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feat: Reimplement the graph code for C (#901)

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* Reimplement the graph code for C

* Free memory of **vertices.
This commit is contained in:
Yudong Jin
2023-10-29 19:52:19 +08:00
committed by GitHub
parent db5d1d21f3
commit 9c28619839
7 changed files with 422 additions and 614 deletions
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367
codes/c/chapter_graph/graph_adjacency_list.c
View File

@ -6,259 +6,166 @@
#include "../utils/common.h"
typedef struct Vertex Vertex;
typedef struct Node Node;
typedef struct LinkedList LinkedList;
// 假设节点最大数量为 100
#define MAX_SIZE 100
void freeVertex(Vertex *);
void freeLinklist(LinkedList *);
LinkedList *newLinklist(Vertex *);
/* 节点结构体 */
typedef struct AdjListNode {
Vertex *vertex; // 顶点
struct AdjListNode *next; // 后继节点
} AdjListNode;
/* 链表节点 */
struct Node {
// 链表节点内包含顶点类和下一个节点地址
Vertex *val;
Node *next;
};
/* 链表节点构造函数 */
Node *newNode() {
Node *n = (Node *)malloc(sizeof(Node));
n->next = 0;
n->val = 0;
return n;
}
/* 顶点节点类 */
struct Vertex {
// 节点值
int val;
// 与其它节点相连接的边的链表
LinkedList *list;
// 索引位，标记该顶点在顶点列表中的索引
unsigned int pos;
};
/* 顶点节点构造函数 */
Vertex *newVertex(int val) {
Vertex *vet = (Vertex *)malloc(sizeof(Vertex));
// 为新节点赋值并建立该节点的链表
vet->val = val;
vet->list = newLinklist(vet);
return vet;
}
/* 顶点内存释放函数 */
void freeVertex(Vertex *val) {
// 释放该顶点和该顶点的链表的内存
freeLinklist(val->list);
free(val);
}
/* 链表 */
struct LinkedList {
Node *head;
Node *tail;
};
/* 链表头插法 */
void pushFront(LinkedList *list, Vertex *val) {
Node *temp = newNode();
temp->val = val;
temp->next = list->head->next;
list->head->next = temp;
if (list->tail == list->head) {
list->tail = temp;
}
}
/* 链表尾插法 */
void pushBack(LinkedList *list, Vertex *val) {
Node *temp = newNode();
temp->val = val;
temp->next = 0;
list->tail->next = temp;
list->tail = temp;
}
/* 根据顶点地址与该顶点连接的删除边 */
void removeLink(LinkedList *list, Vertex *val) {
Node *temp = list->head->next;
Node *front = list->head;
while (temp != 0) {
if (temp->val == val) {
front->next = temp->next;
if (list->tail == temp) {
list->tail = front;
}
free(temp);
return;
}
front = temp;
temp = temp->next;
}
if (temp->next == 0) {
printf("vertex not found!\n");
}
}
/* 根据顶点地址删除顶点 */
void removeItem(LinkedList *list, Vertex *val) {
Node *temp = list->head->next;
Node *front = list->head;
while (temp != 0) {
if (temp->val == val) {
front->next = temp->next;
if (list->tail == temp) {
list->tail = front;
}
freeVertex(val);
free(temp);
return;
}
front = temp;
temp = temp->next;
}
if (temp->next == 0) {
printf("vertex not found!\n");
}
}
/* 释放链表内存 */
void freeLinklist(LinkedList *list) {
Node *temp = list->head->next;
while (temp != 0) {
free(list->head);
list->head = temp;
temp = temp->next;
}
free(list->head);
list->head = 0;
free(list);
}
/* 链表构造函数 */
LinkedList *newLinklist(Vertex *val) {
LinkedList *newLinklist = (LinkedList *)malloc(sizeof(LinkedList));
newLinklist->head = newNode();
newLinklist->head->val = val;
newLinklist->tail = newLinklist->head;
newLinklist->head->next = 0;
return newLinklist;
}
/* 基于邻接链表实现的无向图类结构 */
/* 基于邻接表实现的无向图类 */
typedef struct {
Vertex **vertices; // 邻接表
unsigned int size; // 顶点数量
unsigned int capacity; // 顶点容量
AdjListNode *heads[MAX_SIZE]; // 节点数组
int size; // 节点数量
} GraphAdjList;
/* 添加边 */
void addEdge(GraphAdjList *graph, int i, int j) {
// 越界检查
if (i < 0 || j < 0 || i == j || i >= graph->size || j >= graph->size) {
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
return;
/* 构造函数 */
GraphAdjList *newGraphAdjList() {
