build

docs/chapter_graph/graph_operations.md

@@ -40,14 +40,11 @@ comments: true
     class GraphAdjMat:
         """基于邻接矩阵实现的无向图类"""
 
-        # 顶点列表，元素代表“顶点值”，索引代表“顶点索引”
-        vertices: list[int] = []
-        # 邻接矩阵，行列索引对应“顶点索引”
-        adj_mat: list[list[int]] = []
-
         def __init__(self, vertices: list[int], edges: list[list[int]]):
             """构造方法"""
+            # 顶点列表，元素代表“顶点值”，索引代表“顶点索引”
             self.vertices: list[int] = []
+            # 邻接矩阵，行列索引对应“顶点索引”
             self.adj_mat: list[list[int]] = []
             # 添加顶点
             for val in vertices:
@@ -945,24 +942,72 @@ comments: true
 === "C"
 
     ```c title="graph_adjacency_matrix.c"
-    /* 基于邻接矩阵实现的无向图类结构 */
+    /* 基于邻接矩阵实现的无向图结构体 */
     typedef struct {
-        int *vertices; // 顶点列表
+        int vertices[MAX_SIZE];
-        int **adjMat;  // 邻接矩阵，元素代表“边”，索引代表“顶点索引”
+        int adjMat[MAX_SIZE][MAX_SIZE];
-        int size;      // 顶点数量
+        int size;
-        int capacity;  // 图容量
     } GraphAdjMat;
 
+    /* 构造函数 */
+    GraphAdjMat *newGraphAdjMat() {
+        GraphAdjMat *graph = (GraphAdjMat *)malloc(sizeof(GraphAdjMat));
+        graph->size = 0;
+        for (int i = 0; i < MAX_SIZE; i++) {
+            for (int j = 0; j < MAX_SIZE; j++) {
+                graph->adjMat[i][j] = 0;
+            }
+        }
+        return graph;
+    }
+
+    /* 添加顶点 */
+    void addVertex(GraphAdjMat *graph, int val) {
+        if (graph->size == MAX_SIZE) {
+            fprintf(stderr, "图的顶点数量已达最大值\n");
+            return;
+        }
+        // 添加第 n 个顶点，并将第 n 行和列置零
+        int n = graph->size;
+        graph->vertices[n] = val;
+        for (int i = 0; i <= n; i++) {
+            graph->adjMat[n][i] = graph->adjMat[i][n] = 0;
+        }
+        graph->size++;
+    }
+
+    /* 删除顶点 */
+    void removeVertex(GraphAdjMat *graph, int index) {
+        if (index < 0 || index >= graph->size) {
+            fprintf(stderr, "顶点索引越界\n");
+            return;
+        }
+        // 在顶点列表中移除索引 index 的顶点
+        for (int i = index; i < graph->size - 1; i++) {
+            graph->vertices[i] = graph->vertices[i + 1];
+        }
+        // 在邻接矩阵中删除索引 index 的行
+        for (int i = index; i < graph->size - 1; i++) {
+            for (int j = 0; j < graph->size; j++) {
+                graph->adjMat[i][j] = graph->adjMat[i + 1][j];
+            }
+        }
+        // 在邻接矩阵中删除索引 index 的列
+        for (int i = 0; i < graph->size; i++) {
+            for (int j = index; j < graph->size - 1; j++) {
+                graph->adjMat[i][j] = graph->adjMat[i][j + 1];
+            }
+        }
+        graph->size--;
+    }
+
     /* 添加边 */
     // 参数 i, j 对应 vertices 元素索引
     void addEdge(GraphAdjMat *graph, int i, int j) {
-        // 越界检查
         if (i < 0 || j < 0 || i >= graph->size || j >= graph->size || i == j) {
-            printf("Out of range in %s:%d\n", __FILE__, __LINE__);
+            fprintf(stderr, "边索引越界或相等\n");
-            exit(1);
+            return;
         }
-        // 添加边
-        // 参数 i, j 对应 vertices 元素索引
         graph->adjMat[i][j] = 1;
         graph->adjMat[j][i] = 1;
     }
@@ -970,137 +1015,22 @@ comments: true
     /* 删除边 */
     // 参数 i, j 对应 vertices 元素索引
     void removeEdge(GraphAdjMat *graph, int i, int j) {
-        // 越界检查
         if (i < 0 || j < 0 || i >= graph->size || j >= graph->size || i == j) {
-            printf("Out of range in %s:%d\n", __FILE__, __LINE__);
+            fprintf(stderr, "边索引越界或相等\n");
-            exit(1);
+            return;
         }
-        // 删除边
-        // 参数 i, j 对应 vertices 元素索引
         graph->adjMat[i][j] = 0;
         graph->adjMat[j][i] = 0;
     }
 
