它们的索引。
![线性查找求解两数之和](replace_linear_by_hashing.assets/two_sum_brute_force.png)
![线性查找求解两数之和](replace_linear_by_hashing.assets/two_sum_brute_force.png){ class="animation-figure" }
<p align="center"> 图 10-9 &nbsp; 线性查找求解两数之和 </p>
@@ -237,13 +237,13 @@ comments: true
2. 将键值对 `nums[i]` 和索引 `i` 添加进哈希表。
=== "<1>"
![辅助哈希表求解两数之和](replace_linear_by_hashing.assets/two_sum_hashtable_step1.png)
![辅助哈希表求解两数之和](replace_linear_by_hashing.assets/two_sum_hashtable_step1.png){ class="animation-figure" }
=== "<2>"
![two_sum_hashtable_step2](replace_linear_by_hashing.assets/two_sum_hashtable_step2.png)
![two_sum_hashtable_step2](replace_linear_by_hashing.assets/two_sum_hashtable_step2.png){ class="animation-figure" }
=== "<3>"
![two_sum_hashtable_step3](replace_linear_by_hashing.assets/two_sum_hashtable_step3.png)
![two_sum_hashtable_step3](replace_linear_by_hashing.assets/two_sum_hashtable_step3.png){ class="animation-figure" }
<p align="center"> 图 10-10 &nbsp; 辅助哈希表求解两数之和 </p>

2
docs/chapter_searching/searching_algorithm_revisited.md
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@@ -44,7 +44,7 @@ comments: true
给定大小为 $n$ 的一组数据，我们可以使用线性搜索、二分查找、树查找、哈希查找等多种方法在该数据中搜索目标元素。各个方法的工作原理如图 10-11 所示。
![多种搜索策略](searching_algorithm_revisited.assets/searching_algorithms.png)
![多种搜索策略](searching_algorithm_revisited.assets/searching_algorithms.png){ class="animation-figure" }
<p align="center"> 图 10-11 &nbsp; 多种搜索策略 </p>