邻接表介绍
邻接矩阵是不错的一种图存储结构，但是我们也发现，对于边数相对顶点较少的图，这种结构比较较浪费存储空间。如果不想浪费存储空间，大家肯定会先到链表。需要空间的时候再才想内存去申请，同样适用于图的存储。我们把这种数组与链表相结合的存储方式成为邻接表（Adjacency List）。关于邻接矩阵的详细介绍请看：图：图的邻接矩阵创建、深度优先遍历和广度优先遍历详解 。
邻接表创建图
我们创建边表的单链表时，可以使用头插法和尾插法创建，不过尾插法要麻烦一点，需要先创建头结点，最后还要释放头结点，不过2种方法 效果一样。
//邻接表创建无向网图
GraphAdjList* CreateGraphAdjList()
{
GraphAdjList* graph = (GraphAdjList*)malloc(sizeof(GraphAdjList));
int vexNum, edgeNum;
printf("请输入顶点和边数(用逗号隔开):");
scanf("%d,%d",&vexNum,&edgeNum);
graph->edgeNun = edgeNum;
graph->vexNum = vexNum;
getchar();//消除上面的换行符
printf("请输入顶点的值:");
////输入顶点值
//for (int i = 0; i < vexNum; i++)
//{
// scanf("%c", &graph->list[i].data);
// graph->list[i].first = NULL;//初始化first指针域
//}
////输入边表数据
//for (int k = 0; k < edgeNum; k++)
//{
// int i, j, w;
// printf("请输入(Vi,Vj)对应的顶点下标和权值(用逗号隔开):");
// scanf("%d,%d,%d", &i, &j, &w);
// //i -> j i出度到j
// EdgeNode* edge = (EdgeNode*)malloc(sizeof(EdgeNode));//创建边结点
// edge->vexIndex = j;
// edge->weight = w;
// edge->next = graph->list[i].first;//头插法 往单链表插入结点
// graph->list[i].first = edge;
// //由于是无向的，实现上是双向的，故边数据(Vj,Vi)也要创建
// //j -> i j出度到i
// edge = (EdgeNode*)malloc(sizeof(EdgeNode));
// edge->vexIndex = i;
// edge->weight = w;
// edge->next = graph->list[j].first;;
// graph->list[j].first = edge;
//}
//每个单链表的尾指针数组
EdgeNode** tailArr = (EdgeNode**)malloc(sizeof(EdgeNode*)*vexNum);
//输入顶点值
for (int i = 0; i < vexNum; i++)
{
scanf("%c", &graph->list[i].data);
graph->list[i].first = (EdgeNode*)malloc(sizeof(EdgeNode));//创建头结点，采用尾插入
graph->list[i].first->next = NULL;
tailArr[i] = graph->list[i].first;
}
//输入边表数据
for (int k = 0; k < edgeNum; k++)
{
int i, j, w;
printf("请输入(Vi,Vj)对应的顶点下标和权值(用逗号隔开):");
scanf("%d,%d,%d", &i, &j, &w);
//i -> j i出度到j
EdgeNode* edge = (EdgeNode*)malloc(sizeof(EdgeNode));//创建边结点
edge->vexIndex = j;
edge->weight = w;
edge->next = NULL;
tailArr[i]->next = edge; //采用尾插法
tailArr[i] = edge;
edge = (EdgeNode*)malloc(sizeof(EdgeNode));
edge->vexIndex = i;
edge->weight = w;
edge->next = NULL;
tailArr[j]->next = edge;
tailArr[j] = edge;
}
//将头结点释放
for (int i = 0; i < vexNum; i++)
{
EdgeNode* head = graph->list[i].first;
graph->list[i].first = head->next;
free(head);
}
return graph;
}邻接表的深度优先遍历
void DFTGraphAdjList(GraphAdjList* graph,int vexIndex)
{
//访问过不再访问
if (g_visited[vexIndex] == TRUE)
{
return;
}
g_visited[vexIndex] = TRUE;
VisitGraphAdjListVertex(graph->list[vexIndex].data);
EdgeNode* node = graph->list[vexIndex].first;
while (node)
{
DFTGraphAdjList(graph, node->vexIndex);
node = node->next;
}
return;
}
//深度优先遍历邻接表
void TraverseGraphAdjList(GraphAdjList* graph)
{
if (NULL == graph)
{
return;
}
for (int i = 0; i < graph->vexNum; i++)
{
g_visited[i] = FALSE;
}
for (int i = 0; i < graph->vexNum; i++)
{
if (g_visited[i] == FALSE)
{
DFTGraphAdjList(graph, i);
}
}
return;
}邻接表的广度优先遍历
//广度优先遍历邻接表
void BFTGraphAdjList(GraphAdjList* graph)
{
if (NULL == graph)
{
return;
}
Queue queue;
InitQueue(&queue);
//初始化顶点都没有访问过
for (int i = 0; i < graph->vexNum; i++)
{
g_visited[i] = FALSE;
}
for (int i = 0; i < graph->vexNum; i++)
{
if (g_visited[i] == FALSE)
{
g_visited[i] = TRUE;
VertexType vex = graph->list[i].data;
VisitGraphAdjListVertex(vex);//访问顶点数据
EnQueue(&queue, i);//将访问过的顶点下标入队
//为什么这里要循环出队呢？出队获取已经访问过结点的下标，在内层的for继续访问其相关联结点，将减少外层for循环进入if次数