-    /* 添加顶点 */
+    /* 打印邻接矩阵 */
-    void addVertex(GraphAdjMat *graph, int val) {
+    void printGraphAdjMat(GraphAdjMat *graph) {
-        // 如果实际使用不大于预设空间，则直接初始化新空间
+        printf("顶点列表 = ");
-        if (graph->size < graph->capacity) {
+        printArray(graph->vertices, graph->size);
-            graph->vertices[graph->size] = val; // 初始化新顶点值
+        printf("邻接矩阵 =\n");
-            for (int i = 0; i < graph->size; i++) {
-                graph->adjMat[i][graph->size] = 0; // 邻接矩新列阵置0
-            }
-            memset(graph->adjMat[graph->size], 0, sizeof(int) * (graph->size + 1)); // 将新增行置 0
-            graph->size++;
-            return;
-        }
-        // 扩容，申请新的顶点数组
-        int *temp = (int *)malloc(sizeof(int) * (graph->size * 2));
-        memcpy(temp, graph->vertices, sizeof(int) * graph->size);
-        temp[graph->size] = val;
-        // 释放原数组
-        free(graph->vertices);
-        graph->vertices = temp;
-        // 扩容，申请新的二维数组
-        int **tempMat = (int **)malloc(sizeof(int *) * graph->size * 2);
-        int *tempMatLine = (int *)malloc(sizeof(int) * (graph->size * 2) * (graph->size * 2));
-        memset(tempMatLine, 0, sizeof(int) * (graph->size * 2) * (graph->size * 2));
-        for (int k = 0; k < graph->size * 2; k++) {
-            tempMat[k] = tempMatLine + k * (graph->size * 2);
-        }
         for (int i = 0; i < graph->size; i++) {
-            memcpy(tempMat[i], graph->adjMat[i], sizeof(int) * graph->size); // 原数据复制到新数组
+            printArray(graph->adjMat[i], graph->size);
         }
-        for (int i = 0; i < graph->size; i++) {
-            tempMat[i][graph->size] = 0; // 将新增列置 0
-        }
-        memset(tempMat[graph->size], 0, sizeof(int) * (graph->size + 1)); // 将新增行置 0
-        // 释放原数组
-        free(graph->adjMat[0]);
-        free(graph->adjMat);
-        // 扩容后，指向新地址
-        graph->adjMat = tempMat; // 指向新的邻接矩阵地址
-        graph->capacity = graph->size * 2;
-        graph->size++;
-    }
-
-    /* 删除顶点 */
-    void removeVertex(GraphAdjMat *graph, int index) {
-        // 越界检查
-        if (index < 0 || index >= graph->size) {
-            printf("Out of range in %s:%d\n", __FILE__, __LINE__);
-            exit(1);
-        }
-        for (int i = index; i < graph->size - 1; i++) {
-            graph->vertices[i] = graph->vertices[i + 1]; // 清除删除的顶点，并将其后所有顶点前移
-        }
-        graph->vertices[graph->size - 1] = 0; // 将被前移的最后一个顶点置 0
-        // 清除邻接矩阵中删除的列
-        for (int i = 0; i < graph->size - 1; i++) {
-            if (i < index) {
-                for (int j = index; j < graph->size - 1; j++) {
-                    graph->adjMat[i][j] = graph->adjMat[i][j + 1]; // 被删除列后的所有列前移
-                }
-            } else {
-                memcpy(graph->adjMat[i], graph->adjMat[i + 1], sizeof(int) * graph->size); // 被删除行的下方所有行上移
-                for (int j = index; j < graph->size; j++) {
-                    graph->adjMat[i][j] = graph->adjMat[i][j + 1]; // 被删除列后的所有列前移
-                }
-            }
-        }
-        graph->size--;
-    }
-
-    /* 打印顶点与邻接矩阵 */
-    void printGraph(GraphAdjMat *graph) {
-        if (graph->size == 0) {
-            printf("graph is empty\n");
-            return;
-        }
-        printf("顶点列表 = [");
-        for (int i = 0; i < graph->size; i++) {
-            if (i != graph->size - 1) {
-                printf("%d, ", graph->vertices[i]);
-            } else {
-                printf("%d", graph->vertices[i]);
-            }
-        }
-        printf("]\n");
-        printf("邻接矩阵 =\n[\n");
-        for (int i = 0; i < graph->size; i++) {
-            printf("  [");
-            for (int j = 0; j < graph->size; j++) {
-                if (j != graph->size - 1) {
-                    printf("%u, ", graph->adjMat[i][j]);
-                } else {
-                    printf("%u", graph->adjMat[i][j]);
-                }
-            }
-            printf("],\n");
-        }
-        printf("]\n");
-    }
-
-    /* 构造函数 */
-    GraphAdjMat *newGraphAjdMat(int numberVertices, int *vertices, int **adjMat) {
-        // 申请内存
-        GraphAdjMat *newGraph = (GraphAdjMat *)malloc(sizeof(GraphAdjMat));    // 为图分配内存
-        newGraph->vertices = (int *)malloc(sizeof(int) * numberVertices * 2);  // 为顶点列表分配内存
-        newGraph->adjMat = (int **)malloc(sizeof(int *) * numberVertices * 2); // 为邻接矩阵分配二维内存
-        int *temp = (int *)malloc(sizeof(int) * numberVertices * 2 * numberVertices * 2); // 为邻接矩阵分配一维内存
-        newGraph->size = numberVertices;                                                  // 初始化顶点数量
-        newGraph->capacity = numberVertices * 2;                                          // 初始化图容量
-        // 配置二维数组
-        for (int i = 0; i < numberVertices * 2; i++) {
-            newGraph->adjMat[i] = temp + i * numberVertices * 2; // 将二维指针指向一维数组
-        }
-        // 赋值
-        memcpy(newGraph->vertices, vertices, sizeof(int) * numberVertices);
-        for (int i = 0; i < numberVertices; i++) {
-            memcpy(newGraph->adjMat[i], adjMat[i],
-                   sizeof(int) * numberVertices); // 将传入的邻接矩阵赋值给结构体内邻接矩阵
-        }
-        // 返回结构体指针
-        return newGraph;
     }
     ```
 
