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2
docs/chapter_heap/build_heap.md
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@@ -213,7 +213,7 @@ comments: true
接下来我们来进行更为准确的计算。为了减小计算难度，假设给定一个节点数量为 $n$ ，高度为 $h$ 的“完美二叉树”，该假设不会影响计算结果的正确性。
![完美二叉树的各层节点数量](build_heap.assets/heapify_operations_count.png)
![完美二叉树的各层节点数量](build_heap.assets/heapify_operations_count.png){ class="animation-figure" }
<p align="center"> 图 8-5 &nbsp; 完美二叉树的各层节点数量 </p>

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docs/chapter_heap/heap.md
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@@ -9,7 +9,7 @@ comments: true
- 「大顶堆 max heap」：任意节点的值 $\geq$ 其子节点的值。
- 「小顶堆 min heap」：任意节点的值 $\leq$ 其子节点的值。
![小顶堆与大顶堆](heap.assets/min_heap_and_max_heap.png)
![小顶堆与大顶堆](heap.assets/min_heap_and_max_heap.png){ class="animation-figure" }
<p align="center"> 图 8-1 &nbsp; 小顶堆与大顶堆 </p>
@@ -367,7 +367,7 @@ comments: true
如图 8-2 所示，给定索引 $i$ ，其左子节点索引为 $2i + 1$ ，右子节点索引为 $2i + 2$ ，父节点索引为 $(i - 1) / 2$（向下取整）。当索引越界时，表示空节点或节点不存在。
![堆的表示与存储](heap.assets/representation_of_heap.png)
![堆的表示与存储](heap.assets/representation_of_heap.png){ class="animation-figure" }
<p align="center"> 图 8-2 &nbsp; 堆的表示与存储 </p>
@@ -718,31 +718,31 @@ comments: true
考虑从入堆节点开始，**从底至顶执行堆化**。如图 8-3 所示，我们比较插入节点与其父节点的值，如果插入节点更大，则将它们交换。然后继续执行此操作，从底至顶修复堆中的各个节点，直至越过根节点或遇到无须交换的节点时结束。
=== "<1>"
![元素入堆步骤](heap.assets/heap_push_step1.png)
![元素入堆步骤](heap.assets/heap_push_step1.png){ class="animation-figure" }
=== "<2>"
![heap_push_step2](heap.assets/heap_push_step2.png)
![heap_push_step2](heap.assets/heap_push_step2.png){ class="animation-figure" }
=== "<3>"
![heap_push_step3](heap.assets/heap_push_step3.png)
![heap_push_step3](heap.assets/heap_push_step3.png){ class="animation-figure" }
=== "<4>"
![heap_push_step4](heap.assets/heap_push_step4.png)
![heap_push_step4](heap.assets/heap_push_step4.png){ class="animation-figure" }
=== "<5>"
![heap_push_step5](heap.assets/heap_push_step5.png)
![heap_push_step5](heap.assets/heap_push_step5.png){ class="animation-figure" }
=== "<6>"
![heap_push_step6](heap.assets/heap_push_step6.png)
![heap_push_step6](heap.assets/heap_push_step6.png){ class="animation-figure" }
=== "<7>"
![heap_push_step7](heap.assets/heap_push_step7.png)
![heap_push_step7](heap.assets/heap_push_step7.png){ class="animation-figure" }
=== "<8>"
![heap_push_step8](heap.assets/heap_push_step8.png)
![heap_push_step8](heap.assets/heap_push_step8.png){ class="animation-figure" }
=== "<9>"
![heap_push_step9](heap.assets/heap_push_step9.png)
![heap_push_step9](heap.assets/heap_push_step9.png){ class="animation-figure" }
<p align="center"> 图 8-3 &nbsp; 元素入堆步骤 </p>
@@ -1095,34 +1095,34 @@ comments: true
如图 8-4 所示，**“从顶至底堆化”的操作方向与“从底至顶堆化”相反**，我们将根节点的值与其两个子节点的值进行比较，将最大的子节点与根节点交换。然后循环执行此操作，直到越过叶节点或遇到无须交换的节点时结束。
=== "<1>"
![堆顶元素出堆步骤](heap.assets/heap_pop_step1.png)
![堆顶元素出堆步骤](heap.assets/heap_pop_step1.png){ class="animation-figure" }
=== "<2>"
![heap_pop_step2](heap.assets/heap_pop_step2.png)
![heap_pop_step2](heap.assets/heap_pop_step2.png){ class="animation-figure" }
=== "<3>"
![heap_pop_step3](heap.assets/heap_pop_step3.png)
![heap_pop_step3](heap.assets/heap_pop_step3.png){ class="animation-figure" }
=== "<4>"
![heap_pop_step4](heap.assets/heap_pop_step4.png)
![heap_pop_step4](heap.assets/heap_pop_step4.png){ class="animation-figure" }
=== "<5>"
![heap_pop_step5](heap.assets/heap_pop_step5.png)
![heap_pop_step5](heap.assets/heap_pop_step5.png){ class="animation-figure" }
=== "<6>"
![heap_pop_step6](heap.assets/heap_pop_step6.png)
![heap_pop_step6](heap.assets/heap_pop_step6.png){ class="animation-figure" }
=== "<7>"
![heap_pop_step7](heap.assets/heap_pop_step7.png)
![heap_pop_step7](heap.assets/heap_pop_step7.png){ class="animation-figure" }
=== "<8>"
![heap_pop_step8](heap.assets/heap_pop_step8.png)
![heap_pop_step8](heap.assets/heap_pop_step8.png){ class="animation-figure" }
=== "<9>"
![heap_pop_step9](heap.assets/heap_pop_step9.png)
![heap_pop_step9](heap.assets/heap_pop_step9.png){ class="animation-figure" }
=== "<10>"
![heap_pop_step10](heap.assets/heap_pop_step10.png)
![heap_pop_step10](heap.assets/heap_pop_step10.png){ class="animation-figure" }
<p align="center"> 图 8-4 &nbsp; 堆顶元素出堆步骤 </p>

