图的遍历算法 有两种 ：深度优先搜索遍历 和 广度 优先搜索遍历。深度优先搜索遍历类似与 树的 先序遍历。广度优先搜索遍历类似与树的层序遍历。只不过 图 可以有 不连通的 节点，所以 得 遍历 整个顶点数组。
深搜遍历 总是 先访问当前节点的邻接点，而 广搜算法 是 先访问顶点的邻接点 要 先于 后访问顶点的邻接点 被 访问。
具体遍历顺序如下：
以下代码 以 图的 邻接多重表 为 基本结构进行 遍历。
首先更改 上节 的 查找 邻接点 和 下一个邻接点的 返回值，以及 邻接点的 代码 有误,少加了 一句：
if (next->iIndex == location2 || next->jIndex == location2){
next = next->iIndex == location1 ? next->iNext : next->jNext;
break;
}
next = next->iIndex == location1 ? next->iNext : next->jNext;
int firstAdj(AMLGraph g,int location){
ArcNode * next = g.adjMuList[location].head->iNext;
if (next != NULL)
{
int index = next->iIndex == location ? next->jIndex : next->iIndex;
return index;
}
return -1;
}
int nextAdj(AMLGraph g,int location1 ,int location2){
ArcNode * next = g.adjMuList[location1].head->iNext;
while (next != NULL){
if (next->iIndex == location2 || next->jIndex == location2){
next = next->iIndex == location1 ? next->iNext : next->jNext;
break;
}
next = next->iIndex == location1 ? next->iNext : next->jNext;
}
if (next != NULL){
int index = next->iIndex == location1 ? next->jIndex : next->iIndex;
return index;
}
return -1;
}
然后 是 深搜 和 广搜的 具体代码：
void dfs(AMLGraph g,int i,bool * isVisitedArray){
printf("%c",g.adjMuList[i].vexName);
isVisitedArray[i] = true;
for (int next = firstAdj(g,i); next != -1 ; next = nextAdj(g,i,next)){
if (isVisitedArray[next] == false){
dfs(g,next,isVisitedArray);
}
}
}
//深度优先搜索遍历
void dfsTraver(AMLGraph g){
bool isVisited[MAX_VEX_NUM] = {false};
printf("----------深度优先遍历------------------\n");
for (int i = 0; i < g.vexNum; i++){
if (isVisited[i] == false){
dfs(g,i,isVisited);
}
}
printf("\n");
}
//广度优先搜索遍历
void bfsTraverse(AMLGraph g){
bool isVisited[MAX_VEX_NUM] = {false};
printf("----------广度优先遍历------------------\n");
LinkQueue queue;
queueInit(&queue);
for (int i = 0; i < g.vexNum; i++){
if (isVisited[i] == false){
printf("%c",g.adjMuList[i].vexName);
isVisited[i] = true;
enqueue(&queue,i);
while (!queueEmpty(queue)){
int top;
dequeue(&queue,&top);
for (int next = firstAdj(g,top);next != -1 ; next = nextAdj(g,top,next)){
if (isVisited[next] == false){
printf("%c",g.adjMuList[next].vexName);
isVisited[next] = true;
enqueue(&queue,next);
}
}
}
}
}
queueDestory(&queue);
}
完整 源代码如下：
广搜用到的链队代码没有放进来，想看的 可以 进网盘地址 下载 工程文件。
工程文件网盘地址：点击打开链接
// AMLGraph.cpp : 定义控制台应用程序的入口点。
//无向图的邻接多重表
#include "stdafx.h"
#include <cstdlib>
#include "queue.h"
#define MAX_VEX_NUM 20
enum E_VisitIf
{
unvisited = 0,
visited = 1,
};
struct ArcNode
{
E_VisitIf mark;
int iIndex,jIndex;//顶点i,j在图中的位置
ArcNode * iNext;//与i顶点点相关的下一个弧
ArcNode * jNext;//与j顶点点相关的下一个弧
};
struct VNode
{
char vexName;
ArcNode * head;//头指针
};
struct AMLGraph
{
VNode adjMuList[MAX_VEX_NUM];//顶点数组
int vexNum,arcNum;
};
//获取弧 的 头节点
ArcNode * getHeadNode(){
ArcNode * pNode = (ArcNode *)malloc(sizeof(ArcNode));
if (pNode){
pNode->iIndex = pNode->jIndex = -1;
pNode->iNext = pNode->jNext = NULL;
pNode->mark = unvisited;
}
return pNode;
}
ArcNode * getArcNode(int iIndex,int jIndex){
ArcNode * pNode = getHeadNode();
if (pNode){
pNode->iIndex = iIndex;
pNode->jIndex = jIndex;
}
return pNode;
}
int vexLocation(AMLGraph g,char vex){
for (int i = 0; i < g.vexNum; i++){
if (g.adjMuList[i].vexName == vex){
return i;
}
}
return -1;
}
void createGrahp(AMLGraph * g){
printf("输入图的顶点数 和 边（弧）数\n");
scanf("%d%d%*c",&g->vexNum,&g->arcNum);
//构造顶点集
printf("请输入顶点集\n");
for (int i = 0; i < g->vexNum; i++){
char name;
scanf("%c",&name);
g->adjMuList[i].vexName = name;
g->adjMuList[i].head = getHeadNode();//建立 头节点，并让头指针指向头节点
}
//构造顶点关系
fflush(stdin);
printf("请输入顶点的关系\n");
for (int i = 0; i < g->arcNum; i++){
char vex1,vex2;
scanf("%c%c%*c",&vex1,&vex2);
int location1 = vexLocation(*g,vex1);
int location2 = vexLocation(*g,vex2);
ArcNode * pNode = getArcNode(location1,location2);
pNode->iNext = g->adjMuList[location1].head->iNext;
