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krahets
@ -53,7 +53,7 @@ comments: true
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至此，我们就得到了图 14-11 所示的二维 $dp$ 矩阵，其尺寸与输入网格 $grid$ 相同。
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 14-11 状态定义与 dp 表 </p>
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@ -73,7 +73,7 @@ $$
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dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
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$$
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 14-12 最优子结构与状态转移方程 </p>
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@ -89,7 +89,7 @@ $$
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如图 14-13 所示，由于每个格子是由其左方格子和上方格子转移而来，因此我们使用循环来遍历矩阵，外循环遍历各行，内循环遍历各列。
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 14-13 边界条件与状态转移顺序 </p>
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@ -16,19 +16,19 @@ comments: true
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- **初始化**：传入 $n$ 个顶点，初始化长度为 $n$ 的顶点列表 `vertices` ，使用 $O(n)$ 时间；初始化 $n \times n$ 大小的邻接矩阵 `adjMat` ，使用 $O(n^2)$ 时间。
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=== "初始化邻接矩阵"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "添加边"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "删除边"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "添加顶点"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "删除顶点"
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 9-7 邻接矩阵的初始化、增删边、增删顶点 </p>
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@ -1061,19 +1061,19 @@ comments: true
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- **初始化**：在邻接表中创建 $n$ 个顶点和 $2m$ 条边，使用 $O(n + m)$ 时间。
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=== "初始化邻接表"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "添加边"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "删除边"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "添加顶点"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "删除顶点"
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 9-8 邻接表的初始化、增删边、增删顶点 </p>
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@ -358,19 +358,19 @@ comments: true
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如图 5-8 所示，我们将双向链表的头节点和尾节点视为双向队列的队首和队尾，同时实现在两端添加和删除节点的功能。
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=== "LinkedListDeque"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "push_last()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "push_first()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "pop_last()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "pop_first()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 5-8 基于链表实现双向队列的入队出队操作 </p>
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@ -1996,19 +1996,19 @@ comments: true
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如图 5-9 所示，与基于数组实现队列类似，我们也可以使用环形数组来实现双向队列。
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=== "ArrayDeque"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "push_last()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "push_first()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "pop_last()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "pop_first()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 5-9 基于数组实现双向队列的入队出队操作 </p>
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@ -332,13 +332,13 @@ comments: true
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如图 5-5 所示，我们可以将链表的“头节点”和“尾节点”分别视为“队首”和“队尾”，规定队尾仅可添加节点，队首仅可删除节点。
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=== "LinkedListQueue"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "push()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "pop()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 5-5 基于链表实现队列的入队出队操作 </p>
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@ -1231,13 +1231,13 @@ comments: true
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可以看到，入队和出队操作都只需进行一次操作，时间复杂度均为 $O(1)$ 。
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=== "ArrayQueue"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "push()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "pop()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 5-6 基于数组实现队列的入队出队操作 </p>
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@ -330,13 +330,13 @@ comments: true
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如图 5-2 所示，对于入栈操作，我们只需将元素插入链表头部，这种节点插入方法被称为“头插法”。而对于出栈操作，只需将头节点从链表中删除即可。
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=== "LinkedListStack"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "push()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "pop()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 5-2 基于链表实现栈的入栈出栈操作 </p>
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@ -1094,13 +1094,13 @@ comments: true
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使用数组实现栈时，我们可以将数组的尾部作为栈顶。如图 5-3 所示，入栈与出栈操作分别对应在数组尾部添加元素与删除元素，时间复杂度都为 $O(1)$ 。
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=== "ArrayStack"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "push()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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=== "pop()"
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{ class="animation-figure" }
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{ class="animation-figure" }
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<p align="center"> 图 5-3 基于数组实现栈的入栈出栈操作 </p>
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