Kruskal算法(一)之 C语言详解

// 邻接矩阵
typedef struct _graph
{
    char vexs[MAX];       // 顶点集合
    int vexnum;           // 顶点数
    int edgnum;           // 边数
    int matrix[MAX][MAX]; // 邻接矩阵
}Graph, *PGraph;

// 边的结构体
typedef struct _EdgeData
{
    char start; // 边的起点
    char end;   // 边的终点
    int weight; // 边的权重
}EData;

#include<stdio.h>
#include<stdlib.h>
#include<malloc.h>
#include<string.h>
#define MAX 100
#define INF -1
typedef struct Graph
{
    char vexs[MAX];
    int vexnum;
    int edgnum;
    int matrix[MAX][MAX];
}Graph,*PGraph;

typedef struct EdgeData
{
    char start;
    char end;
    int weight;
}EData;

static int get_position(Graph g,char ch)
{
    int i;
    for(i=0;i<g.vexnum;i++)
        if(g.vexs[i]==ch)
            return i;
    return -1;
}

Graph* create_graph()
{
    char vexs[]= {‘A‘,‘B‘,‘C‘,‘D‘,‘E‘,‘F‘,‘G‘};
    int matrix[][7]= {
        {0,12,INF,INF,INF,16,14},
        {12,0,10,INF,INF,7,INF},
        {INF,10,0,3,5,6,INF},
        {INF,INF,3,0,4,INF,INF},
        {INF,INF,5,4,0,INF,8},
        {16,7,6,INF,2,0,9},
        {14,INF,INF,INF,8,9,0}};
    int vlen=sizeof(vexs)/sizeof(vexs[0]);
    int i,j;
    Graph *pG;
    if((pG=(Graph*)malloc(sizeof(Graph)))==NULL)
        return NULL;
    memset(pG,0,sizeof(pG));
    pG->vexnum=vlen;
    for(i=0;i<pG->vexnum;i++)
        pG->vexs[i]=vexs[i];
    for(i=0;i<pG->vexnum;i++)
        for(j=0;j<pG->vexnum;j++)
            pG->matrix[i][j]=matrix[i][j];
    for(i=0;i<pG->vexnum;i++)
    {
        for(j=0;j<pG->vexnum;j++)
        {
            if(i!=j&&pG->matrix[i][j]!=INF)
                pG->edgnum++;
        }
    }
    pG->edgnum/=2;
    return pG;
}

void print_graph(Graph G)
{
    int i,j;
    printf("Matrix Graph: \n");
    for(i=0;i<G.vexnum;i++)
    {
        for(j=0;j<G.vexnum;j++)
            printf("%10d ",G.matrix[i][j]);
        printf("\n");
    }
}

EData* get_edges(Graph G)
{
    EData *edges;
    edges=(EData*)malloc(G.edgnum*sizeof(EData));
    int i,j;
    int index=0;
    for(i=0;i<G.vexnum;i++)
    {
        for(j=i+1;j<G.vexnum;j++)
        {
            if(G.matrix[i][j]!=INF)
            {
                edges[index].start=G.vexs[i];
                edges[index].end=G.vexs[j];
                edges[index].weight=G.matrix[i][j];
                index++;
            }
        }
    }
    return edges;
}

void sort_edges(EData *edges,int elen)
{
    int i,j;
    for(i=0;i<elen;i++)
    {
        for(j=i+1;j<elen;j++)
        {
            if(edges[i].weight>edges[j].weight)
            {
                EData tmp=edges[i];
                edges[i]=edges[j];
                edges[j]=tmp;
            }
        }
    }
}

int get_end(int vends[],int i)
{
    while(vends[i]!=0)
        i=vends[i];
    return i;
}

void kruskal(Graph G)
{
    int i,m,n,p1,p2;
    int length;
    int index=0;
    int vends[MAX]={0};
    EData rets[MAX];
    EData *edges;
    edges=get_edges(G);
    sort_edges(edges,G.edgnum);

    for(i=0;i<G.edgnum;i++)
        printf("%d ",edges[i].weight);
    printf("\n");
    for(i=0;i<G.edgnum;i++)
    {
        p1=get_position(G,edges[i].start);
        p2=get_position(G,edges[i].end);
        m=get_end(vends,p1);
        n=get_end(vends,p2);
        printf("m= %d,n= %d",m,n);
        if(m!=n)
        {
            vends[m]=n;
            rets[index++]=edges[i];
        }
    }
    free(edges);

    length=0;
    for(i=0;i<index;i++)
        length+=rets[i].weight;
    printf("Kruskal = %d\n",length);
    for(i=0;i<index;i++)
        printf("( %c , %c ) ",rets[i].start,rets[i].end);
    printf("\n");
}

int main()
{
    Graph *pG;
    pG=create_graph();
    print_graph(*pG);
    kruskal(*pG);
}