g->adjMuList[location1].head->iNext = pNode;
pNode->jNext = g->adjMuList[location2].head->iNext;
g->adjMuList[location2].head->iNext = pNode;
}
}
void destoryGraph(AMLGraph * g){
for (int i = 0; i < g->vexNum; i++){
ArcNode * next = g->adjMuList[i].head->iNext;
while (next != NULL){
ArcNode * freeNode = next;
next = next->iIndex == i ? next->iNext : next->jNext;
if (freeNode->iIndex == i){////只释放 iIndex 等于 i的节点,要不会多次释放
free(freeNode);
}
}
free(g->adjMuList[i].head);
g->adjMuList[i].head = NULL;
g->adjMuList[i].vexName = ' ';
g->vexNum = g->arcNum = 0;
}
}
//顶点vex1 和顶点vex2 是否相邻
bool graphIsAdj(AMLGraph g,char vex1,char vex2){
int location = vexLocation(g,vex1);
ArcNode * next = g.adjMuList[location].head->iNext;
while (next != NULL){
if (g.adjMuList[next->iIndex].vexName == vex2 || g.adjMuList[next->jIndex].vexName == vex2){
return true;
}
next = next->iIndex == location ? next->iNext : next->jNext;
}
return false;
}
int graphDegree(AMLGraph g,char vex){
int degree = 0;
int location = vexLocation(g,vex);
ArcNode * next = g.adjMuList[location].head->iNext;//计算所有出度
while (next != NULL){
degree++;
next = next->iIndex == location ? next->iNext : next->jNext;
}
return degree;
}
//插入边（弧）
void insertArc(AMLGraph * g,char vex1,char vex2){
int location1 = vexLocation(*g,vex1);
int location2 = vexLocation(*g,vex2);
ArcNode * node = getArcNode(location1,location2);
node->iNext = g->adjMuList[location1].head->iNext;
g->adjMuList[location1].head->iNext = node;
node->jNext = g->adjMuList[location2].head->iNext;
g->adjMuList[location2].head->iNext = node;
g->arcNum ++;
}
//删除边（弧）
void deleteArc(AMLGraph * g,char vex1,char vex2){
g->arcNum--;
int location1 = vexLocation(*g,vex1);
int location2 = vexLocation(*g,vex2);
ArcNode * next = g->adjMuList[location1].head->iNext;
ArcNode * pre = g->adjMuList[location1].head;
while (next != NULL){
if (next->iIndex == location2){
if (pre == g->adjMuList[location1].head || pre->iIndex == location1){//删除的是第一个节点.或者 前驱的index = location1
pre->iNext = next->jNext;
}
else{
pre->jNext = next->jNext;
}
break;
}
else if(next->jIndex == location2){
if (pre == g->adjMuList[location1].head || pre->iIndex == location1){//删除的是第一个节点.或者 前驱的index = location1
pre->iNext = next->iNext;
}
else{
pre->jNext = next->iNext;
}
break;
}
pre = next;
next = next->iIndex == location1 ? next->iNext : next->jNext;
}
next = g->adjMuList[location2].head->iNext;
pre = g->adjMuList[location2].head;
while (next != NULL){
if (next->iIndex == location1){
if (pre == g->adjMuList[location2].head || pre->iIndex == location2){//删除的是第一个节点.或者 前驱的index = location1
pre->iNext = next->jNext;
}
else{
pre->jNext = next->jNext;
}
free(next);
break;
}
else if(next->jIndex == location1){
if (pre == g->adjMuList[location2].head || pre->iIndex == location2){//删除的是第一个节点.或者 前驱的index = location1
pre->iNext = next->iNext;
}
else{
pre->jNext = next->iNext;
}
free(next);
break;
}
pre = next;
next = next->iIndex == location2 ? next->iNext : next->jNext;
}
}
//插入顶点
void insertVex(AMLGraph * g, char vex){
if (g->vexNum < MAX_VEX_NUM){
g->adjMuList[g->vexNum].vexName = vex;
g->adjMuList[g->vexNum].head = getHeadNode();
g->vexNum++;
}
}
//删除顶点
void deleteVex(AMLGraph * g,char vex){
int location = vexLocation(*g,vex);
//删除顶点 同样需要 遍历整个 图 查找 与 vex 相关的弧节点
for (int i = 0; i < g->vexNum; i++){
ArcNode * next = g->adjMuList[i].head->iNext;
while (next != NULL){
if (next->iIndex == location || next->jIndex == location){
ArcNode * delNode = next;
next = next->iIndex == location ? next->iNext : next->jNext;
char delData1 = g->adjMuList[delNode->iIndex].vexName;
char delData2 = g->adjMuList[delNode->jIndex].vexName;
deleteArc(g,delData1,delData2);
}
else{
next = next->iIndex == location ? next->iNext : next->jNext;
}
}
}
//更改因删除顶点 而导致的元素位置变化..
