[本文是自己学习所做笔记，欢迎转载，但请注明出处：http://blog.csdn.net/jesson20121020]
算法描述：
设图G的初始状态是所有顶点均未被访问过，在G中的任选一顶点vi为初始出发点，则广度优先遍历 可定义如下：首先，访问初始出发点vi，接着依次访问vi的所有邻接点w1,w2,…,wk;然后，依次访问w1,w2,…,wk 的邻接的所有未被访问过的顶点，依次类推，直到图中所有的和初始点vi有路径相通的顶点都被访问过为止。
算法实现：
(1) 访问初始顶点vi
(2) 置顶点v已访问标记
(3) 顶点v入队
(4) while(队不空)｛
取出队首顶点i；
依次搜索顶点i的所有的邻接点；
如果未被访问，则访问该邻接点，并将其入队。
｝
用邻接矩阵实现图的广度优先遍历的源代码如下：
/**
* 广度遍历图
**/
void BFS_MG(MGraph MG,int s){
//清空访问标志
init_Visit();
//定义队列，用于保存当前节点的邻接顶点
int Q[MAX_VEX_NUM];
int front = 0;
int rear = 0;
int i,j,k;
printf("%c\t",MG.vexs[s]);
visit[s] = 1;
Q[rear++] = s;
//遍历队列
while(front < rear){
i = Q[front++];
for (j = 1; j <= MG.vexnum;j++){
if(visit[j] == 0 && MG.arcs[i][j] == 1){
printf("%c\t",MG.vexs[j]);
visit[j] = 1;
Q[rear++] = j;
}
}
}
}用邻接表实现图的广度优先遍历的源代码如下：
/**
* 广度遍历图
**/
void BFS_AG(ALGraph AG,int s){
ArcPtr p;
//清空访问标志
init_Visit();
//定义队列，用于保存当前节点的邻接顶点
int Q[MAX_VERTEX_NUM];
int front = 0;
int rear = 0;
int i,j,k;
printf("%c\t",AG.vertices[s]);
visit[s] = 1;
Q[rear++] = s;
//遍历队列
while(front < rear){
i = Q[front++];
for(p = AG.vertices[i].firstarc;p;p=p->nextarc){
j = p->adjvex;
if(visit[j] == 0){
printf("%c\t",AG.vertices[j].vexdata);
visit[j] = 1;
Q[rear++] = j;
}
}
}
}算法说明：
对有具有n个顶点和e条边的连通图，因为每个基点均需要入队一次，所以while语句需要执行n次，对于邻接矩阵而言，内循环搜索邻接点时同样需要执行n次，故BFS_MG的时间复杂度为O(n^2)；对于邻接表而言，内循环的次数取决于各顶点的边表结点的总个数，所以BFS_AG的时间复杂度为O(n+e)。
可以看出，广度优先遍历需要一个辅助队列，和标志数组，故空间复杂度为O(n)。
完整代码：
用邻接矩阵实现广度优先遍历的完整代码：
/*
============================================================================
Name : Graph.c
Author : jesson20121020
Version : 1.0
Description : create Graph using Adjacency Matrix, Ansi-style
============================================================================
*/
#include <stdio.h>
#include <stdlib.h>
#define MAX_VEX_NUM 50
typedef char VertexType;
typedef enum {
DG, UDG
} GraphType;
typedef struct {
VertexType vexs[MAX_VEX_NUM];
int arcs[MAX_VEX_NUM][MAX_VEX_NUM];
int vexnum, arcnum;
GraphType type;
} MGraph;
//设置图中顶点访问标志
int visit[MAX_VEX_NUM];
/**
* 根据名称得到指定顶点在顶点集合中的下标
* vex 顶点
* return 如果找到，则返回下标，否则，返回０
*/
int getIndexOfVexs(char vex, MGraph *MG) {
int i;
for (i = 1; i <= MG->vexnum; i++) {
if (MG->vexs[i] == vex) {
return i;
}
}
return 0;
}
/**
* 创建邻接矩阵
*/
void create_MG(MGraph *MG) {
int i, j, k;
int v1, v2, type;
char c1, c2;
printf("Please input graph type DG(0) or UDG(1) :");
scanf("%d", &type);
if (type == 0)
MG->type = DG;
else if (type == 1)
MG->type = UDG;
else {
printf("Please input correct graph type DG(0) or UDG(1)!");
return;
}
printf("Please input vexmun : ");
scanf("%d", &MG->vexnum);
printf("Please input arcnum : ");
scanf("%d", &MG->arcnum);
getchar();
for (i = 1; i <= MG->vexnum; i++) {
printf("Please input %dth vex(char):", i);
scanf("%c", &MG->vexs[i]);
getchar();
}
//初始化邻接矩阵
for (i = 1; i <= MG->vexnum; i++) {
for (j = 1; j <= MG->vexnum; j++) {
MG->arcs[i][j] = 0;
}
}
