add c code for graph operation (#601)

* Create chapter_graph

* Delete chapter_graph

* add C code for graph

* add C code for graph

* Create graph_adjacency_list.c

add C code for graph

* Update CMakeLists.txt

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update format and output

* Update graph_adjacency_list.c

* Update CMakeLists.txt for c code of graph

* Update format of c code

* Update format of c code

* Update format of c code

* Update verticesList

Change the data structure of the storage list from a linked list to a linear table

* Update graph_adjacency_list.c

* Update graph_adjacency_matrix.c

* Create graph_adjacency_list_test.c

* Create graph_bfs

* Update CMakeLists.txt

* Update graph_adjacency_list.c

* mv graph_bfs to graph_bfs.c

* Update graph_bfs.c

* Delete graph_bfs

* Update graph_adjacency_list.c

* update c code for graph operation.

* Update CMakeLists.txt

* Update graph_dfs.c

* Update graph_dfs.c

* Update CMakeLists.txt

* Update graph_dfs.c

* Update note of graph_dfs.c

* Update graph_bfs.c

* Update graph_dfs.c

* Update graph_bfs.c

* Update output "初始化后，图为：" of graph_dfs.c

* Update graph_dfs.c

* Update graph_bfs.c

* Update graph_dfs.c

* Update name of arrayVertex

* Update name of arrayVertex

* Update note of graph_dfs.c

* Update note of graph_bfs.c

* Update graph_dfs.c

* Update graph_bfs.c

* Update graph_adjacency_matrix.c

* Update graph_adjacency_list_test.c

* Update graph_adjacency_list.c

* Update graph_dfs.c

* Update graph_bfs.c

* Update comment

* Update comment

* Update graph_adjacency_list.c

* Update graph_adjacency_matrix.c

* update comment

* update comment

* update comment for graph operation

* update comment of graph operation

* update comment

* update comment

---------

Co-authored-by: Yudong Jin <krahets@163.com>
Co-authored-by: libr <libr@info2soft.com>

codes/c/chapter_graph/CMakeLists.txt

@@ -1,4 +1,4 @@
 add_executable(graph_adjacency_matrix graph_adjacency_matrix.c)
-add_executable(graph_adjacency_list graph_adjacency_list.c)
 add_executable(graph_adjacency_list_test graph_adjacency_list_test.c)
 add_executable(graph_bfs graph_bfs.c)
+add_executable(graph_dfs graph_dfs.c)

codes/c/chapter_graph/graph_adjacency_list.c

@@ -41,11 +41,11 @@ struct Vertex {
 
 /* 顶点节点构造函数 */
 Vertex *newVertex(int val) {
-    Vertex *v = (Vertex *)malloc(sizeof(Vertex));
+    Vertex *vet = (Vertex *)malloc(sizeof(Vertex));
     // 为新节点赋值并建立该节点的链表
-    v->val = val;
+    vet->val = val;
-    v->linked = newLinklist(v);
+    vet->linked = newLinklist(vet);
-    return v;
+    return vet;
 }
 
 /* 顶点内存释放函数 */
@@ -103,25 +103,6 @@ void removeLink(linkList *l, Vertex *val) {
     }
 }
 
-/* 根据索引查找链表中节点 */
-Node *findByindex(linkList *l, unsigned int index) {
-    unsigned int i = 0;
-    Node *temp = l->head->next;
-    while (temp != 0) {
-        if (i == index) {
-            return temp;
-        }
-        temp = temp->next;
-        i++;
-    }
-
-    if (temp->next == 0) {
-        printf("vertex not found!\n");
-        return 0;
-    }
-    return 0;
-}
-
 /* 根据顶点地址删除顶点 */
 void removeNode(linkList *l, Vertex *val) {
     Node *temp = l->head->next;
@@ -172,12 +153,9 @@ linkList *newLinklist(Vertex *val) {
 