for (int i = 0; i < g->vexNum; i++){
ArcNode * next = g->adjMuList[i].head->iNext;
while (next != NULL){
if (next->iIndex == i){
if(next->iIndex > location){
next->iIndex --;
}
if(next->jIndex > location){
next->jIndex --;
}
}
next = next->iIndex == location ? next->iNext : next->jNext;
}
}
free(g->adjMuList[location].head);//释放头节点
//vex下面的 顶点上移
for (int i = location + 1; i < g->vexNum; i++){
g->adjMuList[i-1] = g->adjMuList[i];
}
g->vexNum --;
}
void printGrahp(AMLGraph g){
for (int i = 0; i < g.vexNum; i++){
printf("%c的 邻接点有：",g.adjMuList[i].vexName);
ArcNode * next = g.adjMuList[i].head->iNext;//删除所有弧尾
while (next != NULL){
int index = next->iIndex == i ? next->jIndex : next->iIndex;
printf("%c",g.adjMuList[index].vexName);
next = next->iIndex == i ? next->iNext : next->jNext;
}
printf("\n");
}
}
int firstAdj(AMLGraph g,int location){
ArcNode * next = g.adjMuList[location].head->iNext;
if (next != NULL)
{
int index = next->iIndex == location ? next->jIndex : next->iIndex;
return index;
}
return -1;
}
int nextAdj(AMLGraph g,int location1 ,int location2){
ArcNode * next = g.adjMuList[location1].head->iNext;
while (next != NULL){
if (next->iIndex == location2 || next->jIndex == location2){
next = next->iIndex == location1 ? next->iNext : next->jNext;
break;
}
next = next->iIndex == location1 ? next->iNext : next->jNext;
}
if (next != NULL){
int index = next->iIndex == location1 ? next->jIndex : next->iIndex;
return index;
}
return -1;
}
void dfs(AMLGraph g,int i,bool * isVisitedArray){
printf("%c",g.adjMuList[i].vexName);
isVisitedArray[i] = true;
for (int next = firstAdj(g,i); next != -1 ; next = nextAdj(g,i,next)){
if (isVisitedArray[next] == false){
dfs(g,next,isVisitedArray);
}
}
}
//深度优先搜索遍历
void dfsTraver(AMLGraph g){
bool isVisited[MAX_VEX_NUM] = {false};
printf("----------深度优先遍历------------------\n");
for (int i = 0; i < g.vexNum; i++){
if (isVisited[i] == false){
dfs(g,i,isVisited);
}
}
printf("\n");
}
//广度优先搜索遍历
void bfsTraverse(AMLGraph g){
bool isVisited[MAX_VEX_NUM] = {false};
printf("----------广度优先遍历------------------\n");
LinkQueue queue;
queueInit(&queue);
for (int i = 0; i < g.vexNum; i++){
if (isVisited[i] == false){
printf("%c",g.adjMuList[i].vexName);
isVisited[i] = true;
enqueue(&queue,i);
while (!queueEmpty(queue)){
int top;
dequeue(&queue,&top);
for (int next = firstAdj(g,top);next != -1 ; next = nextAdj(g,top,next)){
if (isVisited[next] == false){
printf("%c",g.adjMuList[next].vexName);
isVisited[next] = true;
enqueue(&queue,next);
}
}
}
}
}
queueDestory(&queue);
}
//邻接多重表
int _tmain(int argc, _TCHAR* argv[])
{
AMLGraph g;
createGrahp(&g);
printGrahp(g);
dfsTraver(g);
bfsTraverse(g);
return 0;
}
运行截图：
从 a的邻接表 可以 看到 深搜的结果： 首先访问 a 节点，然后 访问 a的 第一个 邻接点d,然后 访问 d 的第一个邻接点c，然后 访问c的第一个邻接点e,然后访问 e的 邻接点
c和b ,c被访问过了，访问b,然后 访问 b的邻接点，等等.......最后 访问 单独的 顶点 fg.
所以 深搜结果为：adcebfg
广搜结果：先访问a,再访问a的所有邻接点dcb,访问d的所有邻接点ca(都被访问过了跳过），c的所有邻接点edba,只有e没被访问，访问他，然后访问b的所有邻接点：eca等等。。。最后访问单独的顶点 fg
所以广搜结果为：adcbefg
时间： 2024-12-12 06:33:37