From 04000a5e2c702cb879fa0bc6975b56b308cef632 Mon Sep 17 00:00:00 2001 From: krahets Date: Wed, 22 Feb 2023 00:57:04 +0800 Subject: [PATCH] build --- chapter_data_structure/data_and_memory.md | 2 +- chapter_graph/graph_traversal.md | 44 +++++++++---------- chapter_heap/heap.md | 32 +++++++------- .../algorithms_are_everywhere.md | 10 ++--- chapter_searching/binary_search.md | 14 +++--- chapter_sorting/bubble_sort.md | 14 +++--- chapter_sorting/merge_sort.md | 20 ++++----- chapter_sorting/quick_sort.md | 18 ++++---- chapter_tree/avl_tree.md | 8 ++-- chapter_tree/binary_search_tree.md | 16 +++---- 10 files changed, 89 insertions(+), 89 deletions(-) diff --git a/chapter_data_structure/data_and_memory.md b/chapter_data_structure/data_and_memory.md index e2e1084d0..3e189993b 100644 --- a/chapter_data_structure/data_and_memory.md +++ b/chapter_data_structure/data_and_memory.md @@ -32,7 +32,7 @@ comments: true | 浮点数 | **float** | 4 bytes | $-3.4 \times 10^{38}$ ~ $3.4 \times 10^{38}$ | $0.0$ f | | | double | 8 bytes | $-1.7 \times 10^{308}$ ~ $1.7 \times 10^{308}$ | $0.0$ | | 字符 | **char** | 2 bytes / 1 byte | $0$ ~ $2^{16} - 1$ | $0$ | -| 布尔 | **boolean(bool)** | 1 byte / 1 bit | $\text{true}$ 或 $\text{false}$ | $\text{false}$ | +| 布尔 | **bool** | 1 byte / 1 bit | $\text{true}$ 或 $\text{false}$ | $\text{false}$ | diff --git a/chapter_graph/graph_traversal.md b/chapter_graph/graph_traversal.md index 011d8f372..6790ca926 100644 --- a/chapter_graph/graph_traversal.md +++ b/chapter_graph/graph_traversal.md @@ -113,37 +113,37 @@ BFS 常借助「队列」来实现。队列具有“先入先出”的性质， 代码相对抽象，建议对照以下动画图示来加深理解。 -=== "Step 1" +=== "<1>" ![graph_bfs_step1](graph_traversal.assets/graph_bfs_step1.png) -=== "Step 2" +=== "<2>" ![graph_bfs_step2](graph_traversal.assets/graph_bfs_step2.png) -=== "Step 3" +=== "<3>" ![graph_bfs_step3](graph_traversal.assets/graph_bfs_step3.png) -=== "Step 4" +=== "<4>" ![graph_bfs_step4](graph_traversal.assets/graph_bfs_step4.png) -=== "Step 5" +=== "<5>" ![graph_bfs_step5](graph_traversal.assets/graph_bfs_step5.png) -=== "Step 6" +=== "<6>" ![graph_bfs_step6](graph_traversal.assets/graph_bfs_step6.png) -=== "Step 7" +=== "<7>" ![graph_bfs_step7](graph_traversal.assets/graph_bfs_step7.png) -=== "Step 8" +=== "<8>" ![graph_bfs_step8](graph_traversal.assets/graph_bfs_step8.png) -=== "Step 9" +=== "<9>" ![graph_bfs_step9](graph_traversal.assets/graph_bfs_step9.png) -=== "Step 10" +=== "<10>" ![graph_bfs_step10](graph_traversal.assets/graph_bfs_step10.png) -=== "Step 11" +=== "<11>" ![graph_bfs_step11](graph_traversal.assets/graph_bfs_step11.png) !!! question "广度优先遍历的序列是否唯一？" @@ -255,37 +255,37 @@ BFS 常借助「队列」来实现。