 /* 基于邻接链表实现的无向图类结构 */
 struct graphAdjList {
-    // 顶点列表
+    Vertex **verticesList; // 邻接表
-    Vertex **verticesList;
+    unsigned int size;     // 顶点数量
-    // 顶点数量
+    unsigned int capacity; // 顶点容量
-    unsigned int size;
-    // 当前容量
-    unsigned int capacity;
 };
 
 typedef struct graphAdjList graphAdjList;
@@ -189,13 +167,13 @@ void addEdge(graphAdjList *t, int i, int j) {
         printf("Out of range in %s:%d\n", __FILE__, __LINE__);
         return;
     }
-    // 查找待连接的节点
+    // 查找欲添加边的顶点 vet1 - vet2
-    Vertex *v1 = t->verticesList[i];
+    Vertex *vet1 = t->verticesList[i];
-    Vertex *v2 = t->verticesList[j];
+    Vertex *vet2 = t->verticesList[j];
 
-    // 连接节点
+    // 连接顶点 vet1 - vet2
-    pushBack(v1->linked, v2);
+    pushBack(vet1->linked, vet2);
-    pushBack(v2->linked, v1);
+    pushBack(vet2->linked, vet1);
 }
 
 /* 删除边 */
@@ -206,13 +184,13 @@ void removeEdge(graphAdjList *t, int i, int j) {
         return;
     }
 
-    // 查找待删除边的相关节点
+    // 查找欲删除边的顶点 vet1 - vet2
-    Vertex *v1 = t->verticesList[i];
+    Vertex *vet1 = t->verticesList[i];
-    Vertex *v2 = t->verticesList[j];
+    Vertex *vet2 = t->verticesList[j];
 
-    // 移除待删除边
+    // 移除待删除边 vet1 - vet2
-    removeLink(v1->linked, v2);
+    removeLink(vet1->linked, vet2);
-    removeLink(v2->linked, v1);
+    removeLink(vet2->linked, vet1);
 }
 
 /* 添加顶点 */
@@ -221,16 +199,15 @@ void addVertex(graphAdjList *t, int val) {
     if (t->size >= t->capacity) {
         Vertex **tempList = (Vertex **)malloc(sizeof(Vertex *) * 2 * t->capacity);
         memcpy(tempList, t->verticesList, sizeof(Vertex *) * t->size);
-        free(t->verticesList);
+        free(t->verticesList);         // 释放原邻接表内存
-        // 指向新顶点表
+        t->verticesList = tempList;    // 指向新邻接表
-        t->verticesList = tempList;    
+        t->capacity = t->capacity * 2; // 容量扩大至2倍
-        t->capacity = t->capacity * 2;
     }
     // 申请新顶点内存并将新顶点地址存入顶点列表
-    Vertex *newV = newVertex(val);
+    Vertex *newV = newVertex(val);    // 建立新顶点
-    newV->pos = t->size;
+    newV->pos = t->size;              // 为新顶点标记下标
-    newV->linked = newLinklist(newV);
+    newV->linked = newLinklist(newV); // 为新顶点建立链表
-    t->verticesList[t->size] = newV;
+    t->verticesList[t->size] = newV;  // 将新顶点加入邻接表
     t->size++;
 }
 
@@ -242,31 +219,30 @@ void removeVertex(graphAdjList *t, unsigned int index) {
         exit(1);
     }
 
-    // 查找待删节点
+    Vertex *vet = t->verticesList[index]; // 查找待删节点
-    Vertex *v = t->verticesList[index];
+    if (vet == 0) {                       // 若不存在该节点，则返回
-    // 若不存在该节点，则返回
-    if (v == 0) {
         printf("index is:%d\n", index);
         printf("Out of range in %s:%d\n", __FILE__, __LINE__);
         return;
     }
 
-    // 遍历待删除节点链表，将所有与待删除结点有关的边删除
+    // 遍历待删除顶点的链表，将所有与待删除结点有关的边删除
-    Node *temp = v->linked->head->next;
+    Node *temp = vet->linked->head->next;
     while (temp != 0) {
-        removeLink(temp->val->linked, v);
+        removeLink(temp->val->linked, vet); // 删除与该顶点有关的边
         temp = temp->next;                
     }
 
-    // 定点列表前移
+    // 将顶点前移
     for (int i = index; i < t->size - 1; i++) {
-        t->verticesList[i] = t->verticesList[i + 1];
+        t->verticesList[i] = t->verticesList[i + 1]; // 顶点前移
+        t->verticesList[i]->pos--;                   // 所有前移的顶点索引值减1
     }
-    t->verticesList[t->size - 1] = 0;
+    t->verticesList[t->size - 1] = 0; // 将被删除顶点的位置置 0
     t->size--;
 
