最短路径Floyd详解-源代码

//算法6.11　弗洛伊德算法#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;}//LocateVexvoid 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;  elseG.arcs[i][j] = 0;}//for}//forcout << "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 }//forfor(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_Floyedvoid 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]] << "-->";}}//DisplayPathvoid 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