while (!EmptyQueue(&queue))
{
int vexIndex;
DeQueue(&queue, &vexIndex);//将访问过的顶点下标出队
EdgeNode* node = graph->list[vexIndex].first;
//将该节点的连接的结点且没有被访问过的结点进行访问，然后入队
while (node != NULL && g_visited[node->vexIndex] == FALSE)
{
g_visited[node->vexIndex] = TRUE;
VertexType vex = graph->list[node->vexIndex].data;
VisitGraphAdjListVertex(vex);
EnQueue(&queue, node->vexIndex);
node = node->next;
}
}
}
}
return;
}代码汇总
Queue.h
#pragma once
#ifndef __QUEUE_H__
#define __QUEUE_H__
typedef int EleType;//元素类型
typedef enum { ERROR, OK } Status;
typedef enum {FALSE,TRUE} Boolean;
//队列结点
typedef struct QueueNode
{
EleType data;
struct QueueNode* next;
}QueueNode;
//队列
typedef struct Queue
{
QueueNode* front;
QueueNode* tail;
}Queue;
//队列初始化
void InitQueue(Queue* queue);
//入队
int EnQueue(Queue* queue, EleType data);
//出队
int DeQueue(Queue* queue, EleType* data);
//队列是否为空
int EmptyQueue(Queue* queue);
#endif // !__QUEUE_H__
Queue.c
#include <stdlib.h>
#include "Queue.h"
//队列初始化
void InitQueue(Queue* queue)
{
queue->front = NULL;
queue->tail = NULL;
return;
}
//入队
int EnQueue(Queue* queue, EleType data)
{
if (NULL == queue)
{
return ERROR;
}
QueueNode* node = (QueueNode*)malloc(sizeof(QueueNode));
node->data = data;
node->next = NULL;
if (queue->front == NULL)
{
queue->front = queue->tail = node;
}
else
{
queue->tail->next = node;
queue->tail = node;
}
return OK;
}
//出队
int DeQueue(Queue* queue, EleType* data)
{
if (NULL == queue)
{
return ERROR;
}
if (!EmptyQueue(queue))
{
QueueNode* node = queue->front;
*data = node->data;
queue->front = queue->front->next;
if (NULL != node)
{
free(node);
node = NULL;
}
//队列的最后一个元素出队列后，tail指针也要置为空
if (EmptyQueue(queue))
{
queue->tail = queue->front;
}
}
return OK;
}
//队列是否为空
int EmptyQueue(Queue* queue)
{
if (NULL == queue)
{
return ERROR;
}
if (queue->front == NULL)
{
return TRUE;
}
return FALSE;
}GraphAdjList.c
#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <stdlib.h>
#include "Queue.h"
#define MAX_VERTEX 100
typedef char VertexType;//顶点类型
typedef int EdgeType;//边上权值类型
//边表结点数据结构
typedef struct EdgeNode
{
int vexIndex;//顶点下标
EdgeType weight;//权值
struct EdgeNode* next; //指向下一个结点
}EdgeNode;
Boolean g_visited[MAX_VERTEX] = { 0 };//全局变量 顶点访问标志位数组
//顶点表数据结构
typedef struct VextexNode
{
VertexType data;
EdgeNode* first;//边表第一个结点
}VextexNode,AdjList[MAX_VERTEX];
typedef struct GraphAdjList
{
AdjList list;
int vexNum, edgeNun;//顶点，边 的数量
}GraphAdjList;
//邻接表创建无向网图
GraphAdjList* CreateGraphAdjList()
{
GraphAdjList* graph = (GraphAdjList*)malloc(sizeof(GraphAdjList));
int vexNum, edgeNum;
printf("请输入顶点和边数(用逗号隔开):");
scanf("%d,%d",&vexNum,&edgeNum);
graph->edgeNun = edgeNum;
graph->vexNum = vexNum;
getchar();//消除上面的换行符
printf("请输入顶点的值:");
////输入顶点值
//for (int i = 0; i < vexNum; i++)
//{
// scanf("%c", &graph->list[i].data);
// graph->list[i].first = NULL;//初始化first指针域
//}
////输入边表数据
//for (int k = 0; k < edgeNum; k++)
//{
// int i, j, w;
// printf("请输入(Vi,Vj)对应的顶点下标和权值(用逗号隔开):");
// scanf("%d,%d,%d", &i, &j, &w);
// //i -> j i出度到j
// EdgeNode* edge = (EdgeNode*)malloc(sizeof(EdgeNode));//创建边结点
// edge->vexIndex = j;
// edge->weight = w;
// edge->next = graph->list[i].first;//头插法 往单链表插入结点
// graph->list[i].first = edge;
// //由于是无向的，实现上是双向的，故边数据(Vj,Vi)也要创建
// //j -> i j出度到i