     //释放被删除顶点的内存
-    freeVertex(v);
+    freeVertex(vet);
 }
 
 /* 打印顶点与邻接矩阵 */
@@ -288,14 +264,14 @@ void printGraph(graphAdjList *t) {
 }
 
 /* 构造函数 */
-graphAdjList *newGraphic(unsigned int verticesNumber) {
+graphAdjList *newGraphAdjList(unsigned int verticesCapacity) {
     // 申请内存
     graphAdjList *newGraph = (graphAdjList *)malloc(sizeof(graphAdjList));
     // 建立顶点表并分配内存
-    newGraph->verticesList = (Vertex **)malloc(sizeof(Vertex *) * verticesNumber);
+    newGraph->verticesList = (Vertex **)malloc(sizeof(Vertex *) * verticesCapacity); // 为顶点列表分配内存
-    memset(newGraph->verticesList, 0, sizeof(Vertex *) * verticesNumber);
+    memset(newGraph->verticesList, 0, sizeof(Vertex *) * verticesCapacity);          // 顶点列表置 0
-    // 初始化大小和容量
+    newGraph->size = 0;                                                              // 初始化顶点数量
-    newGraph->size = 0;
+    newGraph->capacity = verticesCapacity;                                           // 初始化顶点容量
-    newGraph->capacity = verticesNumber;
+    // 返回图指针
     return newGraph;                
 }

codes/c/chapter_graph/graph_adjacency_list_test.c

@@ -10,7 +10,7 @@
 int main() {
 
     /* 初始化无向图 */
-    graphAdjList *graph = newGraphic(5);
+    graphAdjList *graph = newGraphAdjList(5);
     // 初始化顶点
     addVertex(graph, 1);
     addVertex(graph, 3);

codes/c/chapter_graph/graph_adjacency_matrix.c

@@ -8,32 +8,38 @@
 
 /* 基于邻接矩阵实现的无向图类结构 */
 struct graphAdjMat {
-    int *vertices;
+    int *vertices;         // 顶点列表
-    unsigned int **adjMat;
+    unsigned int **adjMat; // 邻接矩阵，元素代表“边”，索引代表“顶点索引”
-    unsigned int size;
+    unsigned int size;     // 顶点数量
-    unsigned int capacity;
+    unsigned int capacity; // 图容量
 };
 
 typedef struct graphAdjMat graphAdjMat;
 
 /* 添加边 */
+// 参数 i, j 对应 vertices 元素索引
 void addEdge(graphAdjMat *t, int i, int j) {
     // 越界检查
     if (i < 0 || j < 0 || i >= t->size || j >= t->size || i == j) {
         printf("Out of range in %s:%d\n", __FILE__, __LINE__);
         exit(1);
     }
+    // 添加边
+    // 参数 i, j 对应 vertices 元素索引
     t->adjMat[i][j] = 1;
     t->adjMat[j][i] = 1;
 }
 
 /* 删除边 */
+// 参数 i, j 对应 vertices 元素索引
 void removeEdge(graphAdjMat *t, int i, int j) {
     // 越界检查
     if (i < 0 || j < 0 || i >= t->size || j >= t->size || i == j) {
         printf("Out of range in %s:%d\n", __FILE__, __LINE__);
         exit(1);
     }
+    // 删除边
+    // 参数 i, j 对应 vertices 元素索引
     t->adjMat[i][j] = 0;
     t->adjMat[j][i] = 0;
 }
@@ -42,13 +48,13 @@ void removeEdge(graphAdjMat *t, int i, int j) {
 void addVertex(graphAdjMat *t, int val) {
     // 如果实际使用不大于预设空间，则直接初始化新空间
     if (t->size < t->capacity) {
-        t->vertices[t->size] = val;
+        t->vertices[t->size] = val; // 初始化新顶点值
+
         
