图的广度优先搜索遍历：
- 存储的数据结构为无向图的多重邻接表
- 类似于树的层序遍历，依次按照路径为1，2，3…进行遍历，因而每次要获得一个节点然后得到这点的未经访问的邻近点后再将此点抛弃，因此我们用队列这一结构。
void BFSReverse(AMLGraph G) {
queue<int> a;
for(int i = 0; i < G.vexnum; ++i) {
visit[i] = unvisited;
}
for(int i = 0; i < G.vexnum; ++i) {
if (visit[i] == unvisited) {
a.push(i);
visit[i] = visited;
cout << G.adjmulist[i].data << endl;
while (!a.empty()) {
int v = a.front();
a.pop();
for (int w = FirstAdjVex(G, v); w >= 0; w = NextAdjVex(G, v, w)) {
if (visit[w] == unvisited) {
a.push(w);
cout << G.adjmulist[w].data << endl;
visit[w] = visited;
}
}
}
}
}
}
求图的任意两点间的最短路径：
如下：
将队列的结构改为如图所示，即每次不将队列的头部退出队列内而是每次通过移动头部指针来完成，而其他节点都附加一个前向指针(front)，指向引导当前节点的前一个节点，也就是每一次的head。
struct Node {
Node *next;
Node *front;
int data;
};
int BFSPath(AMLGraph G, string v1, string v2) {
int i1 = LocateVex(G.adjmulist, G.vexnum, v1);
int i2 = LocateVex(G.adjmulist, G.vexnum, v2);
//int num = 0;
Node *head;
Node *rear;
head = NULL;
rear = NULL;
for(int i = 0; i < G.vexnum; ++i) {
visit[i] = unvisited;
}
visit[i1] = visited;
Node *temp = new Node;
temp->data = i1;
temp->front = NULL;
temp->next = NULL;
head = rear = temp;
while (head) {
int v = head->data;
for (int w = FirstAdjVex(G, v); w >= 0; w = NextAdjVex(G, v, w)) {
if (visit[w] == unvisited) {
Node *temp0 = new Node;
temp0->data = w;
temp0->front = head;
temp0->next = NULL;
rear->next = temp0;
rear = temp0;
visit[w] = visited;
if (rear->data == i2) {
Node *p = rear;
while(p) {
cout << p->data << endl;
p = p->front;
}
return 1;
}
}
}
head = head->next;
}
cout << "Not Find!" << endl;
return 0;
}
用如下效果图测试：
有两个连通图：
最后附上全部代码：
//无向图的邻接多重表
//广度优先搜索的实现
//求两个顶点之间一条路径长度最短的路径
#include <iostream>
#include <stack>
#include <list>
#include <queue>
using namespace std;
#define MAX_VERTEX_NUM 20
enum VisitIf {unvisited, visited};
VisitIf visit[MAX_VERTEX_NUM];
class EBox {
public:
VisitIf mark; //访问标记
int ivex, jvex; //该边依附的两个顶点位置
EBox *ilink, *jlink; //分别指向依附这两个顶点的下一条边
};
class VexBox {
public:
string data;
EBox *firstedge; //指向第一条依附该顶点的边
};
class AMLGraph {
public:
VexBox adjmulist[MAX_VERTEX_NUM];
int vexnum, edgenum; //无向图的当前顶点数和边数
};
struct Node {
Node *next;
Node *front;
int data;
};
int LocateVex(VexBox adj[], int num, string v) {
for (int i = 0; i < num; i++) {
if (adj[i].data == v) {
return i;
}
}
}
void CreateGraph(AMLGraph *G) {
cout << "请输入顶点数和弧数: " << endl;
cin >> G->vexnum >> G->edgenum;
cout << "请输入顶点: " << endl;
for (int i = 0; i < G->vexnum; i++) {
cin >> G->adjmulist[i].data;
G->adjmulist[i].firstedge = NULL;
}
for (int i = 0; i < G->edgenum; i++) {
cout << "请输入边的两个顶点: " << endl;
string v1, v2;
cin >> v1 >> v2;
int i1 = LocateVex(G->adjmulist, G->vexnum, v1);
int i2 = LocateVex(G->adjmulist, G->vexnum, v2);
//cout << i1 << "...." << i2 << endl;
EBox *p = new EBox;
p->mark = unvisited;
p->ivex = i1;
p->jvex = i2;
p->ilink = G->adjmulist[i1].firstedge;
p->jlink = G->adjmulist[i2].firstedge;
G->adjmulist[i1].firstedge = p;
G->adjmulist[i2].firstedge = p;
}
}
int FirstAdjVex(AMLGraph G, int v) {