GraphAdjList *graph = (GraphAdjList *)malloc(sizeof(GraphAdjList));
if (!graph) {
return NULL;
}
// 查找欲添加边的顶点 vet1 - vet2
Vertex *vet1 = graph->vertices[i];
Vertex *vet2 = graph->vertices[j];
// 连接顶点 vet1 - vet2
pushBack(vet1->list, vet2);
pushBack(vet2->list, vet1);
graph->size = 0;
for (int i = 0; i < MAX_SIZE; i++) {
graph->heads[i] = NULL;
}
return graph;
}
/* 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;
}
/* 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);
}
/* 删除边 */
void removeEdge(GraphAdjList *graph, int i, int j) {
// 越界检查
if (i < 0 || j < 0 || i == j || i >= graph->size || j >= graph->size) {
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
return;
}
// 查找欲删除边的顶点 vet1 - vet2
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);
void removeEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {
AdjListNode *head1 = findNode(graph, vet1);
AdjListNode *head2 = findNode(graph, vet2);
assert(head1 != NULL && head2 != NULL);
// 删除边 vet1 - vet2
removeEdgeHelper(head1, head2->vertex);
removeEdgeHelper(head2, head1->vertex);
}
/* 添加顶点 */
void addVertex(GraphAdjList *graph, int val) {
// 若大小超过容量，则扩容
if (graph->size >= graph->capacity) {
Vertex **tempList = (Vertex **)malloc(sizeof(Vertex *) * 2 * graph->capacity);
memcpy(tempList, graph->vertices, sizeof(Vertex *) * graph->size);
free(graph->vertices); // 释放原邻接表内存
graph->vertices = tempList; // 指向新邻接表
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++;
void addVertex(GraphAdjList *graph, Vertex *vet) {
assert(graph != NULL && graph->size < MAX_SIZE);
AdjListNode *head = (AdjListNode *)malloc(sizeof(AdjListNode));
head->vertex = vet;
head->next = NULL;
// 在邻接表中添加一个新链表
graph->heads[graph->size++] = head;
}
/* 删除顶点 */
void removeVertex(GraphAdjList *graph, unsigned int index) {
// 越界检查
if (index < 0 || index >= graph->size) {
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
exit(1);
void removeVertex(GraphAdjList *graph, Vertex *vet) {
AdjListNode *node = findNode(graph, vet);
assert(node != NULL);
// 在邻接表中删除顶点 vet 对应的链表
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
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;
// 遍历其他顶点的链表，删除所有包含 vet 的边
for (int i = 0; i < graph->size; i++) {
cur = graph->heads[i];
pre = NULL;
while (cur) {
pre = cur;
cur = cur->next;
if (cur && cur->vertex == vet) {
pre->next = cur->next;
free(cur);
break;
}
}
}
// 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;
// 将该顶点之后的顶点向前移动，以填补空缺
int i;
for (i = 0; i < graph->size; i++) {
if (graph->heads[i] == node)
break;
}
// 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
for (int j = i; j < graph->size - 1; j++) {
graph->heads[j] = graph->heads[j + 1];
}
graph->vertices[graph->size - 1] = 0;
graph->size--;
// 释放内存
freeVertex(vet);
free(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;
printf("%d: [", graph->vertices[i]->val);
while (n != 0) {
if (n->next != 0) {
printf("%d, ", n->val->val);
} else {
printf("%d", n->val->val);
}
n = n->next;
/* 打印邻接表 */
void printGraph(const GraphAdjList *graph) {
printf("邻接表 =\n");
for (int i = 0; i < graph->size; ++i) {
AdjListNode *node = graph->heads[i];
printf("%d: [", node->vertex->val);
node = node->next;
while (node) {
printf("%d, ", node->vertex->val);
node = node->next;
}
printf("]\n");
}
}
/* 构造函数 */
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->vertices = (Vertex **)malloc(sizeof(Vertex *) * verticesCapacity); // 为顶点列表分配内存
memset(newGraph->vertices, 0, sizeof(Vertex *) * verticesCapacity); // 顶点列表置 0
newGraph->size = 0; // 初始化顶点数量
newGraph->capacity = verticesCapacity; // 初始化顶点容量
// 返回图指针
return newGraph;
}

