广度优先遍历是连通图的一种遍历策略。其基本思想如下：
1、从图中某个顶点V0出发，并访问此顶点；
2、从V0出发，访问V0的各个未曾访问的邻接点W1，W2，…,Wk;然后,依次从W1,W2,…,Wk出发访问各自未被访问的邻接点；
3、重复步骤2，直到全部顶点都被访问为止。
例如下图中：
1.从0开始，首先找到0的关联顶点3,4 2.由3出发，找到1，2；由4出发，找到1，但是1已经遍历过，所以忽略。 3.由1出发，没有关联顶点；由2出发，没有关联顶点。 所以最后顺序是0,3,4,1,2 c语言实现如下：（使用邻接矩阵存储）
#include <stdio.h>
#include <malloc.h>
#define VERTEXNUM 5
//队列的元素
typedef struct qElement{
int value;
struct qElement* pre;
struct qElement* next;
}st_qElement;
//队列的前端和后端，最后一个入队列的元素为rear，第一个出队列的元素为front
st_qElement* front = NULL;
st_qElement* rear = NULL;
void createGraph(int (*edge)[VERTEXNUM], int start, int end);
void displayGraph(int (*edge)[VERTEXNUM]);
void BFT(int (*edge)[VERTEXNUM],int* vertexStatusArr);
void BFTcore(int (*edge)[VERTEXNUM],int i,int* vertexStatusArr);
void putQueue(int vertex);
int* getQueue();
void putRelatedInQueue(int (*edge)[VERTEXNUM], int vertex);
int main(void){
//动态创建存放边的二维数组
int (*edge)[VERTEXNUM] = (int (*)[VERTEXNUM])malloc(sizeof(int)*VERTEXNUM*VERTEXNUM);
int i,j;
for(i=0;i<VERTEXNUM;i++){
for(j=0;j<VERTEXNUM;j++){
edge[i][j] = 0;
}
}
//存放顶点的遍历状态，0：未遍历，1：已遍历
int* vertexStatusArr = (int*)malloc(sizeof(int)*VERTEXNUM);
for(i=0;i<VERTEXNUM;i++){
vertexStatusArr[i] = 0;
}
printf("after init:\n");
displayGraph(edge);
//创建图
createGraph(edge,0,3);
createGraph(edge,0,4);
createGraph(edge,3,1);
createGraph(edge,3,2);
createGraph(edge,4,1);
printf("after create:\n");
displayGraph(edge);
//广度优先遍历
BFT(edge,vertexStatusArr);
free(edge);
return 0;
}
//创建图
void createGraph(int (*edge)[VERTEXNUM], int start, int end){
edge[start][end] = 1;
}
//打印存储的图
void displayGraph(int (*edge)[VERTEXNUM]){
int i,j;
for(i=0;i<VERTEXNUM;i++){
for(j=0;j<VERTEXNUM;j++){
printf("%d ",edge[i][j]);
}
printf("\n");
}
}
//广度优先遍历
void BFT(int (*edge)[VERTEXNUM], int* vertexStatusArr){
printf("start BFT graph:\n");
int i;
for(i=0;i<VERTEXNUM;i++){
BFTcore(edge,i,vertexStatusArr);
}
printf("\n");
}
void BFTcore(int (*edge)[VERTEXNUM],int i,int* vertexStatusArr){
putQueue(i);
int* qeValue = NULL;
while((qeValue = getQueue()) != NULL){
if(vertexStatusArr[*qeValue] == 0){
printf("%d ",*qeValue);
vertexStatusArr[*qeValue] = 1;
putRelatedInQueue(edge, *qeValue);
}
free(qeValue);
qeValue = NULL;
}
}
//将元素放到队列中
void putQueue(int vertex){
st_qElement* qe = (st_qElement*)malloc(sizeof(st_qElement));
qe->value = vertex;
qe->next = NULL;
qe->pre = NULL;
if(front == NULL || rear == NULL){
front = rear = qe;
}else{
rear->next = qe;
qe->pre = rear;
rear = qe;
}
}
//从队列中获取一个元素
int* getQueue(){
if(front == NULL || rear == NULL){
return NULL;
}else{
int* res = (int*)malloc(sizeof(int));
*res = front->value;
st_qElement* p = front;
front = front->next;
if(front == NULL){
rear = front;
}else{
front->pre = NULL;
}
free(p);
p = NULL;
return res;
}
}
//将顶点关联的元素放到队列中
void putRelatedInQueue(int (*edge)[VERTEXNUM], int vertex){
int i;
for(i=0;i<VERTEXNUM;i++){
if(edge[vertex][i] == 1){
putQueue(i);
}
}
}c语言实现如下：（使用邻接表存储）
#include <stdio.h>
#include <malloc.h>
#define VERTEXNUM 5
//存放顶点的邻接表元素
typedef struct edge{