-        // 邻接矩新列阵置0
         for (int i = 0; i < t->size; i++) {
-            t->adjMat[i][t->size] = 0;
+            t->adjMat[i][t->size] = 0; // 邻接矩新列阵置0
         }
-        memset(t->adjMat[t->size], 0, sizeof(unsigned int) * (t->size + 1));
+        memset(t->adjMat[t->size], 0, sizeof(unsigned int) * (t->size + 1)); // 将新增行置 0
         t->size++;
         return;
     }
@@ -70,23 +76,21 @@ void addVertex(graphAdjMat *t, int val) {
         tempMat[k] = tempMatLine + k * (t->size * 2);
     }
 
-    // 原数据复制到新数组
     for (int i = 0; i < t->size; i++) {
-        memcpy(tempMat[i], t->adjMat[i], sizeof(unsigned int) * t->size);
+        memcpy(tempMat[i], t->adjMat[i], sizeof(unsigned int) * t->size); // 原数据复制到新数组
     }
 
-    // 新列置0
     for (int i = 0; i < t->size; i++) {
-        tempMat[i][t->size] = 0;
+        tempMat[i][t->size] = 0; // 将新增列置 0
     }
-    memset(tempMat[t->size], 0, sizeof(unsigned int) * (t->size + 1));
+    memset(tempMat[t->size], 0, sizeof(unsigned int) * (t->size + 1)); // 将新增行置 0
 
     // 释放原数组
     free(t->adjMat[0]);
     free(t->adjMat);
 
     // 扩容后，指向新地址
-    t->adjMat = tempMat;
+    t->adjMat = tempMat;  // 指向新的邻接矩阵地址
     t->capacity = t->size * 2;
     t->size++;
 }
@@ -98,28 +102,21 @@ void removeVertex(graphAdjMat *t, unsigned int index) {
         printf("Out of range in %s:%d\n", __FILE__, __LINE__);
         exit(1);
     }
-
-    // 清除删除的顶点，并将其后所有顶点前移
     for (int i = index; i < t->size - 1; i++) {
-        t->vertices[i] = t->vertices[i + 1];
+        t->vertices[i] = t->vertices[i + 1]; // 清除删除的顶点，并将其后所有顶点前移
     }
-
+    t->vertices[t->size - 1] = 0; // 将被前移的最后一个顶点置 0
-    // 将被前移的最后一个顶点置0
-    t->vertices[t->size - 1] = 0;
 
     // 清除邻接矩阵中删除的列
     for (int i = 0; i < t->size - 1; i++) {
         if (i < index) {
-            // 被删除列后的所有列前移
             for (int j = index; j < t->size - 1; j++) {
-                t->adjMat[i][j] = t->adjMat[i][j + 1];
+                t->adjMat[i][j] = t->adjMat[i][j + 1]; // 被删除列后的所有列前移
             }
         } else { 
-            // 被删除行的下方所有行上移
+            memcpy(t->adjMat[i], t->adjMat[i + 1], sizeof(unsigned int) * t->size); // 被删除行的下方所有行上移
-            memcpy(t->adjMat[i], t->adjMat[i + 1], sizeof(unsigned int) * t->size);
-            // 被删除列后的所有列前移
             for (int j = index; j < t->size; j++) {
-                t->adjMat[i][j] = t->adjMat[i][j + 1];
+                t->adjMat[i][j] = t->adjMat[i][j + 1]; // 被删除列后的所有列前移
             }
         }
     }
@@ -157,45 +154,41 @@ void printGraph(graphAdjMat *t) {
 }
 
 /* 构造函数 */
-graphAdjMat *newGraphic(unsigned int numberVertices, int *vertices, unsigned int **adjMat) {
+graphAdjMat *newGraphAjdMat(unsigned int numberVertices, int *vertices, unsigned int **adjMat) {
-    // 函数指针
-    graphAdjMat *newGraph = (graphAdjMat *)malloc(sizeof(graphAdjMat));
-
     // 申请内存
-    newGraph->vertices = (int *)malloc(sizeof(int) * numberVertices * 2);
+    graphAdjMat *newGraph = (graphAdjMat *)malloc(sizeof(graphAdjMat));                                          // 为图分配内存
-    newGraph->adjMat = (unsigned int **)malloc(sizeof(unsigned int *) * numberVertices * 2);
+    newGraph->vertices = (int *)malloc(sizeof(int) * numberVertices * 2);                                        // 为顶点列表分配内存
-    unsigned int *temp = (unsigned int *)malloc(sizeof(unsigned int) * numberVertices * 2 * numberVertices * 2);
+    newGraph->adjMat = (unsigned int **)malloc(sizeof(unsigned int *) * numberVertices * 2);                     // 为邻接矩阵分配二维内存
-    newGraph->size = numberVertices;
+    unsigned int *temp = (unsigned int *)malloc(sizeof(unsigned int) * numberVertices * 2 * numberVertices * 2); // 为邻接矩阵分配一维内存
-    newGraph->capacity = numberVertices * 2;
+    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;
+        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(unsigned int) * numberVertices);
+        memcpy(newGraph->adjMat[i], adjMat[i], sizeof(unsigned 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;
 }
 