队列具有“先入先出”的性质， 为了加深理解，请你将图示与代码结合起来，在脑中（或者用笔画下来）模拟整个 DFS 过程，包括每个递归方法何时开启、何时返回。 -=== "Step 1" +=== "<1>" ![graph_dfs_step1](graph_traversal.assets/graph_dfs_step1.png) -=== "Step 2" +=== "<2>" ![graph_dfs_step2](graph_traversal.assets/graph_dfs_step2.png) -=== "Step 3" +=== "<3>" ![graph_dfs_step3](graph_traversal.assets/graph_dfs_step3.png) -=== "Step 4" +=== "<4>" ![graph_dfs_step4](graph_traversal.assets/graph_dfs_step4.png) -=== "Step 5" +=== "<5>" ![graph_dfs_step5](graph_traversal.assets/graph_dfs_step5.png) -=== "Step 6" +=== "<6>" ![graph_dfs_step6](graph_traversal.assets/graph_dfs_step6.png) -=== "Step 7" +=== "<7>" ![graph_dfs_step7](graph_traversal.assets/graph_dfs_step7.png) -=== "Step 8" +=== "<8>" ![graph_dfs_step8](graph_traversal.assets/graph_dfs_step8.png) -=== "Step 9" +=== "<9>" ![graph_dfs_step9](graph_traversal.assets/graph_dfs_step9.png) -=== "Step 10" +=== "<10>" ![graph_dfs_step10](graph_traversal.assets/graph_dfs_step10.png) -=== "Step 11" +=== "<11>" ![graph_dfs_step11](graph_traversal.assets/graph_dfs_step11.png) !!! question "深度优先遍历的序列是否唯一？" diff --git a/chapter_heap/heap.md b/chapter_heap/heap.md index b24758aa5..46d4973d3 100644 --- a/chapter_heap/heap.md +++ b/chapter_heap/heap.md @@ -556,22 +556,22 @@ comments: true 考虑从入堆结点开始，**从底至顶执行堆化**。具体地，比较插入结点与其父结点的值，若插入结点更大则将它们交换；并循环以上操作，从底至顶地修复堆中的各个结点；直至越过根结点时结束，或当遇到无需交换的结点时提前结束。 -=== "Step 1" +=== "<1>" ![heap_push_step1](heap.assets/heap_push_step1.png) -=== "Step 2" +=== "<2>" ![heap_push_step2](heap.assets/heap_push_step2.png) -=== "Step 3" +=== "<3>" ![heap_push_step3](heap.assets/heap_push_step3.png) -=== "Step 4" +=== "<4>" ![heap_push_step4](heap.assets/heap_push_step4.png) -=== "Step 5" +=== "<5>" ![heap_push_step5](heap.assets/heap_push_step5.png) -=== "Step 6" +=== "<6>" ![heap_push_step6](heap.assets/heap_push_step6.png) 设结点总数为 $n$ ，则树的高度为 $O(\log n)$ ，易得堆化操作的循环轮数最多为 $O(\log n)$ ，**因而元素入堆操作的时间复杂度为 $O(\log n)$** 。 @@ -820,34 +820,34 @@ comments: true 顾名思义，**从顶至底堆化的操作方向与从底至顶堆化相反**，我们比较根结点的值与其两个子结点的值，将最大的子结点与根结点执行交换，并循环以上操作，直到越过叶结点时结束，或当遇到无需交换的结点时提前结束。 -=== "Step 1" +=== "<1>" ![heap_poll_step1](heap.assets/heap_poll_step1.png) -=== "Step 2" +=== "<2>" ![heap_poll_step2](heap.assets/heap_poll_step2.png) -=== "Step 3" +=== "<3>" ![heap_poll_step3](heap.assets/heap_poll_step3.png) -=== "Step 4" +=== "<4>" ![heap_poll_step4](heap.assets/heap_poll_step4.png) -=== "Step 5" +=== "<5>" ![heap_poll_step5](heap.assets/heap_poll_step5.png) -=== "Step 6" +=== "<6>" ![heap_poll_step6](heap.assets/heap_poll_step6.png) -=== "Step 7" +=== "<7>" ![heap_poll_step7](heap.assets/heap_poll_step7.png) -=== "Step 8" +=== "<8>" ![heap_poll_step8](heap.assets/heap_poll_step8.png) -=== "Step 9" +=== "<9>" ![heap_poll_step9](heap.assets/heap_poll_step9.png) -=== "Step 10" +=== "<10>" ![heap_poll_step10](heap.assets/heap_poll_step10.png) 与元素入堆操作类似，**堆顶元素出堆操作的时间复杂度为 $O(\log n)$** 。 