52
codes/c/chapter_graph/graph_adjacency_list_test.c
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@ -8,46 +8,48 @@
/* Driver Code */
int main() {
/* 初始化无向图 */
GraphAdjList *graph = newGraphAdjList(5);
// 初始化顶点
addVertex(graph, 1);
addVertex(graph, 3);
addVertex(graph, 2);
addVertex(graph, 5);
addVertex(graph, 4);
// 初始化边
addEdge(graph, 0, 1);
addEdge(graph, 0, 3);
addEdge(graph, 1, 2);
addEdge(graph, 2, 3);
addEdge(graph, 2, 4);
addEdge(graph, 3, 4);
printf("\n初始化后，图为:\n");
int vals[] = {1, 3, 2, 5, 4};
int size = sizeof(vals) / sizeof(vals[0]);
Vertex **v = valsToVets(vals, size);
Vertex *edges[][2] = {{v[0], v[1]}, {v[0], v[3]}, {v[1], v[2]}, {v[2], v[3]}, {v[2], v[4]}, {v[3], v[4]}};
int egdeSize = sizeof(edges) / sizeof(edges[0]);
GraphAdjList *graph = newGraphAdjList();
// 添加所有顶点和边
for (int i = 0; i < size; i++) {
addVertex(graph, v[i]);
}
for (int i = 0; i < egdeSize; i++) {
addEdge(graph, edges[i][0], edges[i][1]);
}
printf("\n初始化后，图为\n");
printGraph(graph);
/* 添加边 */
// 顶点 1, 2 的索引分别为 0, 2
addEdge(graph, 0, 2);
printf("\n添加边 1-2 后图为\n");
// 顶点 1, 2 即 v[0], v[2]
addEdge(graph, v[0], v[2]);
printf("\n添加边 1-2 后，图为\n");
printGraph(graph);
/* 删除边 */
// 顶点 1, 3 的索引分别为 0, 1
removeEdge(graph, 0, 1);
// 顶点 1, 3 即 v[0], v[1]
removeEdge(graph, v[0], v[1]);
printf("\n删除边 1-3 后，图为\n");
printGraph(graph);
/* 添加顶点 */
addVertex(graph, 6);
Vertex *v5 = newVertex(6);
addVertex(graph, v5);
printf("\n添加顶点 6 后，图为\n");
printGraph(graph);
/* 删除顶点 */
// 顶点 3 的索引为 1
removeVertex(graph, 1);
printf("\n删除顶点 3 后，图为\n");
// 顶点 3 即 v[1]
removeVertex(graph, v[1]);
printf("\n删除顶点 3 后，图为:\n");
printGraph(graph);
// 释放内存
delGraphAdjList(graph);
free(v);
return 0;
}