@@ -1967,120 +1897,160 @@ comments: true
 === "C"
 
     ```c title="graph_adjacency_list.c"
-    /* 基于邻接链表实现的无向图类结构 */
+    /* 节点结构体 */
+    typedef struct AdjListNode {
+        Vertex *vertex;           // 顶点
+        struct AdjListNode *next; // 后继节点
+    } AdjListNode;
+
+    /* 查找顶点对应的节点 */
+    AdjListNode *findNode(GraphAdjList *graph, Vertex *vet) {
+        for (int i = 0; i < graph->size; i++) {
+            if (graph->heads[i]->vertex == vet) {
+                return graph->heads[i];
+            }
+        }
+        return NULL;
+    }
+
+    /* 添加边辅助函数 */
+    void addEdgeHelper(AdjListNode *head, Vertex *vet) {
+        AdjListNode *node = (AdjListNode *)malloc(sizeof(AdjListNode));
+        node->vertex = vet;
+        // 头插法
+        node->next = head->next;
+        head->next = node;
+    }
+
+    /* 删除边辅助函数 */
+    void removeEdgeHelper(AdjListNode *head, Vertex *vet) {
+        AdjListNode *pre = head;
+        AdjListNode *cur = head->next;
+        // 在链表中搜索 vet 对应节点
+        while (cur != NULL && cur->vertex != vet) {
+            pre = cur;
+            cur = cur->next;
+        }
+        if (cur == NULL)
+            return;
+        // 将 vet 对应节点从链表中删除
+        pre->next = cur->next;
+        // 释放内存
+        free(cur);
+    }
+
+    /* 基于邻接表实现的无向图类 */
     typedef struct {
-        Vertex **vertices;     // 邻接表
+        AdjListNode *heads[MAX_SIZE]; // 节点数组
-        unsigned int size;     // 顶点数量
+        int size;                     // 节点数量
-        unsigned int capacity; // 顶点容量
     } GraphAdjList;
 