diff --git a/chapter_introduction/algorithms_are_everywhere.md b/chapter_introduction/algorithms_are_everywhere.md index 980fba81e..a4d5de68b 100644 --- a/chapter_introduction/algorithms_are_everywhere.md +++ b/chapter_introduction/algorithms_are_everywhere.md @@ -18,15 +18,15 @@ comments: true 2. 由于在英文字母表中 $r$ 在 $m$ 的后面，因此应排除字典前半部分，查找范围仅剩后半部分； 3. 循环执行步骤 1-2 ，直到找到拼音首字母为 $r$ 的页码时终止。 -=== "Step 1" +=== "<1>" ![look_up_dictionary_step_1](algorithms_are_everywhere.assets/look_up_dictionary_step_1.png) -=== "Step 2" +=== "<2>" ![look_up_dictionary_step_2](algorithms_are_everywhere.assets/look_up_dictionary_step_2.png) -=== "Step 3" +=== "<3>" ![look_up_dictionary_step_3](algorithms_are_everywhere.assets/look_up_dictionary_step_3.png) -=== "Step 4" +=== "<4>" ![look_up_dictionary_step_4](algorithms_are_everywhere.assets/look_up_dictionary_step_4.png) -=== "Step 5" +=== "<5>" ![look_up_dictionary_step_5](algorithms_are_everywhere.assets/look_up_dictionary_step_5.png) 查字典这个小学生的标配技能，实际上就是大名鼎鼎的「二分查找」。从数据结构角度，我们可以将字典看作是一个已排序的「数组」；而从算法角度，我们可将上述查字典的一系列指令看作是「二分查找」算法。 diff --git a/chapter_searching/binary_search.md b/chapter_searching/binary_search.md index 337506cb2..1db91deda 100755 --- a/chapter_searching/binary_search.md +++ b/chapter_searching/binary_search.md @@ -28,25 +28,25 @@ $$ 首先，我们先采用“双闭区间”的表示，在数组 `nums` 中查找目标元素 `target` 的对应索引。 -=== "Step 1" +=== "<1>" ![binary_search_step1](binary_search.assets/binary_search_step1.png) -=== "Step 2" +=== "<2>" ![binary_search_step2](binary_search.assets/binary_search_step2.png) -=== "Step 3" +=== "<3>" ![binary_search_step3](binary_search.assets/binary_search_step3.png) -=== "Step 4" +=== "<4>" ![binary_search_step4](binary_search.assets/binary_search_step4.png) -=== "Step 5" +=== "<5>" ![binary_search_step5](binary_search.assets/binary_search_step5.png) -=== "Step 6" +=== "<6>" ![binary_search_step6](binary_search.assets/binary_search_step6.png) -=== "Step 7" +=== "<7>" ![binary_search_step7](binary_search.assets/binary_search_step7.png) 二分查找“双闭区间”表示下的代码如下所示。 diff --git a/chapter_sorting/bubble_sort.md b/chapter_sorting/bubble_sort.md index 3da3abd44..64413b8aa 100755 --- a/chapter_sorting/bubble_sort.md +++ b/chapter_sorting/bubble_sort.md @@ -14,25 +14,25 @@ comments: true 完成此次冒泡操作后，**数组最大元素已在正确位置，接下来只需排序剩余 $n - 1$ 个元素**。 -=== "Step 1" +=== "<1>" ![bubble_operation_step1](bubble_sort.assets/bubble_operation_step1.png) -=== "Step 2" +=== "<2>" ![bubble_operation_step2](bubble_sort.assets/bubble_operation_step2.png) -=== "Step 3" +=== "<3>" ![bubble_operation_step3](bubble_sort.assets/bubble_operation_step3.png) -=== "Step 4" +=== "<4>" ![bubble_operation_step4](bubble_sort.assets/bubble_operation_step4.png) -=== "Step 5" +=== "<5>" ![bubble_operation_step5](bubble_sort.assets/bubble_operation_step5.png) -=== "Step 6" +=== "<6>" ![bubble_operation_step6](bubble_sort.assets/bubble_operation_step6.png) -=== "Step 7" +=== "<7>" ![bubble_operation_step7](bubble_sort.assets/bubble_operation_step7.png)

Fig. 冒泡操作

diff --git a/chapter_sorting/merge_sort.md b/chapter_sorting/merge_sort.md index 70d635eff..5e530f2e2 100755 --- a/chapter_sorting/merge_sort.md +++ b/chapter_sorting/merge_sort.md @@ -24,34 +24,34 @@ comments: true 需要注意，由于从长度为 1 的子数组开始合并，所以 **每个子数组都是有序的**。因此，合并任务本质是要 **将两个有序子数组合并为一个有序数组**。 -=== "Step1" +=== "<1>" ![merge_sort_step1](merge_sort.assets/merge_sort_step1.png) -=== "Step2" +=== "<2>" ![merge_sort_step2](merge_sort.assets/merge_sort_step2.png) -=== "Step3" +=== "<3>" ![merge_sort_step3](merge_sort.assets/merge_sort_step3.png) -=== "Step4" +=== "<4>" ![merge_sort_step4](merge_sort.assets/merge_sort_step4.png) -=== "Step5" +=== "<5>" ![merge_sort_step5](merge_sort.assets/merge_sort_step5.png) -=== "Step6" +=== "<6>" ![merge_sort_step6](merge_sort.assets/merge_sort_step6.png) -=== "Step7" +=== "<7>" ![merge_sort_step7](merge_sort.assets/merge_sort_step7.png) -=== "Step8" +=== "<8>" ![merge_sort_step8](merge_sort.assets/merge_sort_step8.png) -=== "Step9" +=== "<9>" ![merge_sort_step9](merge_sort.assets/merge_sort_step9.png) -=== "Step10" +=== "<10>" ![merge_sort_step10](merge_sort.assets/merge_sort_step10.png) 观察发现，归并排序的递归顺序就是二叉树的「后序遍历」。 diff --git a/chapter_sorting/quick_sort.md b/chapter_sorting/quick_sort.md index b8cd33e69..200bc93e2 100755 --- a/chapter_sorting/quick_sort.md +++ b/chapter_sorting/quick_sort.md @@ -14,31 +14,31 @@ comments: true 「哨兵划分」执行完毕后，原数组被划分成两个部分，即 **左子数组** 和 **右子数组**，且满足 **左子数组任意元素 < 基准数 < 右子数组任意元素**。因此，接下来我们只需要排序两个子数组即可。 -=== "Step 1" +=== "<1>" ![pivot_division_step1](quick_sort.assets/pivot_division_step1.png) -=== "Step 2" +=== "<2>" ![pivot_division_step2](quick_sort.assets/pivot_division_step2.png) -=== "Step 3" +=== "<3>" ![pivot_division_step3](quick_sort.assets/pivot_division_step3.png) -=== "Step 4" +=== "<4>" ![pivot_division_step4](quick_sort.assets/pivot_division_step4.png) -=== "Step 5" +=== "<5>" ![pivot_division_step5](quick_sort.assets/pivot_division_step5.png) -=== "Step 6" +=== "<6>" ![pivot_division_step6](quick_sort.assets/pivot_division_step6.png) -=== "Step 7" +=== "<7>" ![pivot_division_step7](quick_sort.assets/pivot_division_step7.png) -=== "Step 8" +=== "<8>" ![pivot_division_step8](quick_sort.assets/pivot_division_step8.png) -=== "Step 9" +=== "<9>" ![pivot_division_step9](quick_sort.assets/pivot_division_step9.png)

Fig. 哨兵划分

diff --git a/chapter_tree/avl_tree.md b/chapter_tree/avl_tree.md index e1b7b9108..7514584a3 100644 --- a/chapter_tree/avl_tree.md +++ b/chapter_tree/avl_tree.md @@ -454,16 +454,16 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影 如下图所示（结点下方为「平衡因子」），从底至顶看，二叉树中首个失衡结点是 **结点 3**。我们聚焦在以该失衡结点为根结点的子树上，将该结点记为 `node` ，将其左子结点记为 `child` ，执行「右旋」操作。完成右旋后，该子树已经恢复平衡，并且仍然为二叉搜索树。 -=== "Step 1" +=== "<1>" ![right_rotate_step1](avl_tree.assets/right_rotate_step1.png) -=== "Step 2" +=== "<2>" ![right_rotate_step2](avl_tree.assets/right_rotate_step2.png) -=== "Step 3" +=== "<3>" ![right_rotate_step3](avl_tree.assets/right_rotate_step3.png) -=== "Step 4" +=== "<4>" ![right_rotate_step4](avl_tree.assets/right_rotate_step4.png) 进而，如果结点 `child` 本身有右子结点（记为 `grandChild` ），则需要在「右旋」中添加一步：将 `grandChild` 作为 `node` 的左子结点。 diff --git a/chapter_tree/binary_search_tree.md b/chapter_tree/binary_search_tree.md index 8c0144a62..1c89035d8 100755 --- a/chapter_tree/binary_search_tree.md +++ b/chapter_tree/binary_search_tree.md @@ -21,16 +21,16 @@ comments: true - 若 `cur.val > num` ，说明目标结点在 `cur` 的左子树中，因此执行 `cur = cur.left` ； - 若 `cur.val = num` ，说明找到目标结点，跳出循环并返回该结点即可； -=== "Step 1" +=== "<1>" ![bst_search_1](binary_search_tree.assets/bst_search_1.png) -=== "Step 2" +=== "<2>" ![bst_search_2](binary_search_tree.assets/bst_search_2.png) -=== "Step 3" +=== "<3>" ![bst_search_3](binary_search_tree.assets/bst_search_3.png) -=== "Step 4" +=== "<4>" ![bst_search_4](binary_search_tree.assets/bst_search_4.png) 二叉搜索树的查找操作和二分查找算法如出一辙，也是在每轮排除一半情况。循环次数最多为二叉树的高度，当二叉树平衡时，使用 $O(\log n)$ 时间。 @@ -561,16 +561,16 @@ comments: true 2. 在树中递归删除结点 `nex` ； 3. 使用 `nex` 替换待删除结点； -=== "Step 1" +=== "<1>" ![bst_remove_case3_1](binary_search_tree.assets/bst_remove_case3_1.png) -=== "Step 2" +=== "<2>" ![bst_remove_case3_2](binary_search_tree.assets/bst_remove_case3_2.png) -=== "Step 3" +=== "<3>" ![bst_remove_case3_3](binary_search_tree.assets/bst_remove_case3_3.png) -=== "Step 4" +=== "<4>" ![bst_remove_case3_4](binary_search_tree.assets/bst_remove_case3_4.png) 删除结点操作也使用 $O(\log n)$ 时间，其中查找待删除结点 $O(\log n)$ ，获取中序遍历后继结点 $O(\log n)$ 。