247
codes/c/chapter_graph/graph_adjacency_matrix.c
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@ -6,24 +6,75 @@
#include "../utils/common.h"
/* 基于邻接矩阵实现的无向图类结构 */
// 假设顶点数量最大为 100
#define MAX_SIZE 100
/* 基于邻接矩阵实现的无向图结构体 */
typedef struct {
int *vertices; // 顶点列表
int **adjMat; // 邻接矩阵，元素代表“边”，索引代表“顶点索引”
int size; // 顶点数量
int capacity; // 图容量
int vertices[MAX_SIZE];
int adjMat[MAX_SIZE][MAX_SIZE];
int size;
} 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__);
exit(1);
fprintf(stderr, "边索引越界或相等\n");
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;
}
@ -31,186 +82,64 @@ void addEdge(GraphAdjMat *graph, int i, int j) {
/* 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__);
exit(1);
fprintf(stderr, "边索引越界或相等\n");
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 */
void addVertex(GraphAdjMat *graph, 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 (graph->size < graph->capacity) {
graph->vertices[graph->size] = val; // 初始化新顶点值
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);
}
/* 打印邻接矩阵 */
void printGraphAdjMat(GraphAdjMat *graph) {
printf("顶点列表 = ");
printArray(graph->vertices, graph->size);
printf("邻接矩阵 =\n");
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;
}
/* Driver Code */
int main() {
/* 初始化无向图 */
int vertices[5] = {1, 3, 2, 5, 4};
int **edge = (int **)malloc(sizeof(int *) * 5);
// 用于构建二维数组的一维指针
int *temp = (int *)malloc(sizeof(int) * 25);
memset(temp, 0, sizeof(int) * 25);
for (int k = 0; k < 5; k++) {
edge[k] = temp + k * 5;
// 初始化无向图
GraphAdjMat *graph = newGraphAdjMat();
int vertices[] = {1, 3, 2, 5, 4};
for (int i = 0; i < 5; i++) {
addVertex(graph, vertices[i]);
}
// 初始化边
edge[0][1] = edge[1][0] = 1;
edge[0][3] = edge[3][0] = 1;
edge[1][2] = edge[2][1] = 1;
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 = newGraphAjdMat(5, vertices, edge);
free(edge);
free(temp);
printf("\n初始化后，图为:\n");
printGraph(graph);
int edges[][2] = {{0, 1}, {0, 3}, {1, 2}, {2, 3}, {2, 4}, {3, 4}};
for (int i = 0; i < 6; i++) {
addEdge(graph, edges[i][0], edges[i][1]);
}
printf("\n初始化后，图为\n");
printGraphAdjMat(graph);
/* 添加边 */
// 顶点 1, 2 的索引分别为 0, 2
addEdge(graph, 0, 2);
printf("\n添加边 1-2 后图为\n");
printGraph(graph);
printf("\n添加边 1-2 后，图为\n");
printGraphAdjMat(graph);
/* 删除边 */
// 顶点 1, 3 的索引分别为 0, 1
removeEdge(graph, 0, 1);
printf("\n删除边 1-3 后，图为\n");
printGraph(graph);
printGraphAdjMat(graph);
/* 添加顶点 */
addVertex(graph, 6);
printf("\n添加顶点 6 后，图为\n");
printGraph(graph);
printGraphAdjMat(graph);
/* 删除顶点 */
// 顶点 3 的索引为 1
removeVertex(graph, 1);
printf("\n删除顶点 3 后，图为\n");
printGraph(graph);
printGraphAdjMat(graph);
// 释放内存
free(graph);
return 0;
}