//输入边的信息，建立邻接矩阵
for (k = 1; k <= MG->arcnum; k++) {
printf("Please input %dth arc v1(char) v2(char) : ", k);
scanf("%c %c", &c1, &c2);
v1 = getIndexOfVexs(c1, MG);
v2 = getIndexOfVexs(c2, MG);
if (MG->type == 1)
MG->arcs[v1][v2] = MG->arcs[v2][v1] = 1;
else
MG->arcs[v1][v2] = 1;
getchar();
}
}
/**
* 打印邻接矩阵和顶点信息
*/
void print_MG(MGraph MG) {
int i, j;
if(MG.type == DG){
printf("Graph type: Direct graph\n");
}
else{
printf("Graph type: Undirect graph\n");
}
printf("Graph vertex number: %d\n",MG.vexnum);
printf("Graph arc number: %d\n",MG.arcnum);
printf("Vertex set:\n ");
for (i = 1; i <= MG.vexnum; i++)
printf("%c\t", MG.vexs[i]);
printf("\nAdjacency Matrix:\n");
for (i = 1; i <= MG.vexnum; i++) {
j = 1;
for (; j < MG.vexnum; j++) {
printf("%d\t", MG.arcs[i][j]);
}
printf("%d\n", MG.arcs[i][j]);
}
}
/**
* 初始化顶点访问标志
**/
void init_Visit(){
int i;
for(i = 0;i < MAX_VEX_NUM;i++)
visit[i] = 0;
}
/**
* 广度遍历图
**/
void BFS_MG(MGraph MG,int s){
//清空访问标志
init_Visit();
//定义队列，用于保存当前节点的邻接顶点
int Q[MAX_VEX_NUM];
int front = 0;
int rear = 0;
int i,j,k;
printf("%c\t",MG.vexs[s]);
visit[s] = 1;
Q[rear++] = s;
//遍历队列
while(front < rear){
i = Q[front++];
for (j = 1; j <= MG.vexnum;j++){
if(visit[j] == 0 && MG.arcs[i][j] == 1){
printf("%c\t",MG.vexs[j]);
visit[j] = 1;
Q[rear++] = j;
}
}
}
}
/**
* 主函数
*/
int main(void) {
MGraph MG;
create_MG(&MG);
print_MG(MG);
printf("\nThe result of BFS:\n");
BFS_MG(MG,1);
return EXIT_SUCCESS;
}
用邻接表实现广度优先遍历的完整代码：
/*
============================================================================
Name : ALGraph.c
Author : jesson20121020
Version :
Copyright : Your copyright notice
Description : Graph using linkList, Ansi-style
============================================================================
*/
#include <stdio.h>
#include <stdlib.h>
#include <stdio.h>
#define MAX_VERTEX_NUM 50
typedef enum {
DG, UDG
} GraphType;
typedef char VertexType;
//表节点
typedef struct ArcNode {
int adjvex; //邻接节点
int weight; //边权重
struct ArcNode *nextarc; //下一个节点指针
} ArcNode, *ArcPtr;
//头节点
typedef struct {
VertexType vexdata;
int id;
ArcPtr firstarc;
} VNode;
//头节点数组
typedef struct {
VNode vertices[MAX_VERTEX_NUM];
int vexnum, arcnum;
GraphType type;
} ALGraph;
int visit[MAX_VERTEX_NUM];
/**
* 根据顶点字符得到在顶点数组中的下标
*/
int getIndexOfVexs(char vex, ALGraph *AG) {
int i;
for (i = 1; i <= AG->vexnum; i++) {
if (AG->vertices[i].vexdata == vex) {
return i;
}
}
return 0;
}
/**
* 创建邻接表
*/
void create_AG(ALGraph *AG) {
ArcPtr p,q;
int i, j, k, type;
VertexType v1, v2;
printf("Please input graph type UG(0) or UDG(1) :");
scanf("%d", &type);
if (type == 0)
AG->type = DG;
else if (type == 1)
AG->type = UDG;
else {
printf("Please input correct graph type UG(0) or UDG(1)!");
return;
}
printf("please input vexnum:");
scanf("%d", &AG->vexnum);
printf("please input arcnum:");
scanf("%d", &AG->arcnum);
getchar();