int i = v;
if (G.adjmulist[i].firstedge) {
if (G.adjmulist[i].firstedge->ivex == i) {
return G.adjmulist[i].firstedge->jvex;
}
else {
return G.adjmulist[i].firstedge->ivex;
}
}
else
return -1;
}
//v是G中的某个顶点，w是v的邻接顶点
//返回v的(相对于w的)下一个邻接顶点。若w是v的最后一个邻接点，则返回空
int NextAdjVex(AMLGraph G, int v, int w) {
int i1 = v;
int i2 = w;
EBox *p = G.adjmulist[i1].firstedge;
while (p) {
if (p->ivex == i1 && p->jvex != i2) {
p = p->ilink;
}
else {
if (p->ivex != i2 && p->jvex == i1) {
p = p->jlink;
}
else {
break;
}
}
}
if (p && p->ivex == i1 && p->jvex == i2) {
p = p->ilink;
if (p&&p->ivex == i1) {
return p->jvex;
}
else if (p&&p->jvex == i1)
return p->ivex;
}
if (p && p->ivex == i2 && p->jvex == i1) {
p = p->jlink;
if (p&&p->ivex == i1) {
return p->jvex;
}
else if (p&&p->jvex == i1)
return p->ivex;
}
return -1;
}
void BFSReverse(AMLGraph G) {
queue<int> a;
for(int i = 0; i < G.vexnum; ++i) {
visit[i] = unvisited;
}
for(int i = 0; i < G.vexnum; ++i) {
if (visit[i] == unvisited) {
cout << "连通图：" << endl;
a.push(i);
visit[i] = visited;
cout << G.adjmulist[i].data << endl;
while (!a.empty()) {
int v = a.front();
a.pop();
for (int w = FirstAdjVex(G, v); w >= 0; w = NextAdjVex(G, v, w)) {
if (visit[w] == unvisited) {
a.push(w);
cout << G.adjmulist[w].data << endl;
visit[w] = visited;
}
}
}
}
}
}
int BFSPath(AMLGraph G, string v1, string v2) {
if (v1 == v2) {
cout << "the same point!" << endl;
return 0;
}
int i1 = LocateVex(G.adjmulist, G.vexnum, v1);
int i2 = LocateVex(G.adjmulist, G.vexnum, v2);
//int num = 0;
Node *head;
Node *rear;
head = NULL;
rear = NULL;
for(int i = 0; i < G.vexnum; ++i) {
visit[i] = unvisited;
}
visit[i1] = visited;
Node *temp = new Node;
temp->data = i1;
temp->front = NULL;
temp->next = NULL;
head = rear = temp;
stack<string> a;
while (head) {
int v = head->data;
for (int w = FirstAdjVex(G, v); w >= 0; w = NextAdjVex(G, v, w)) {
if (visit[w] == unvisited) {
Node *temp0 = new Node;
temp0->data = w;
temp0->front = head;
temp0->next = NULL;
rear->next = temp0;
rear = temp0;
visit[w] = visited;
if (rear->data == i2) {
Node *p = rear;
while(p) {
a.push(G.adjmulist[p->data].data);
p = p->front;
}
cout << a.top();
a.pop();
while (!a.empty()) {
cout << "->" << a.top();
a.pop();
}
cout << endl;
return 1;
}
}
}
head = head->next;
}
cout << "Not Find!" << endl;
return 0;
}
void PrintGraph(AMLGraph G)
{
EBox *p;
for(int i = 0; i < G.vexnum; ++i)
{
p = G.adjmulist[i].firstedge;
while(p != NULL)
{
if(p->ivex == i) //判断相等才能知道连接上的是ivex还是jvex;
{
cout << G.adjmulist[p->ivex].data << "------" << G.adjmulist[p->jvex].data << endl;
//printf("%d--%d\n", G.adjmulist[p->ivex].data, G.adjmulist[p->jvex].data);
p = p->ilink;
}
else
{
cout << G.adjmulist[p->jvex].data << "------" << G.adjmulist[p->ivex].data << endl;
p = p->jlink;
}
}
}
}
int main () {
AMLGraph g;
CreateGraph(&g);
//PrintGraph(g);
BFSReverse(g);
//DFSTraverse(g);
while (1) {
string v1, v2;
cout << "请输入你想查询的两点: " << endl;
cin >> v1 >> v2;
BFSPath(g, v1, v2);
}
return 0;
}