int vertex;
struct edge* next;
}st_edge;
//队列的元素
typedef struct qElement{
int value;
struct qElement* pre;
struct qElement* next;
}st_qElement;
//队列的前端和后端，最后一个入队列的元素为rear，第一个出队列的元素为front
st_qElement* front = NULL;
st_qElement* rear = NULL;
void createGraph(st_edge** edge, int start, int end);
void displayGraph(st_edge** edge);
void delGraph(st_edge** edge);
void BFT(st_edge** edge,int* vertexStatusArr);
void BFTcore(st_edge** edge,int i,int* vertexStatusArr);
void putQueue(int vertex);
int* getQueue();
void putRelatedInQueue(st_edge** edge, int vertex);
int main(void){
//动态创建存放边的指针数组
st_edge** edge = (st_edge**)malloc(sizeof(st_edge*)*VERTEXNUM);
int i;
for(i=0;i<VERTEXNUM;i++){
edge[i] = NULL;
}
//存放顶点的遍历状态，0：未遍历，1：已遍历
int* vertexStatusArr = (int*)malloc(sizeof(int)*VERTEXNUM);
for(i=0;i<VERTEXNUM;i++){
vertexStatusArr[i] = 0;
}
printf("after init:\n");
displayGraph(edge);
//创建图
createGraph(edge,0,3);
createGraph(edge,0,4);
createGraph(edge,3,1);
createGraph(edge,3,2);
createGraph(edge,4,1);
printf("after create:\n");
displayGraph(edge);
//广度优先遍历
BFT(edge,vertexStatusArr);
//释放邻接表占用的内存
delGraph(edge);
edge = NULL;
free(vertexStatusArr);
vertexStatusArr = NULL;
return 0;
}
//创建图
void createGraph(st_edge** edge, int start, int end){
st_edge* newedge = (st_edge*)malloc(sizeof(st_edge));
newedge->vertex = end;
newedge->next = NULL;
edge = edge + start;
while(*edge != NULL){
edge = &((*edge)->next);
}
*edge = newedge;
}
//打印存储的图
void displayGraph(st_edge** edge){
int i;
st_edge* p;
for(i=0;i<VERTEXNUM;i++){
printf("%d:",i);
p = *(edge+i);
while(p != NULL){
printf("%d ",p->vertex);
p = p->next;
}
printf("\n");
}
}
//释放邻接表占用的内存
void delGraph(st_edge** edge){
int i;
st_edge* p;
st_edge* del;
for(i=0;i<VERTEXNUM;i++){
p = *(edge+i);
while(p != NULL){
del = p;
p = p->next;
free(del);
}
edge[i] = NULL;
}
free(edge);
}
//广度优先遍历
void BFT(st_edge** edge,int* vertexStatusArr){
printf("start BFT graph:\n");
int i;
for(i=0;i<VERTEXNUM;i++){
BFTcore(edge,i,vertexStatusArr);
}
printf("\n");
}
void BFTcore(st_edge** edge,int i,int* vertexStatusArr){
putQueue(i);
int* qeValue = NULL;
while((qeValue = getQueue()) != NULL){
if(vertexStatusArr[*qeValue] == 0){
printf("%d ",*qeValue);
vertexStatusArr[*qeValue] = 1;
putRelatedInQueue(edge, *qeValue);
}
free(qeValue);
qeValue = NULL;
}
}
//将元素放到队列中
void putQueue(int vertex){
st_qElement* qe = (st_qElement*)malloc(sizeof(st_qElement));
qe->value = vertex;
qe->next = NULL;
qe->pre = NULL;
if(front == NULL || rear == NULL){
front = rear = qe;
}else{
rear->next = qe;
qe->pre = rear;
rear = qe;
}
}
//从队列中获取一个元素
int* getQueue(){
if(front == NULL || rear == NULL){
return NULL;
}else{
int* res = (int*)malloc(sizeof(int));
*res = front->value;
st_qElement* p = front;
front = front->next;
if(front == NULL){
rear = front;
}else{
front->pre = NULL;
}
free(p);
p = NULL;
return res;
}
}
//将顶点关联的元素放到队列中
void putRelatedInQueue(st_edge** edge, int vertex){
st_edge* p = *(edge+vertex);
while(p != NULL){
putQueue(p->vertex);
p = p->next;
}
}