// edge = (EdgeNode*)malloc(sizeof(EdgeNode));
// edge->vexIndex = i;
// edge->weight = w;
// edge->next = graph->list[j].first;;
// graph->list[j].first = edge;
//}
//每个单链表的尾指针数组
EdgeNode** tailArr = (EdgeNode**)malloc(sizeof(EdgeNode*)*vexNum);
//输入顶点值
for (int i = 0; i < vexNum; i++)
{
scanf("%c", &graph->list[i].data);
graph->list[i].first = (EdgeNode*)malloc(sizeof(EdgeNode));//创建头结点，采用尾插入
graph->list[i].first->next = NULL;
tailArr[i] = graph->list[i].first;
}
//输入边表数据
for (int k = 0; k < edgeNum; k++)
{
int i, j, w;
printf("请输入(Vi,Vj)对应的顶点下标和权值(用逗号隔开):");
scanf("%d,%d,%d", &i, &j, &w);
//i -> j i出度到j
EdgeNode* edge = (EdgeNode*)malloc(sizeof(EdgeNode));//创建边结点
edge->vexIndex = j;
edge->weight = w;
edge->next = NULL;
tailArr[i]->next = edge; //采用尾插法
tailArr[i] = edge;
edge = (EdgeNode*)malloc(sizeof(EdgeNode));
edge->vexIndex = i;
edge->weight = w;
edge->next = NULL;
tailArr[j]->next = edge;
tailArr[j] = edge;
}
//将头结点释放
for (int i = 0; i < vexNum; i++)
{
EdgeNode* head = graph->list[i].first;
graph->list[i].first = head->next;
free(head);
}
return graph;
}
//打印 邻接表的无向图
void PrintGraphAdjList(GraphAdjList* graph)
{
printf("顶点数据:\n");
//顶点数据
for (int i = 0; i < graph->vexNum; i++)
{
printf("%c ",graph->list[i].data);
}
printf("\n边数据:\n");
EdgeNode* temp = NULL;
//边数据
for (int i = 0; i < graph->vexNum; i++)
{
temp = graph->list[i].first;
while (temp)
{
printf("%d\t",temp->weight);
temp = temp->next;
}
printf("\n");
}
return;
}
//访问顶点元素
void VisitGraphAdjListVertex(VertexType data)
{
printf("%c ", data);
return;
}
void DFTGraphAdjList(GraphAdjList* graph,int vexIndex)
{
//访问过不再访问
if (g_visited[vexIndex] == TRUE)
{
return;
}
g_visited[vexIndex] = TRUE;
VisitGraphAdjListVertex(graph->list[vexIndex].data);
EdgeNode* node = graph->list[vexIndex].first;
while (node)
{
DFTGraphAdjList(graph, node->vexIndex);
node = node->next;
}
return;
}
//深度优先遍历邻接表
void TraverseGraphAdjList(GraphAdjList* graph)
{
if (NULL == graph)
{
return;
}
for (int i = 0; i < graph->vexNum; i++)
{
g_visited[i] = FALSE;
}
for (int i = 0; i < graph->vexNum; i++)
{
if (g_visited[i] == FALSE)
{
DFTGraphAdjList(graph, i);
}
}
return;
}
//广度优先遍历邻接表
void BFTGraphAdjList(GraphAdjList* graph)
{
if (NULL == graph)
{
return;
}
Queue queue;
InitQueue(&queue);
//初始化顶点都没有访问过
for (int i = 0; i < graph->vexNum; i++)
{
g_visited[i] = FALSE;
}
for (int i = 0; i < graph->vexNum; i++)
{
if (g_visited[i] == FALSE)
{
g_visited[i] = TRUE;
VertexType vex = graph->list[i].data;
VisitGraphAdjListVertex(vex);//访问顶点数据
EnQueue(&queue, i);//将访问过的顶点下标入队
//为什么这里要循环出队呢？出队获取已经访问过结点的下标，在内层的for继续访问其相关联结点，将减少外层for循环进入if次数
while (!EmptyQueue(&queue))
{
int vexIndex;
DeQueue(&queue, &vexIndex);//将访问过的顶点下标出队
EdgeNode* node = graph->list[vexIndex].first;
//将该节点的连接的结点且没有被访问过的结点进行访问，然后入队
while (node != NULL && g_visited[node->vexIndex] == FALSE)
{
g_visited[node->vexIndex] = TRUE;
VertexType vex = graph->list[node->vexIndex].data;
VisitGraphAdjListVertex(vex);
EnQueue(&queue, node->vexIndex);
node = node->next;
}
}
}
}
return;
}
int main(int argc, char *argv[])
{
GraphAdjList* graph = CreateGraphAdjList();
PrintGraphAdjList(graph);
printf("深度优先遍历邻接表:\n");
TraverseGraphAdjList(graph);
printf("\n广度优先遍历邻接表:\n");
BFTGraphAdjList(graph);
printf("\n");
return 0;
}
代码运行测试
我们来创建如下图的一个图，图是教材上的。
代码运行结果：