for (i = 1; i <= AG->vexnum; i++) {
printf("please input the %dth vex(char) : ", i);
scanf("%c", &AG->vertices[i].vexdata);
getchar();
AG->vertices[i].firstarc = NULL;
}
for (k = 1; k <= AG->arcnum; k++) {
printf("please input the %dth arc v1(char) v2(char) :", k);
scanf("%c %c", &v1, &v2);
i = getIndexOfVexs(v1, AG);
j = getIndexOfVexs(v2, AG);
//根据图的类型创建邻接表
//方法1，插入到链表头
/*
if (AG->type == DG) { //有向图
p = (ArcPtr) malloc(sizeof(ArcNode));
p->adjvex = j;
p->nextarc = AG->vertices[i].firstarc;
AG->vertices[i].firstarc = p;
} else { //无向图
p = (ArcPtr) malloc(sizeof(ArcNode));
p->adjvex = j;
p->nextarc = AG->vertices[i].firstarc;
AG->vertices[i].firstarc = p;
p = (ArcPtr) malloc(sizeof(ArcNode));
p->adjvex = i;
p->nextarc = AG->vertices[j].firstarc;
AG->vertices[j].firstarc = p;
}
*/
//方法2，插入到链表尾
if (AG->type == DG) { //有向图
p = (ArcPtr) malloc(sizeof(ArcNode));
p->adjvex = j;
//表为空
if(AG->vertices[i].firstarc == NULL){
AG->vertices[i].firstarc = p;
}
else{
//找最后一个表节点
q = AG->vertices[i].firstarc;
while(q->nextarc != NULL){
q = q->nextarc;
}
q->nextarc = p;
}
p->nextarc = NULL;
} else { //无向图
p = (ArcPtr) malloc(sizeof(ArcNode));
p->adjvex = j;
//表为空
if(AG->vertices[i].firstarc == NULL){
AG->vertices[i].firstarc = p;
}
else{
//找最后一个表节点
q = AG->vertices[i].firstarc;
while(q->nextarc != NULL){
q = q->nextarc;
}
q->nextarc = p;
}
p->nextarc = NULL;
p = (ArcPtr) malloc(sizeof(ArcNode));
p->adjvex = i;
//表为空
if(AG->vertices[j].firstarc == NULL){
AG->vertices[j].firstarc = p;
}
else{
//找最后一个表节点
q = AG->vertices[j].firstarc;
while(q->nextarc != NULL){
q = q->nextarc;
}
q->nextarc = p;
}
p->nextarc = NULL;
}
getchar();
}
}
/**
* 输出图的相关信息
*/
void print_AG(ALGraph AG) {
ArcPtr p;
int i;
if (AG.type == DG) {
printf("Graph type: Direct graph\n");
} else {
printf("Graph type: Undirect graph\n");
}
printf("Graph vertex number: %d\n", AG.vexnum);
printf("Graph arc number: %d\n", AG.arcnum);
printf("Vertex set :\n");
for (i = 1; i <= AG.vexnum; i++)
printf("%c\t", AG.vertices[i].vexdata);
printf("\nAdjacency List:\n");
for (i = 1; i <= AG.vexnum; i++) {
printf("%d", i);
p = AG.vertices[i].firstarc;
while (p != NULL) {
printf("-->%d", p->adjvex);
p = p->nextarc;
}
printf("\n");
}
}
/**
* 初始化顶点访问标志
**/
void init_Visit(){
int i;
for(i = 0;i < MAX_VERTEX_NUM;i++)
visit[i] = 0;
}
/**
* 广度遍历图
**/
void BFS_AG(ALGraph AG,int s){
ArcPtr p;
//清空访问标志
init_Visit();
//定义队列，用于保存当前节点的邻接顶点
int Q[MAX_VERTEX_NUM];
int front = 0;
int rear = 0;
int i,j,k;
printf("%c\t",AG.vertices[s]);
visit[s] = 1;
Q[rear++] = s;
//遍历队列
while(front < rear){
i = Q[front++];
for(p = AG.vertices[i].firstarc;p;p=p->nextarc){
j = p->adjvex;
if(visit[j] == 0){
printf("%c\t",AG.vertices[j].vexdata);
visit[j] = 1;
Q[rear++] = j;
}
}
}
}
int main(void) {
ALGraph AG;
create_AG(&AG);
print_AG(AG);
printf("\nThe result of BFS:\n");
BFS_AG(AG,1);
return EXIT_SUCCESS;
}