 /* Driver Code */
 int main() {
-
     /* 初始化无向图 */
     int vertices[5] = {1, 3, 2, 5, 4};
     unsigned int **edge = (unsigned int **)malloc(sizeof(unsigned int *) * 5);
-
     // 用于构建二维数组的一维指针
     unsigned int *temp = (unsigned int *)malloc(sizeof(unsigned int) * 25);
     memset(temp, 0, sizeof(unsigned int) * 25);
     for (int k = 0; k < 5; k++) {
         edge[k] = temp + k * 5;
     }
-
     // 初始化边
     edge[0][1] = edge[1][0] = 1;
     edge[0][3] = edge[3][0] = 1;
@@ -203,9 +196,8 @@ int main() {
     edge[2][3] = edge[3][2] = 1;
     edge[2][4] = edge[4][2] = 1;
     edge[3][4] = edge[4][3] = 1;
-
     // 建立无向图
-    graphAdjMat *graph = newGraphic(5, vertices, edge);
+    graphAdjMat *graph = newGraphAjdMat(5, vertices, edge);
     free(edge);
     free(temp);
     printf("\n初始化后，图为:\n");

codes/c/chapter_graph/graph_bfs.c

@@ -30,11 +30,11 @@ void hashMark(hashTable *h, int index) {
 
 /* 查询顶点是否已被标记 */
 int hashQuery(hashTable *h, int index) {
-    // 若顶点已被标记，则返回 0
+    // 若顶点已被标记，则返回 1
     if (h->array[index % h->size] == 1) {
-        return 0;
-    } else {
         return 1;
+    } else {
+        return 0;
     }
 }
 
@@ -66,8 +66,8 @@ queue *newQueue(unsigned int size) {
 }
 
 /* 入队 */
-void queuePush(queue *q, Vertex *v) {
+void queuePush(queue *q, Vertex *vet) {
-    q->list[q->tail] = v;
+    q->list[q->tail] = vet;
     q->tail++;
 }
 
@@ -88,46 +88,49 @@ void freeQueue(queue *q) {
 }
 
 /* 广度优先遍历 */
-void graphBFS(graphAdjList *t) {
+// 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点
-    // 初始化队列与哈希表
+Vertex **graphBFS(graphAdjList *t, Vertex *startVet) {
+    // 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);
+    // 哈希表，用于记录已被访问过的顶点
     hashTable *visited = newHash(t->size);
-    // 将第一个元素入队
+    int resIndex = 0;
-    queuePush(que, t->verticesList[0]);
+    queuePush(que, startVet);         // 将第一个元素入队
-    hashMark(visited, t->verticesList[0]->pos);
+    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
-    printf("\n[");
     while (que->head < que->tail) {
         // 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
         Node *n = queueTop(que)->linked->head->next;
         while (n != 0) {
             // 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
-            if (hashQuery(visited, n->val->pos) != 0) {
+            if (hashQuery(visited, n->val->pos) == 1) {
-                queuePush(que, n->val);
-                hashMark(visited, n->val->pos);
-            }
                 n = n->next;
+                continue; // 跳过已被访问过的顶点
             }
-        // 打印队首元素
+            queuePush(que, n->val);         // 只入队未访问的顶点
-        if (que->head == que->tail - 1) {
+            hashMark(visited, n->val->pos); // 标记该顶点已被访问
-            printf("%d]\n", queueTop(que)->val);
-        } else {
-            printf("%d, ", queueTop(que)->val);
         }
-        // 队首元素出队
+        // 队首元素存入数组
-        queuePop(que);
+        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
     }
-    printf("\n");
 