-    /* 添加边 */
+    /* 构造函数 */
-    void addEdge(GraphAdjList *graph, int i, int j) {
+    GraphAdjList *newGraphAdjList() {
-        // 越界检查
+        GraphAdjList *graph = (GraphAdjList *)malloc(sizeof(GraphAdjList));
-        if (i < 0 || j < 0 || i == j || i >= graph->size || j >= graph->size) {
+        if (!graph) {
-            printf("Out of range in %s:%d\n", __FILE__, __LINE__);
+            return NULL;
-            return;
         }
-        // 查找欲添加边的顶点 vet1 - vet2
+        graph->size = 0;
-        Vertex *vet1 = graph->vertices[i];
+        for (int i = 0; i < MAX_SIZE; i++) {
-        Vertex *vet2 = graph->vertices[j];
+            graph->heads[i] = NULL;
-        // 连接顶点 vet1 - vet2
+        }
-        pushBack(vet1->list, vet2);
+        return graph;
-        pushBack(vet2->list, vet1);
+    }
+
+    /* 析构函数 */
+    void delGraphAdjList(GraphAdjList *graph) {
+        for (int i = 0; i < graph->size; i++) {
+            AdjListNode *cur = graph->heads[i];
+            while (cur != NULL) {
+                AdjListNode *next = cur->next;
+                if (cur != graph->heads[i]) {
+                    free(cur);
+                }
+                cur = next;
+            }
+            free(graph->heads[i]->vertex);
+            free(graph->heads[i]);
+        }
+        free(graph);
+    }
+
+    /* 查找顶点对应的节点 */
+    AdjListNode *findNode(GraphAdjList *graph, Vertex *vet) {
+        for (int i = 0; i < graph->size; i++) {
+            if (graph->heads[i]->vertex == vet) {
+                return graph->heads[i];
+            }
+        }
+        return NULL;
+    }
+
+    /* 添加边 */
+    void addEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {
+        AdjListNode *head1 = findNode(graph, vet1);
+        AdjListNode *head2 = findNode(graph, vet2);
+        assert(head1 != NULL && head2 != NULL && head1 != head2);
+        // 添加边 vet1 - vet2
+        addEdgeHelper(head1, vet2);
+        addEdgeHelper(head2, vet1);
     }
 
     /* 删除边 */
-    void removeEdge(GraphAdjList *graph, int i, int j) {
+    void removeEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {
-        // 越界检查
+        AdjListNode *head1 = findNode(graph, vet1);
-        if (i < 0 || j < 0 || i == j || i >= graph->size || j >= graph->size) {
+        AdjListNode *head2 = findNode(graph, vet2);
-            printf("Out of range in %s:%d\n", __FILE__, __LINE__);
+        assert(head1 != NULL && head2 != NULL);
-            return;
+        // 删除边 vet1 - vet2
-        }
+        removeEdgeHelper(head1, head2->vertex);
-        // 查找欲删除边的顶点 vet1 - vet2
+        removeEdgeHelper(head2, head1->vertex);
-        Vertex *vet1 = graph->vertices[i];
-        Vertex *vet2 = graph->vertices[j];
-        // 移除待删除边 vet1 - vet2
-        removeLink(vet1->list, vet2);
-        removeLink(vet2->list, vet1);
     }
 
