c++邻接矩阵创建有向图，利用深度优先判断是否存在路径

Question

以邻接矩阵表示法创建有向图，并基于图的深度优先遍历策略设计一算法，判断有向图中是否存在由顶点A到顶点B的路径。(代码注释详细点)

Answer 1

代码如下：

#define _CRT_SECURE_NO_WARNINGS 1
#include <iostream>
using namespace std;
#define MVNUM 100                //最大顶点数
#define MAXINT 32767                //极大值相当于无穷大
 
int visited[MVNUM] = { 0 };            //辅助数组，判断遍历过了没
int visit[MVNUM] = { 0 };            //同理
typedef struct
{
    char vexs[MVNUM];            //顶点数据数组
    int arr[MVNUM][MVNUM];            //邻接矩阵
    int vexnum, arcnum;            //现有顶点数与边数
}AMGraph;                            
typedef struct
{
    int* base;                //队列数组
    int front;                //队头的下标
    int rear;                //队尾的下标
}sqQueue;
 
int initGraph(AMGraph& G);            //初始化邻接矩阵
void showGraph(AMGraph G);            //打印邻接矩阵
int locatVex(AMGraph G, char u);        //定位顶点在邻接矩阵的下标
int createGraph(AMGraph& G);            //建立邻接矩阵
void dfsAM(AMGraph G,int i);            //深度优先搜索遍历
void bfsAM(AMGraph G, int i);            //广度优先搜索遍历
int initQueue(sqQueue& Q);            //初始化队列
int enQueue(sqQueue& Q, int i);            //入队
int firstVEX(AMGraph G, int u);            //第一个邻接顶点        
int nextVEX(AMGraph G,int w ,int u);    //下一个邻接顶点
 
int main()
{
    AMGraph G;                            
    initGraph(G);
    createGraph(G);
    showGraph(G);
    cout << "the result of dfs is:";
    dfsAM(G,0);
    cout << endl;
    cout << "the result of bfs is:";
    bfsAM(G,0);
}
int initGraph(AMGraph& G)
{
    cout << "please input some vexnum and arcnum!" << endl;
    cin >> G.vexnum >> G.arcnum;            //输入你想要的顶点数和边数
    cout << "please input data of vex!" << endl;
    for (int i = 0; i < G.vexnum; i++)
    {
        cin >>G.vexs[i];            //输入顶点数据
    }
    
    for (int i = 0; i < G.vexnum; i++)
    {
        for (int j = 0; j < G.vexnum; j++)
        {
            G.arr[i][j] = MAXINT;        //邻接矩阵的初值都为无穷大
        }    
    }
        
    return 1;
}
void showGraph(AMGraph G)
{
    for (int i = 0; i < G.vexnum; i++)
    {
        for (int j = 0; j < G.vexnum; j++)
        {
            if (G.arr[i][j] == MAXINT)    //无穷大弄得更好看点
                cout << "∞" << " ";
            else
                cout << " " << G.arr[i][j] << " ";
        }
        cout << endl;
    }
    cout << endl;
}
 
int locateVex(AMGraph G, char u)
{
    for (int i = 0; i < G.vexnum; i++)    
    {
        if (u == G.vexs[i])            //如果u的值和顶点数据匹配，就返回顶点在矩阵中的下标
            return i;
    }
    return -1;
}
 
int createGraph(AMGraph& G)
{
    int i = 0; int j = 0;int w = 0;            //i,j代表顶点下标,w代表权值
    char v1 = 0; char v2 = 0;            //v1,v2为顶点数据
    cout << "please input w of v1 to v2 in graph!" << endl;
    for (int k = 0; k < G.arcnum; k++)
    {
        cin >> v1 >> v2 >> w;            
        i = locateVex(G, v1);            //找到v1在顶点表的下标，并返回赋值给i
        j = locateVex(G, v2);
        G.arr[i][j] = w;
        G.arr[j][i] = G.arr[i][j];        //无向图的矩阵是对称矩阵
    }
 
    cout << endl;
    return 1;
}
 
void dfsAM(AMGraph G, int i)
{//随机选一个顶点下标，这里为0
    cout << G.vexs[i]<<" ";            //输出0下标在顶点表的值    
    visited[i] = 1;                //辅助数组对应下标i的值置为1
    for (int j = 0; j < G.vexnum; j++)
    {
        if (G.arr[i][j] != MAXINT && (!visited[j]))    //只要是邻接的顶点并且没有访问过
        {                        //不然就退回，也是递归结束条件
            dfsAM(G, j);                //递归使用函数
        }
    }
}
int initQueue(sqQueue& Q)
{
    Q.base = (int *)malloc(sizeof(int) * MVNUM);    
    //给base动态分配一个int*类型MVNUM个int大小的一维数组空间
    Q.front = Q.rear = 0;    //队头和对尾下标都置为0
    return 1;
}
int enQueue(sqQueue& Q, int i)
{
    if ((Q.rear + 1) % MVNUM == Q.front)            //队满
        return 0;
    Q.base[Q.rear] = i;                    //先赋值再加
    Q.rear = (Q.rear + 1) % MVNUM;
    return 1;
}
 
int deQueue(sqQueue& Q, int &u)
{
    if (Q.rear == Q.front)                    //队空
        return 0;
    u = Q.base[Q.front];                    //要删的值给u然后再加
    Q.front = (Q.front + 1) % MVNUM;
    return 1;
}
 
int firstVEX(AMGraph G, int u)
{//在邻接矩阵u行0列开始遍历，如果找到不等于无穷的，
//并且没有访问过的就返回列的下标，否则就返回无穷
    for (int i = 0; i < G.vexnum; i++)        
    {
        if (G.arr[u][i] != MAXINT && visit[i] == 0) 
        {
            return i;
        }
    }
    return MAXINT;
}
 
int nextVEX(AMGraph G, int w, int u)
{//在邻接矩阵u行w+1列开始遍历，如果找到不等于无穷的，
//并且没有访问过的就返回列的下标，否则就返回无穷
    for (int i = w + 1; i < G.vexnum; i++)
    {
        if (G.arr[u][i] != MAXINT && visit[i] == 0)
        {
            return i;
        }    
    }
    return MAXINT;
}
 
void bfsAM(AMGraph G, int i)
{//随机选一个顶点下标，这里为0
    cout << G.vexs[i] << " ";        //输出i下标在顶点表的值    
    visit[i] = 1;                //辅助数值对应下标i的值置为1
    sqQueue Q;                    
    initQueue(Q);
    enQueue(Q, i);                //i为矩阵中顶点的行下标，让它入队(顶点表的下标和矩阵的列下标，行下标一致，本算法中说谁的下标都一样)
    while (Q.rear != Q.front)        //队不为空
    {
        int u = 0;            //接收矩阵中顶点的行下标，因为是邻接矩阵
        deQueue(Q,u);            //出队并让u接收矩阵中顶点的行下标
        for (int w = firstVEX(G, u); w != MAXINT; w = nextVEX(G, w, u))
        {//注意在一次循环中u不变
            if (!visit[w])
            {
                cout << G.vexs[w] << " ";
                visit[w] = 1;
                enQueue(Q, w);
            }
        }
    }
    
}

望采纳。