带负权图的单源最短路径算法：Bellman-Ford算法

#include<iostream>
using namespace std;
const int  MaxEdges= 100;
const int MaxVertex= 20;
const int  MaxWeight= 10000;


struct MyEdge
{
    int v1,v2;
    int weight;
    MyEdge()
    {
        v1 = -1;
        v2 = -1;
        weight = MaxWeight;
    }
};
struct MyGraph
{
    MyEdge edges[MaxEdges];    
    int NumVertex;
    int NumEdges;    
};


void createGraph(MyGraph *mg)
{

    cout<<"请输入顶点数和边数："<<endl;
    cin>>mg->NumVertex >>mg->NumEdges;
    cout<<"请依次输入各边权重（v1,v2,weight）:"<<endl;
    int v1,v2 ,weight;
    for (int j=0;j<mg->NumEdges;j++)
    {
        cin>>v1>>v2>>weight;
        mg->edges[j].v1=v1;
        mg->edges[j].v2=v2;
        mg->edges[j].weight = weight;    
    }    
}


bool Bellman_ford(MyGraph *mg,int s,int *dis,int *pre)
{    
    int numV = mg->NumVertex;
    
    for(int i = 0;i<numV;i++) //初始化距离
    {
        dis[i] = (i==s)? 0:MaxWeight;
        pre[i] = -1; //前一个点初始为-1
    }
    pre[s]=s;
    for(int i=1;i<numV;i++)//松弛操作
    {
        for(int j=0;j<mg->NumEdges;j++)
        {
            if(dis[mg->edges[j].v2] > dis[mg->edges[j].v1] + mg->edges[j].weight)
            {
                dis[mg->edges[j].v2] = dis[mg->edges[j].v1] + mg->edges[j].weight;
                pre[mg->edges[j].v2] = mg->edges[j].v1;
            }
        }
    }
    for(int j=0;j<mg->NumEdges;j++)//判断是否含有负权回路
    {
        if(dis[mg->edges[j].v2] > dis[mg->edges[j].v1] + mg->edges[j].weight)
            return false;
    }
    return true;
}

void print_path( int j,int *pre)
{
    while(pre[j]!=-1 && pre[j]!= j)
    {
        cout<<j<<"-->";
        j=pre[j];
    }
    if(j ==pre[j])
        cout<<j;
    
}

void test_BellmanFord()
{
    int dis[MaxVertex];//
    int pre[MaxVertex];
    MyGraph MG;
    createGraph(&MG);
    
    cout<<"输入Bellman_ford算法的起点：";
    int start;
    cin>>start;
    if(Bellman_ford(&MG,start,dis,pre))
    {
        for(int j=0;j<MG.NumVertex;j++)
        {
            cout<<"到点"<<j <<"的最短路径："<<dis[j]<<endl;
            cout<<"路径：";
            print_path(j,pre);
            cout<<endl;
        }
    }
    else
        cout<<"存在负权环，算法无法实行！"<<endl;
}