弗洛伊德算法

　弗洛伊德算法

求最短路径

#include <iostream>
using namespace std;

#define MaxInt 32767                        //表示极大值，即∞
#define MVNum 100                           //最大顶点数

typedef char VerTexType;                    //假设顶点的数据类型为字符型
typedef int ArcType;                        //假设边的权值类型为整型

int Path[MVNum][MVNum];                     //最短路径上顶点vj的前一顶点的序号
int D[MVNum][MVNum];                        //记录顶点vi和vj之间的最短路径长度

//------------图的邻接矩阵---------------
typedef struct{
    VerTexType vexs[MVNum];                 //顶点表
    ArcType arcs[MVNum][MVNum];             //邻接矩阵
    int vexnum,arcnum;                      //图的当前点数和边数
}AMGraph;

int LocateVex(AMGraph G , VerTexType v){
    //确定点v在G中的位置
    for(int i = 0; i < G.vexnum; ++i)
        if(G.vexs[i] == v)
            return i;
        return -1;
}//LocateVex

void CreateUDN(AMGraph &G){
    //采用邻接矩阵表示法，创建有向网G
    int i , j , k;
    cout <<"请输入总顶点数，总边数，以空格隔开:";
    cin >> G.vexnum >> G.arcnum;                            //输入总顶点数，总边数
    cout << endl;

    cout << "输入点的名称，如a" << endl;

    for(i = 0; i < G.vexnum; ++i){
        cout << "请输入第" << (i+1) << "个点的名称:";
        cin >> G.vexs[i];                                   //依次输入点的信息
    }
    cout << endl;
    for(i = 0; i < G.vexnum; ++i){                          //初始化邻接矩阵，边的权值均置为极大值MaxInt
        for(j = 0; j < G.vexnum; ++j){
            if(j != i)
                G.arcs[i][j] = MaxInt;
            else
                G.arcs[i][j] = 0;
        }//for
    }//for

    cout << "输入边依附的顶点及权值，如a b 3" << endl;
    for(k = 0; k < G.arcnum;++k){                       //构造邻接矩阵
        VerTexType v1 , v2;
        ArcType w;
        cout << "请输入第" << (k + 1) << "条边依附的顶点及权值:";
        cin >> v1 >> v2 >> w;                           //输入一条边依附的顶点及权值
        i = LocateVex(G, v1);  j = LocateVex(G, v2);    //确定v1和v2在G中的位置，即顶点数组的下标
        G.arcs[i][j] = w;                               //边<v1, v2>的权值置为w
    }//for
}//CreateUDN

void ShortestPath_Floyed(AMGraph G){
    //用Floyd算法求有向网G中各对顶点i和j之间的最短路径
    int i , j , k ;
    for (i = 0; i < G.vexnum; ++i)                  //各对结点之间初始已知路径及距离
        for(j = 0; j < G.vexnum; ++j){
            D[i][j] = G.arcs[i][j];
            if(D[i][j] < MaxInt && i != j)  Path[i][j]=i;   //如果i和j之间有弧，则将j的前驱置为i
            else Path [i][j] = -1;                      //如果i和j之间无弧，则将j的前驱置为-1
        }//for
        for(k = 0; k < G.vexnum; ++k)
            for(i = 0; i < G.vexnum; ++i)
                for(j = 0; j < G.vexnum; ++j)
                    if(D[i][k] + D[k][j] < D[i][j]){        //从i经k到j的一条路径更短
                        D[i][j] = D[i][k]+D[k][j];          //更新D[i][j]
                        Path[i][j] = Path[k][j];                //更改j的前驱为k
                    }//if
}//ShortestPath_Floyed

void DisplayPath(AMGraph G , int begin ,int temp ){
    //显示最短路径
    if(Path[begin][temp] != -1){
        DisplayPath(G , begin ,Path[begin][temp]);
        cout << G.vexs[Path[begin][temp]] << "-->";
    }
}//DisplayPath

int main(){
    cout << "************算法6.11　弗洛伊德算法**************" << endl << endl;
    AMGraph G;
    char start , destination;
    int num_start , num_destination;

    CreateUDN(G);

    cout <<endl;
    cout << "有向网G创建完成！" << endl;
    ShortestPath_Floyed(G);

    cout << "请依次输入路径的起点与终点的名称：";
    cin >> start >> destination;
    num_start = LocateVex(G , start);
    num_destination = LocateVex(G , destination);

    DisplayPath(G , num_start , num_destination);
    cout << G.vexs[num_destination] << endl;
    cout << "最短路径的长度为：" << D[num_start][num_destination] << endl;
    cout <<endl;
}//main