Floyd算法

#include<stdio.h>
#include<stdlib.h>
#define MAXVEX 100      //最大顶点数
typedef char VertexType;     //顶点
typedef int EdgeType;   //权值
#define INFINITY 65535      /*用65535来代表∞*/

//Dist的存储结构
typedef struct
{
    int length; //当前最短路径长度
    int pre;    //路径最后经过的顶点
}Dist;

typedef struct
{
    int from;   //边的始点
    int to; //边的终点
    EdgeType weight;    //权重
}Edge;  //边的结构


//图的结构
typedef struct
{
    int numVertex;  //顶点个数
    int numEdge;    //边的个数
    VertexType vexs[MAXVEX];    /*顶点表*/
    int Indegree[MAXVEX];   //顶点入度
    EdgeType arc[MAXVEX][MAXVEX];   //边表
    Dist D[MAXVEX][MAXVEX];
}Graph;


//初始化图
void InitGraph(Graph * G,int numVert,int numEd )    //传入顶点个数,边数
{
    G->numVertex=numVert;
    G->numEdge=numEd;
    for(int i=0;i<numVert;i++)
    {
        G->Indegree[i]=0;
        for(int j=0;j<numVert;j++)
        {
            G->arc[i][j]=INFINITY;
            if(i==j)
            {
                G->arc[i][j]=0;
            }
        }
    }
    return ;
}


//判断是否为边
bool IsEdge(Edge oneEdge)
{
    if(oneEdge.weight>0 && oneEdge.weight!=INFINITY && oneEdge.to>=0)
    {
        return true;
    }
    else
    {
        return false;
    }
}




//建立有向图的邻接矩阵
void CreatGraph(Graph * G)
{
    int i,j,k,w;
    printf("请输入%d个顶点元素：\n",G->numVertex);
    for(i=0;i<G->numVertex;i++)
    {
        scanf(" %c",&G->vexs[i]);
    }
    for(k=0;k<G->numEdge;k++)
    {
        printf("请输入边(Vi,Vj)的下标Vi,Vj,和权重w:\n");
        scanf("%d%d%d",&i,&j,&w);
        G->Indegree[j]++;
        G->arc[i][j]=w;
    }
}



//返回顶点个数
int VerticesNum(Graph * G)
{
    return G->numVertex;
}



//返回依附于顶点的第一条边
Edge FirstEdge(Graph * G,int oneVertex)
{
    Edge firstEdge;
    firstEdge.from=oneVertex;
    for(int i=0;i<G->numVertex;i++)
    {
        if(G->arc[oneVertex][i]!=0 && G->arc[oneVertex][i]!=INFINITY)
        {
            firstEdge.to=i;
            firstEdge.weight=G->arc[oneVertex][i];
            break;
        }

    }
    return firstEdge;
}   



//返回oneEdge的终点
int ToVertex(Edge oneEdge)
{
    return oneEdge.to;
}



//返回与preEdge有相同顶点的下一条边
Edge NextEdge(Graph * G,Edge preEdge)
{
    Edge myEdge;
    myEdge.from=preEdge.from;   //边的始点与preEdge的始点相同
    if(preEdge.to<G->numVertex) //如果preEdge.to+1>=G->numVertex;将不存在下一条边
        for(int i=preEdge.to+1;i<G->numVertex;i++)  //找下一个arc[oneVertex][i]
        {                                           //不为0的i
            if(G->arc[preEdge.from][i]!=0 && G->arc[preEdge.from][i]!=INFINITY)
            {
                myEdge.to=i;
                myEdge.weight=G->arc[preEdge.from][i];
                break;
            }
        }
        return myEdge;
}



//初始化Dist数组
void Init_Dist(Graph * G)   
{
    int i,j;
    for(i=0;i<G->numVertex;i++)
    {
        for(j=0;j<G->numVertex;j++)
        {
            if(i==j)
            {
                G->D[i][j].length=0;
                G->D[i][j].pre=i;
            }
            else
            {
                G->D[i][j].length=INFINITY;
                G->D[i][j].pre=-1;
            }
        }
    }
}




void Floyd(Graph * G)
{
    int v;
    Init_Dist(G);   //初始化Dist数组
    for(v=0;v<G->numVertex;v++) 
    {
        for(Edge e=FirstEdge(G,v);IsEdge(e);e=NextEdge(G,e))
        {
            G->D[v][ToVertex(e)].length=e.weight;
            G->D[v][ToVertex(e)].pre=v;
        }
    }   //更改Dist数组的数据

    //顶点i到顶点j的路径经过顶点v,如果变短就改变Dist数组里的数据
    for(v=0;v<G->numVertex;v++)
    {
        for(int i=0;i<G->numVertex;i++)
        {
            for(int j=0;j<G->numVertex;j++)
            {
                if(G->D[i][j].length>(G->D[i][v].length+G->D[v][j].length))
                {
                    G->D[i][j].length=G->D[i][v].length+G->D[v][j].length;
                    G->D[i][j].pre=G->D[v][j].pre;
                }
            }
        }
    }
}


//输出Dist数组
void Print_Dist(Graph * G)
{
    for(int i=0;i<G->numVertex;i++)
    {
        for(int j=0;j<G->numVertex;j++)
        {
            printf("elem:%c   length:%d   pre:%d\n",G->vexs[i],G->D[i][j].length,G->D[i][j].pre);
        }
    }
    printf("\n");
}



int main()
{
    Graph G;
    int numVert,numEd;
    printf("请输入顶点数和边数：\n");
    scanf("%d%d",&numVert,&numEd);
    InitGraph(&G,numVert,numEd);
    CreatGraph(&G);
    Floyd(&G);
    Print_Dist(&G);
    return 0;
}