     /* 添加顶点 */
-    void addVertex(GraphAdjList *graph, int val) {
+    void addVertex(GraphAdjList *graph, Vertex *vet) {
-        // 若大小超过容量，则扩容
+        assert(graph != NULL && graph->size < MAX_SIZE);
-        if (graph->size >= graph->capacity) {
+        AdjListNode *head = (AdjListNode *)malloc(sizeof(AdjListNode));
-            Vertex **tempList = (Vertex **)malloc(sizeof(Vertex *) * 2 * graph->capacity);
+        head->vertex = vet;
-            memcpy(tempList, graph->vertices, sizeof(Vertex *) * graph->size);
+        head->next = NULL;
-            free(graph->vertices);                 // 释放原邻接表内存
+        // 在邻接表中添加一个新链表
-            graph->vertices = tempList;            // 指向新邻接表
+        graph->heads[graph->size++] = head;
-            graph->capacity = graph->capacity * 2; // 容量扩大至2倍
-        }
-        // 申请新顶点内存并将新顶点地址存入顶点列表
-        Vertex *newV = newVertex(val);       // 建立新顶点
-        newV->pos = graph->size;             // 为新顶点标记下标
-        newV->list = newLinklist(newV);      // 为新顶点建立链表
-        graph->vertices[graph->size] = newV; // 将新顶点加入邻接表
-        graph->size++;
     }
 
     /* 删除顶点 */
-    void removeVertex(GraphAdjList *graph, unsigned int index) {
+    void removeVertex(GraphAdjList *graph, Vertex *vet) {
-        // 越界检查
+        AdjListNode *node = findNode(graph, vet);
-        if (index < 0 || index >= graph->size) {
+        assert(node != NULL);
-            printf("Out of range in %s:%d\n", __FILE__, __LINE__);
+        // 在邻接表中删除顶点 vet 对应的链表
-            exit(1);
+        AdjListNode *cur = node, *pre = NULL;
+        while (cur) {
+            pre = cur;
+            cur = cur->next;
+            free(pre);
         }
-        Vertex *vet = graph->vertices[index]; // 查找待删节点
+        // 遍历其他顶点的链表，删除所有包含 vet 的边
-        if (vet == 0) {                       // 若不存在该节点，则返回
-            printf("index is:%d\n", index);
-            printf("Out of range in %s:%d\n", __FILE__, __LINE__);
-            return;
-        }
-        // 遍历待删除顶点的链表，将所有与待删除节点有关的边删除
-        Node *temp = vet->list->head->next;
-        while (temp != 0) {
-            removeLink(temp->val->list, vet); // 删除与该顶点有关的边
-            temp = temp->next;
-        }
-        // 将顶点前移
-        for (int i = index; i < graph->size - 1; i++) {
-            graph->vertices[i] = graph->vertices[i + 1]; // 顶点前移
-            graph->vertices[i]->pos--;                   // 所有前移的顶点索引值减 1
-        }
-        graph->vertices[graph->size - 1] = 0;
-        graph->size--;
-        // 释放内存
-        freeVertex(vet);
-    }
-
-    /* 打印顶点与邻接矩阵 */
-    void printGraph(GraphAdjList *graph) {
-        printf("邻接表  =\n");
         for (int i = 0; i < graph->size; i++) {
-            Node *n = graph->vertices[i]->list->head->next;
+            cur = graph->heads[i];
-            printf("%d: [", graph->vertices[i]->val);
+            pre = NULL;
-            while (n != 0) {
+            while (cur) {
-                if (n->next != 0) {
+                pre = cur;
-                    printf("%d, ", n->val->val);
+                cur = cur->next;
-                } else {
+                if (cur && cur->vertex == vet) {
-                    printf("%d", n->val->val);
+                    pre->next = cur->next;
+                    free(cur);
+                    break;
                 }
-                n = n->next;
             }
-            printf("]\n");
         }
-    }
+        // 将该顶点之后的顶点向前移动，以填补空缺
-
+        int i;
-    /* 构造函数 */
+        for (i = 0; i < graph->size; i++) {
-    GraphAdjList *newGraphAdjList(unsigned int verticesCapacity) {
+            if (graph->heads[i] == node)
-        // 申请内存
+                break;
-        GraphAdjList *newGraph = (GraphAdjList *)malloc(sizeof(GraphAdjList));
+        }
-        // 建立顶点表并分配内存
+        for (int j = i; j < graph->size - 1; j++) {
-        newGraph->vertices = (Vertex **)malloc(sizeof(Vertex *) * verticesCapacity); // 为顶点列表分配内存
+            graph->heads[j] = graph->heads[j + 1];
-        memset(newGraph->vertices, 0, sizeof(Vertex *) * verticesCapacity);          // 顶点列表置 0
+        }
-        newGraph->size = 0;                                                          // 初始化顶点数量
+        graph->size--;
-        newGraph->capacity = verticesCapacity;                                       // 初始化顶点容量
+        free(vet);
-        // 返回图指针
-        return newGraph;
     }
     ```
 