197
codes/c/chapter_graph/graph_bfs.c
View File

@ -6,156 +6,111 @@
#include "graph_adjacency_list.c"
/* 哈希表 */
// 假设节点最大数量为 100
#define MAX_SIZE 100
/* 节点队列结构体 */
typedef struct {
unsigned int size;
unsigned int *array;
} 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);
}
/* 队列 */
typedef struct {
Vertex **list;
unsigned int size;
int head;
int tail;
Vertex *vertices[MAX_SIZE];
int front, rear, size;
} Queue;
/* 初始化队列 */
Queue *newQueue(unsigned int size) {
/* 构造函数 */
Queue *newQueue() {
Queue *q = (Queue *)malloc(sizeof(Queue));
q->size = size;
q->list = (Vertex **)malloc(sizeof(Vertex *) * size);
q->head = 0;
q->tail = 0;
q->front = q->rear = q->size = 0;
return q;
}
/* 入队 */
void queuePush(Queue *q, Vertex *vet) {
q->list[q->tail] = vet;
q->tail++;
/* 判断队列是否为空 */
int isEmpty(Queue *q) {
return q->size == 0;
}
/* 出队 */
void queuePop(Queue *q) {
q->head++;
/* 入队操作 */
void enqueue(Queue *q, Vertex *vet) {
q->vertices[q->rear] = vet;
q->rear = (q->rear + 1) % MAX_SIZE;
q->size++;
}
/* 队首元素 */
Vertex *queueTop(Queue *q) {
return q->list[q->head];
/* 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;
}
/* 释放队列内存 */
void freeQueue(Queue *q) {
free(q->list);
free(q);
/* 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 */
/* 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) {
// 顶点遍历序列
Vertex **res = (Vertex **)malloc(sizeof(Vertex *) * t->size);
memset(res, 0, sizeof(Vertex *) * t->size);
void graphBFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize, Vertex **visited, int *visitedSize) {
// 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);
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
Queue *queue = newQueue();
enqueue(queue, startVet);
visited[(*visitedSize)++] = startVet;
// 以顶点 vet 为起点，循环直至访问完所有顶点
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)->list->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) == 1) {
n = n->next;
continue; // 跳过已被访问过的顶点
while (!isEmpty(queue)) {
Vertex *vet = dequeue(queue); // 队首顶点出队
res[(*resSize)++] = vet; // 记录访问顶点
// 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(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
hashMark(visited, n->val->pos); // 标记该顶点已被访问
node = node->next;
}
// 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);
freeHash(visited);
resIndex = 0;
// 返回顶点遍历序列
return res;
free(queue);
}
/* Driver Code */
int main() {
/* 初始化无向图 */
GraphAdjList *graph = newGraphAdjList(3);
// 初始化顶点
for (int i = 0; i < 10; i++) {
addVertex(graph, i);
// 初始化无向图
int vals[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
int size = sizeof(vals) / sizeof(vals[0]);
Vertex **v = valsToVets(vals, size);
Vertex *edges[][2] = {{v[0], v[1]}, {v[0], v[3]}, {v[1], v[2]}, {v[1], v[4]}, {v[2], v[5]}, {v[3], v[4]},
{v[3], v[6]}, {v[4], v[5]}, {v[4], v[7]}, {v[5], v[8]}, {v[6], v[7]}, {v[7], v[8]}};
int egdeSize = sizeof(edges) / sizeof(edges[0]);
GraphAdjList *graph = newGraphAdjList();
// 添加所有顶点和边
for (int i = 0; i < size; i++) {
addVertex(graph, v[i]);
}
// 初始化边
addEdge(graph, 0, 1);
addEdge(graph, 0, 3);
addEdge(graph, 1, 2);
addEdge(graph, 1, 4);
addEdge(graph, 2, 5);
addEdge(graph, 3, 4);
addEdge(graph, 3, 6);
addEdge(graph, 4, 5);
addEdge(graph, 4, 7);
addEdge(graph, 5, 8);
addEdge(graph, 6, 7);
addEdge(graph, 7, 8);
printf("\n初始化后，图为:\n");
for (int i = 0; i < egdeSize; i++) {
addEdge(graph, edges[i][0], edges[i][1]);
}
printf("\n初始化后，图为\n");
printGraph(graph);
// 广度优先遍历 BFS
// 顶点遍历序列
Vertex *res[MAX_SIZE];
int resSize = 0;
// 用于记录已被访问过的顶点
Vertex *visited[MAX_SIZE];
int visitedSize = 0;
graphBFS(graph, v[0], res, &resSize, visited, &visitedSize);
printf("\n广度优先遍历（BFS）顶点序列为\n");
Vertex **vets = graphBFS(graph, graph->vertices[0]);
// 打印广度优先遍历数组
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);
printArray(vetsToVals(res, resSize), resSize);
// 释放内存
delGraphAdjList(graph);
free(v);
return 0;
}

