数据结构——邻接矩阵表示的图的Floyd算法

#include <iostream>#include <iomanip>using namespace std;        #define MAX_VERTEX_NUM    10        //最大顶点个数#define TRUE 1#define FALSE 0#define INFINITY 32767 /* 用整型最大值代替∞ */typedef char VERTYPE;typedef struct{    VERTYPE    vexs[MAX_VERTEX_NUM];    //顶点向量    int        arcs[MAX_VERTEX_NUM][MAX_VERTEX_NUM];                    //邻接矩阵    int        vexnum,arcnum;            //图的当前顶点数和弧数}mgraph, * MGraph;typedef int DistancMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];        //存放路径长度typedef int PathMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM][MAX_VERTEX_NUM];                //存放路径，P[0][1][]表示顶点0到顶点1的路径，经过哪个点P[0][1][i]就是TRUE。void init_mgraph(MGraph &g)    //初始化图{    g=(MGraph)malloc(sizeof(mgraph));    g->vexnum=0;    g->arcnum=0;    for(int i=0;i<MAX_VERTEX_NUM;i++)        g->vexs[i]=0;    for(i=0;i<MAX_VERTEX_NUM;i++)        for(int j=0;j<MAX_VERTEX_NUM;j++)            g->arcs[i][j]=INFINITY;}void add_vexs(MGraph &g)    //增加顶点{    cout<<"请输入顶点的个数:"<<endl;    cin>>g->vexnum;    cout<<"请输入顶点的值"<<endl;    for(int i=0;i<g->vexnum;i++)    {        cin>>g->vexs[i];    }}void add_arcs(MGraph &g)    //增加边{    cout<<"请输入边的个数:"<<endl;    cin>>g->arcnum;    VERTYPE ch1,ch2;    int row,col,weight;    for(int i=0;i<g->arcnum;i++)    {            cin>>ch1>>ch2>>weight;        for(int j=0;j<g->vexnum;j++)        {            if(g->vexs[j]==ch1)            {                row=j;            }            if(g->vexs[j]==ch2)            {                col=j;            }        }        g->arcs[row][col]=weight;    //有向带权图只需把1改为weight    }}void creat_mgraph(MGraph &g) //创建图    {    add_vexs(g);    //增加顶点    add_arcs(g);    //增加边}void print_mgraph(MGraph &g) //打印图{    for(int i=0;i<g->vexnum;i++)        cout<<"   "<<g->vexs[i]<<"  ";    cout<<endl;    for(i=0;i<g->vexnum;i++)    {        cout<<g->vexs[i]<<" ";        for(int j=0;j<g->vexnum;j++)        {            cout<<setw(5)<<g->arcs[i][j]<<"  ";        }        cout<<endl;    }}void ShortestPath_FLOYD(MGraph &g, PathMatrix &P, DistancMatrix &D){    //用Floyd算法求有向网G中各顶点对v和w之间的最短路径P[v][w]及其带权长度D[v][w]。    //若P[v][w][u]为TRUE，则u是从v到w当前求得最短路径上的顶点。    int v,w,u,i;    for(v=0; v<g->vexnum; ++v)        for(w=0; w<g->vexnum; ++w)        {            D[v][w] = g->arcs[v][w];            for(u=0; u<g->vexnum; ++u)    //初始化                P[v][w][u] = FALSE;            if(D[v][w] < INFINITY)        //从v到w有直接路径            {                P[v][w][v] = TRUE;        //起点                P[v][w][w] = TRUE;        //终点            }//if        }//for    for(u=0; u<g->vexnum; ++u)        for(v=0; v<g->vexnum; ++v)            for(w=0; w<g->vexnum; ++w)            {                if(u==v || v==w || w==u)                    continue;                if(D[v][u] + D[u][w] < D[v][w])        //从v经u到w的一条路径更短                {                     D[v][w] = D[v][u] + D[u][w];                     for(i=0; i<g->vexnum; ++i)                         P[v][w][i] = P[v][u][i] || P[u][w][i];                }//if            }}void print_PathMatrix(MGraph &g, PathMatrix &P) //打印路径矩阵{    cout<<"        ";    for(int i=0;i<g->vexnum;i++)        cout<<g->vexs[i]<<"  ";    cout<<endl;    for(i=0;i<g->vexnum;i++)    {        for(int j=0;j<g->vexnum;j++)        {            cout<<i<<"-->"<<j<<":  ";                for(int k=0;k<g->vexnum;k++)                cout<<P[i][j][k]<<"  ";            cout<<endl;        }        cout<<endl;    }}void print_DistancMatrix(MGraph &g, DistancMatrix &D) //打印距离矩阵{    for(int i=0;i<g->vexnum;i++)        cout<<"   "<<g->vexs[i]<<"  ";    cout<<endl;    for(i=0;i<g->vexnum;i++)    {        cout<<g->vexs[i]<<" ";        for(int j=0;j<g->vexnum;j++)        {            cout<<setw(5)<<D[i][j]<<" ";        }        cout<<endl;    }}int main(){    MGraph G;    init_mgraph(G);        //初始化图    creat_mgraph(G);    //创建图    print_mgraph(G);    //打印图        DistancMatrix D;    PathMatrix P;    ShortestPath_FLOYD(G,P,D);    print_DistancMatrix(G,D);    //打印距离    print_PathMatrix(G,P);        //打印路径    return 0;}