docs/chapter_graph/graph_traversal.md

@@ -342,43 +342,73 @@ BFS 通常借助队列来实现。队列具有“先入先出”的性质，这
 === "C"
 
     ```c title="graph_bfs.c"
-    /* 广度优先遍历 */
+    /* 节点队列结构体 */
+    typedef struct {
+        Vertex *vertices[MAX_SIZE];
+        int front, rear, size;
+    } Queue;
+
+    /* 构造函数 */
+    Queue *newQueue() {
+        Queue *q = (Queue *)malloc(sizeof(Queue));
+        q->front = q->rear = q->size = 0;
+        return q;
+    }
+
+    /* 判断队列是否为空 */
+    int isEmpty(Queue *q) {
+        return q->size == 0;
+    }
+
+    /* 入队操作 */
+    void enqueue(Queue *q, Vertex *vet) {
+        q->vertices[q->rear] = vet;
+        q->rear = (q->rear + 1) % MAX_SIZE;
+        q->size++;
+    }
+
+    /* 出队操作 */
+    Vertex *dequeue(Queue *q) {
+        Vertex *vet = q->vertices[q->front];
+        q->front = (q->front + 1) % MAX_SIZE;
+        q->size--;
+        return vet;
+    }
+
+    /* 检查顶点是否已被访问 */
+    int isVisited(Vertex **visited, int size, Vertex *vet) {
+        // 遍历查找节点，使用 O(n) 时间
+        for (int i = 0; i < size; i++) {
+            if (visited[i] == vet)
+                return 1;
+        }
+        return 0;
+    }
+
+    /* 广度优先遍历 BFS */
     // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点
-    Vertex **graphBFS(GraphAdjList *t, Vertex *startVet) {
+    void graphBFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize, Vertex **visited, int *visitedSize) {
-        // 顶点遍历序列
-        Vertex **res = (Vertex **)malloc(sizeof(Vertex *) * t->size);
-        memset(res, 0, sizeof(Vertex *) * t->size);
         // 队列用于实现 BFS
-        Queue *que = newQueue(t->size);
+        Queue *queue = newQueue();
-        // 哈希表，用于记录已被访问过的顶点
+        enqueue(queue, startVet);
-        HashTable *visited = newHash(t->size);
+        visited[(*visitedSize)++] = startVet;
-        int resIndex = 0;
-        queuePush(que, startVet);         // 将第一个元素入队
-        hashMark(visited, startVet->pos); // 标记第一个入队的顶点
         // 以顶点 vet 为起点，循环直至访问完所有顶点
-        while (que->head < que->tail) {
+        while (!isEmpty(queue)) {
-            // 遍历该顶点的边链表，将所有与该顶点有连接的，并且未被标记的顶点入队
+            Vertex *vet = dequeue(queue); // 队首顶点出队
-            Node *n = queueTop(que)->list->head->next;
+            res[(*resSize)++] = vet;      // 记录访问顶点
-            while (n != 0) {
+            // 遍历该顶点的所有邻接顶点
-                // 查询哈希表，若该索引的顶点已入队，则跳过，否则入队并标记
+            AdjListNode *node = findNode(graph, vet);
-                if (hashQuery(visited, n->val->pos) == 1) {
+            while (node != NULL) {
-                    n = n->next;
+                // 跳过已被访问过的顶点
-                    continue; // 跳过已被访问过的顶点
+                if (!isVisited(visited, *visitedSize, node->vertex)) {
+                    enqueue(queue, node->vertex);             // 只入队未访问的顶点
+                    visited[(*visitedSize)++] = node->vertex; // 标记该顶点已被访问
                 }
-                queuePush(que, n->val);         // 只入队未访问的顶点
+                node = node->next;
-                hashMark(visited, n->val->pos); // 标记该顶点已被访问
             }
-            // 队首元素存入数组
-            res[resIndex] = queueTop(que); // 队首顶点加入顶点遍历序列
-            resIndex++;
-            queuePop(que); // 队首元素出队
         }
         // 释放内存
-        freeQueue(que);
+        free(queue);
-        freeHash(visited);
-        resIndex = 0;
-        // 返回顶点遍历序列
-        return res;
     }
     ```
 