123
codes/c/chapter_graph/graph_dfs.c
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@ -6,105 +6,70 @@
#include "graph_adjacency_list.c"
/* 哈希表 */
typedef struct {
unsigned int size;
unsigned int *array;
} HashTable;
// 假设节点最大数量为 100
#define MAX_SIZE 100
/* 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;
/* 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;
}
}
}
/* 释放哈希表内存 */
void freeHash(HashTable *h) {
free(h->array);
free(h);
return 0;
}
/* 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
void dfs(GraphAdjList *graph, Vertex **res, int *resSize, Vertex *vet) {
// 记录访问顶点
res[(*resSize)++] = vet;
// 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) {
// 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;
void graphDFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize) {
dfs(graph, res, resSize, startVet);
}
/* Driver Code */
int main() {
GraphAdjList *graph = newGraphAdjList(10);
for (int i = 0; i < 7; i++) {
addVertex(graph, i);
// 初始化无向图
int vals[] = {0, 1, 2, 3, 4, 5, 6};
int size = sizeof(vals) / sizeof(vals[0]);
Vertex **v = valsToVets(vals, size);
Vertex *edges[][2] = {{v[0], v[1]}, {v[0], v[3]}, {v[1], v[2]}, {v[2], v[5]}, {v[4], v[5]}, {v[5], v[6]}};
int egdeSize = sizeof(edges) / sizeof(edges[0]);
GraphAdjList *graph = newGraphAdjList();
// 添加所有顶点和边
for (int i = 0; i < size; i++) {
addVertex(graph, v[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");
for (int i = 0; i < egdeSize; i++) {
addEdge(graph, edges[i][0], edges[i][1]);
}
printf("\n初始化后，图为\n");
printGraph(graph);
// 深度优先遍历 DFS
Vertex **vet = graphDFS(graph, graph->vertices[0]);
// 输出遍历结果
Vertex *res[MAX_SIZE];
int resSize = 0;
graphDFS(graph, v[0], res, &resSize);
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");
printArray(vetsToVals(res, resSize), resSize);
// 释放内存
free(vet);
delGraphAdjList(graph);
free(v);
return 0;
}

1
codes/c/utils/common.h
View File

@ -18,6 +18,7 @@
#include "list_node.h"
#include "print_util.h"
#include "tree_node.h"
#include "vertex.h"
// hash table lib
#include "uthash.h"

49
codes/c/utils/vertex.h Normal file
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@ -0,0 +1,49 @@
/**
* File: vertex.h
* Created Time: 2023-10-28
* Author: Krahets (krahets@163.com)
*/
#ifndef VERTEX_H
#define VERTEX_H
#ifdef __cplusplus
extern "C" {
#endif
/* 顶点结构体 */
typedef struct {
int val;
} Vertex;
/* 构造函数，初始化一个新节点 */
Vertex *newVertex(int val) {
Vertex *vet;
vet = (Vertex *)malloc(sizeof(Vertex));
vet->val = val;
return vet;
}
/* 将值数组转换为顶点数组 */
Vertex **valsToVets(int *vals, int size) {
Vertex **vertices = (Vertex **)malloc(size * sizeof(Vertex *));
for (int i = 0; i < size; ++i) {
vertices[i] = newVertex(vals[i]);
}
return vertices;
}
/* 将顶点数组转换为值数组 */
int *vetsToVals(Vertex **vertices, int size) {
int *vals = (int *)malloc(size * sizeof(int));
for (int i = 0; i < size; ++i) {
vals[i] = vertices[i]->val;
}
return vals;
}
#ifdef __cplusplus
}
#endif
#endif // VERTEX_H