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

22
docs/chapter_heap/top_k.md
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@@ -16,7 +16,7 @@ comments: true
此方法只适用于 $k \ll n$ 的情况，因为当 $k$ 与 $n$ 比较接近时，其时间复杂度趋向于 $O(n^2)$ ，非常耗时。
![遍历寻找最大的 k 个元素](top_k.assets/top_k_traversal.png)
![遍历寻找最大的 k 个元素](top_k.assets/top_k_traversal.png){ class="animation-figure" }
<p align="center"> 图 8-6 &nbsp; 遍历寻找最大的 k 个元素 </p>
@@ -30,7 +30,7 @@ comments: true
显然，该方法“超额”完成任务了，因为我们只需要找出最大的 $k$ 个元素即可，而不需要排序其他元素。
![排序寻找最大的 k 个元素](top_k.assets/top_k_sorting.png)
![排序寻找最大的 k 个元素](top_k.assets/top_k_sorting.png){ class="animation-figure" }
<p align="center"> 图 8-7 &nbsp; 排序寻找最大的 k 个元素 </p>
@@ -44,31 +44,31 @@ comments: true
4. 遍历完成后，堆中保存的就是最大的 $k$ 个元素。
=== "<1>"
![基于堆寻找最大的 k 个元素](top_k.assets/top_k_heap_step1.png)
![基于堆寻找最大的 k 个元素](top_k.assets/top_k_heap_step1.png){ class="animation-figure" }
=== "<2>"
![top_k_heap_step2](top_k.assets/top_k_heap_step2.png)
![top_k_heap_step2](top_k.assets/top_k_heap_step2.png){ class="animation-figure" }
=== "<3>"
![top_k_heap_step3](top_k.assets/top_k_heap_step3.png)
![top_k_heap_step3](top_k.assets/top_k_heap_step3.png){ class="animation-figure" }
=== "<4>"
![top_k_heap_step4](top_k.assets/top_k_heap_step4.png)
![top_k_heap_step4](top_k.assets/top_k_heap_step4.png){ class="animation-figure" }
=== "<5>"
![top_k_heap_step5](top_k.assets/top_k_heap_step5.png)
![top_k_heap_step5](top_k.assets/top_k_heap_step5.png){ class="animation-figure" }
=== "<6>"
![top_k_heap_step6](top_k.assets/top_k_heap_step6.png)
![top_k_heap_step6](top_k.assets/top_k_heap_step6.png){ class="animation-figure" }
=== "<7>"
![top_k_heap_step7](top_k.assets/top_k_heap_step7.png)
![top_k_heap_step7](top_k.assets/top_k_heap_step7.png){ class="animation-figure" }
=== "<8>"
![top_k_heap_step8](top_k.assets/top_k_heap_step8.png)
![top_k_heap_step8](top_k.assets/top_k_heap_step8.png){ class="animation-figure" }
=== "<9>"
![top_k_heap_step9](top_k.assets/top_k_heap_step9.png)
![top_k_heap_step9](top_k.assets/top_k_heap_step9.png){ class="animation-figure" }
<p align="center"> 图 8-8 &nbsp; 基于堆寻找最大的 k 个元素 </p>