@@ -749,39 +779,37 @@ BFS 通常借助队列来实现。队列具有“先入先出”的性质，这
 === "C"
 
     ```c title="graph_dfs.c"
+    /* 检查顶点是否已被访问 */
+    int isVisited(Vertex **res, int size, Vertex *vet) {
+        // 遍历查找节点，使用 O(n) 时间
+        for (int i = 0; i < size; i++) {
+            if (res[i] == vet) {
+                return 1;
+            }
+        }
+        return 0;
+    }
+
     /* 深度优先遍历 DFS 辅助函数 */
-    int resIndex = 0;
+    void dfs(GraphAdjList *graph, Vertex **res, int *resSize, Vertex *vet) {
-    void dfs(GraphAdjList *graph, HashTable *visited, Vertex *vet, Vertex **res) {
+        // 记录访问顶点
-        if (hashQuery(visited, vet->pos) == 1) {
+        res[(*resSize)++] = vet;
-            return; // 跳过已被访问过的顶点
+        // 遍历该顶点的所有邻接顶点
+        AdjListNode *node = findNode(graph, vet);
+        while (node != NULL) {
+            // 跳过已被访问过的顶点
+            if (!isVisited(res, *resSize, node->vertex)) {
+                // 递归访问邻接顶点
+                dfs(graph, res, resSize, node->vertex);
+            }
+            node = node->next;
         }
-        hashMark(visited, vet->pos); // 标记顶点并将顶点存入数组
-        res[resIndex] = vet;         // 将顶点存入数组
-        resIndex++;
-        // 遍历该顶点链表
-        Node *n = vet->list->head->next;
-        while (n != 0) {
-            // 递归访问邻接顶点
-            dfs(graph, visited, n->val, res);
-            n = n->next;
-        }
-        return;
     }
 
     /* 深度优先遍历 DFS */
     // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点
-    Vertex **graphDFS(GraphAdjList *graph, Vertex *startVet) {
+    void graphDFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize) {
-        // 顶点遍历序列
+        dfs(graph, res, resSize, startVet);
-        Vertex **res = (Vertex **)malloc(sizeof(Vertex *) * graph->size);
-        memset(res, 0, sizeof(Vertex *) * graph->size);
-        // 哈希表，用于记录已被访问过的顶点
-        HashTable *visited = newHash(graph->size);
-        dfs(graph, visited, startVet, res);
-        // 释放哈希表内存并将数组索引归零
-        freeHash(visited);
-        resIndex = 0;
-        // 返回遍历数组
-        return res;
     }
     ```
 

docs/chapter_hashing/hash_collision.md

@@ -1164,7 +1164,7 @@ comments: true
         Node **buckets;   // 桶数组
     } HashMapChaining;
 