-    // 释放队列与哈希表内存
+    // 释放内存
     freeQueue(que);
     freeHash(visited);
+    resIndex = 0;
+    // 返回顶点遍历序列
+    return res;
 }
 
+/* Driver Code */
 int main() {
-
     /* 初始化无向图 */
-    graphAdjList *graph = newGraphic(3);
+    graphAdjList *graph = newGraphAdjList(3);
     // 初始化顶点
     for (int i = 0; i < 10; i++) {
         addVertex(graph, i);
@@ -145,13 +148,19 @@ int main() {
     addEdge(graph, 5, 8);
     addEdge(graph, 6, 7);
     addEdge(graph, 7, 8);
-
     printf("\n初始化后，图为:\n");
     printGraph(graph);
+    printf("\n广度优先遍历（BFS）顶点序列为\n");
+    Vertex **vets = graphBFS(graph, graph->verticesList[0]);
 
-    printf("\n广度优先遍历（BFS）顶点序列为");
+    // 打印广度优先遍历数组
-    graphBFS(graph);
+    printf("[");
+    printf("%d", vets[0]->val);
+    for (int i = 1; i < graph->size && vets[i] != 0; i++) {
+        printf(", %d", vets[i]->val);
+    }
+    printf("]\n");
+    free(vets);
 
     return 0;
 }
-

codes/c/chapter_graph/graph_dfs.c

@@ -0,0 +1,112 @@
+/**
+ * File: graph_dfs.c
+ * Created Time: 2023-07-13
+ * Author: NI-SW (947743645@qq.com)
+ */
+
+#include "graph_adjacency_list.c"
+
+/* 哈希表 */
+struct hashTable {
+    unsigned int size;
+    unsigned int *array;
+};
+
+typedef struct hashTable hashTable;
+
+/* 初始化哈希表 */
+hashTable *newHash(unsigned int size) {
+    hashTable *h = (hashTable *)malloc(sizeof(hashTable));
+    h->array = (unsigned int *)malloc(sizeof(unsigned int) * size);
+    memset(h->array, 0, sizeof(unsigned int) * size);
+    h->size = size;
+    return h;
+}
+
+/* 标记索引过的顶点 */
+void hashMark(hashTable *h, int index) {
+    h->array[index % h->size] = 1;
+}
+
+/* 查询顶点是否已被标记 */
+int hashQuery(hashTable *h, int index) {
+    // 若顶点已被标记，则返回 1
+    if (h->array[index % h->size] == 1) {
+        return 1;
+    } else {
+        return 0;
+    }
+}
+
+/* 释放哈希表内存 */
+void freeHash(hashTable *h) {
+    free(h->array);
+    free(h);
+}
+
+/* 深度优先遍历 DFS 辅助函数 */
+int resIndex = 0;
+void dfs(graphAdjList *graph, hashTable *visited, Vertex *vet, Vertex **res) {
+    if (hashQuery(visited, vet->pos) == 1) {
+        return; // 跳过已被访问过的顶点
+    }
+    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->linked->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) {
+    // 顶点遍历序列
+    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;
+}
+
+/* Driver Code */
+int main() {
+    graphAdjList *graph = newGraphAdjList(10);
+    for (int i = 0; i < 7; i++) {
+        addVertex(graph, i);
+    }
+    addEdge(graph, 0, 1);
+    addEdge(graph, 0, 3);
+    addEdge(graph, 1, 2);
+    addEdge(graph, 2, 5);
+    addEdge(graph, 5, 4);
+    addEdge(graph, 5, 6);
+    printf("\n初始化后，图为:\n");
+    printGraph(graph);
+
+    // 深度优先遍历 DFS
+    Vertex **vet = graphDFS(graph, graph->verticesList[0]);
+
+    // 输出遍历结果
+    printf("\n深度优先遍历（DFS）顶点序列为\n");
+    printf("[");
+    printf("%d", vet[0]->val);
+    for (int i = 1; i < graph->size && vet[i] != 0; i++) {
+        printf(", %d", vet[i]->val);
+    }
+    printf("]\n");
+
+    // 释放内存
+    free(vet);
+    return 0;
+}