-    /* 构造方法 */
+    /* 构造函数 */
     HashMapChaining *initHashMapChaining() {
         HashMapChaining *hashMap = (HashMapChaining *)malloc(sizeof(HashMapChaining));
         hashMap->size = 0;
@@ -1178,7 +1178,7 @@ comments: true
         return hashMap;
     }
 
-    /* 析构方法 */
+    /* 析构函数 */
     void freeHashMapChaining(HashMapChaining *hashMap) {
         for (int i = 0; i < hashMap->capacity; i++) {
             Node *cur = hashMap->buckets[i];
@@ -2682,7 +2682,7 @@ comments: true
         Pair *TOMBSTONE;  // 删除标记
     } HashMapOpenAddressing;
 
-    /* 构造方法 */
+    /* 构造函数 */
     HashMapOpenAddressing *newHashMapOpenAddressing() {
         HashMapOpenAddressing *hashMap = (HashMapOpenAddressing *)malloc(sizeof(HashMapOpenAddressing));
         hashMap->size = 0;
@@ -2697,7 +2697,7 @@ comments: true
         return hashMap;
     }
 
-    /* 析构方法 */
+    /* 析构函数 */
     void delHashMapOpenAddressing(HashMapOpenAddressing *hashMap) {
         for (int i = 0; i < hashMap->capacity; i++) {
             Pair *pair = hashMap->buckets[i];

docs/chapter_heap/top_k.md

@@ -259,33 +259,49 @@ comments: true
 === "TS"
 
     ```typescript title="top_k.ts"
-    [class]{}-[func]{pushMinHeap}
+    /* 元素入堆 */
+    function pushMinHeap(maxHeap: MaxHeap, val: number): void {
+        // 元素取反
+        maxHeap.push(-val);
+    }
 
-    [class]{}-[func]{popMinHeap}
+    /* 元素出堆 */
+    function popMinHeap(maxHeap: MaxHeap): number {
+        // 元素取反
+        return -maxHeap.pop();
+    }
 
-    [class]{}-[func]{peekMinHeap}
+    /* 访问堆顶元素 */
+    function peekMinHeap(maxHeap: MaxHeap): number {
+        // 元素取反
+        return -maxHeap.peek();
+    }
 
-    [class]{}-[func]{getMinHeap}
+    /* 取出堆中元素 */
+    function getMinHeap(maxHeap: MaxHeap): number[] {
+        // 元素取反
+        return maxHeap.getMaxHeap().map((num: number) => -num);
+    }
 
     /* 基于堆查找数组中最大的 k 个元素 */
     function topKHeap(nums: number[], k: number): number[] {
-        // 将堆中所有元素取反，从而用大顶堆来模拟小顶堆
+        // 初始化小顶堆
-        const invertedNums = nums.map((num) => -num);
+        // 请注意：我们将堆中所有元素取反，从而用大顶堆来模拟小顶堆
+        const maxHeap = new MaxHeap([]);
         // 将数组的前 k 个元素入堆
-        const heap = new MaxHeap(invertedNums.slice(0, k));
+        for (let i = 0; i < k; i++) {
+            pushMinHeap(maxHeap, nums[i]);
+        }
         // 从第 k+1 个元素开始，保持堆的长度为 k
-        for (let i = k; i < invertedNums.length; i++) {
+        for (let i = k; i < nums.length; i++) {
-            // 若当前元素小于堆顶元素，则将堆顶元素出堆、当前元素入堆
+            // 若当前元素大于堆顶元素，则将堆顶元素出堆、当前元素入堆
-            if (invertedNums[i] < heap.peek()) {
+            if (nums[i] > peekMinHeap(maxHeap)) {
-                heap.pop();
+                popMinHeap(maxHeap);
-                heap.push(invertedNums[i]);
+                pushMinHeap(maxHeap, nums[i]);
             }
         }
-        // 取出堆中元素
+        // 返回堆中元素
-        const maxHeap = heap.getMaxHeap();
+        return getMinHeap(maxHeap);
-        // 对堆中元素取相反数
-        const invertedMaxHeap = maxHeap.map((num) => -num);
-        return invertedMaxHeap;
     }
     ```