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最小生成树Prim算法朴素版 C语言实现

标签：数据结构 最小生成树

1、带权无向图，给出节点个数以及所有边权值，用Prim算法求最小生成树。2、2个for循环都是从2开始的，因为一般我们默认开始就把第一个节点加入生成树，因此之后不需要再次寻找它。3、lowcost[i]记录的是以节点i为终点的最小边权值。初始化时因为默认把第一个节点加入生成树，因此lowcost[i] = graph[1][i]，即最小边权值就是各节点到1号节点的边权值。4、mst[i]记录的是lowcost[i]对应的起点，这样有起点，有终点，即可唯一确定一条边了。初始化时mst[i] = 1，即每条边都是从1号节点出发。

/*    prim朴素实现    reference: http://www.slyar.com/blog/prim-simplicity-c.html*/#include 
   
    #define MAX 100#define INF 0x3f3f3f3fint graph[MAX][MAX];int Prim(int graph[][MAX], int n){    int lowcost[MAX], mst[MAX];    /*        lowcost[i]记录以i为终点的边的最小权值，当lowcost[i]=0时表示终点i加入生成树        mst[i]记录对应lowcost[i]的起点，当mst[i]=0时表示起点i加入生成树    */    int i, j, min, minid, sum = 0;    for (i = 2; i <= n; i++)  //默认选择1号节点加入生成树，从2号节点开始初始化    {        lowcost[i] = graph[1][i];  //最短距离初始化为其他节点到1号节点的距离        mst[i] = 1;  //标记所有节点的起点皆为默认的1号节点    }    mst[1] = 0;  //标记1号节点加入生成树    for (i = 2; i <= n; i++)  //n个节点至少需要n-1条边构成最小生成树    {        min = INF;        minid = 0;        for (j = 2; j <= n; j++)  //找满足条件的最小权值边的节点minid        {            if (lowcost[j] < min && lowcost[j] != 0)  //边权值较小且不在生成树中            {                min = lowcost[j];                minid = j;            }        }        printf("%c - %c : %d\n", mst[minid] + 'A' - 1, minid + 'A' - 1, min);  //输出生成树边的信息:起点，终点，权值        sum += min;  //累加权值        lowcost[minid] = 0;  //标记节点minid加入生成树        for (j = 2; j <= n; j++)  //更新当前节点minid到其他节点的权值        {            if (graph[minid][j] < lowcost[j])  ///发现更小的权值            {                lowcost[j] = graph[minid][j];  //更新权值信息                mst[j] = minid;  //更新最小权值边的起点            }        }    }    return sum;  //返回最小权值和}int main(){    int m, n, weight;    char chx, chy;    scanf("%d %d", &m, &n);  //读取节点和边的数目    getchar();    for (int i = 1; i <= m; i++)  //初始化图，所有节点间距离为无穷大        for (int j = 1; j <= m; j++)            graph[i][j] = INF;    for (int k = 0; k < n; k++)  //读取边信息    {        scanf("%c %c %d", &chx, &chy, &weight);        getchar();        int i = chx - 'A' + 1, j = chy - 'A' + 1;  ///ABCDEF        graph[i][j] = weight;        graph[j][i] = weight;    }    printf("Total: %d\n", Prim(graph, m));    return 0;}
   

测试样例

//清新版#include 
   
    #define MAX 100#define INF 0x3f3f3f3fint graph[MAX][MAX];int Prim(int graph[][MAX], int n){    int lowcost[MAX], mst[MAX];    int i, j, min, minid, sum = 0;    for (i = 2; i <= n; i++)    {        lowcost[i] = graph[1][i];        mst[i] = 1;    }    mst[1] = 0;    for (i = 2; i <= n; i++)    {        min = INF;        minid = 0;        for (j = 2; j <= n; j++)            if (lowcost[j] < min && lowcost[j] != 0)            {                min = lowcost[j];                minid = j;            }        printf("%c - %c : %d\n", mst[minid] + 'A' - 1, minid + 'A' - 1, min);        sum += min;        lowcost[minid] = 0;        for (j = 2; j <= n; j++)            if (graph[minid][j] < lowcost[j])            {                lowcost[j] = graph[minid][j];                mst[j] = minid;            }    }    return sum;}int main(){    int m, n, weight;    char chx, chy;    scanf("%d %d", &m, &n);    getchar();    for (int i = 1; i <= m; i++)        for (int j = 1; j <= m; j++)            graph[i][j] = INF;    for (int k = 0; k < n; k++)    {        scanf("%c %c %d", &chx, &chy, &weight);        getchar();        int i = chx - 'A' + 1, j = chy - 'A' + 1;        graph[i][j] = weight;        graph[j][i] = weight;    }    printf("Total: %d\n", Prim(graph, m));    return 0;}
   

//只输出最小权值, 去掉mst[]数组(起点)#include 
   
    #define MAX 100#define INF 0x3f3f3f3fint graph[MAX][MAX];int Prim(int graph[][MAX], int n){    int lowcost[MAX];    int i, j, min, minid, sum = 0;    for (i = 2; i <= n; i++)  lowcost[i] = graph[1][i];    lowcost[1] = 0;    for (i = 2; i <= n; i++)    {        min = INF;        minid = 0;        for (j = 2; j <= n; j++)            if (lowcost[j] < min && lowcost[j] != 0)            {                min = lowcost[j];                minid = j;            }        sum += min;        lowcost[minid] = 0;        for (j = 2; j <= n; j++)            if (graph[minid][j] < lowcost[j])  lowcost[j] = graph[minid][j];    }    return sum;}int main(){    int m, n, weight;    char chx, chy;    scanf("%d %d", &m, &n);    getchar();    for (int i = 1; i <= m; i++)        for (int j = 1; j <= m; j++)            graph[i][j] = INF;    for (int k = 0; k < n; k++)    {        scanf("%c %c %d", &chx, &chy, &weight);        getchar();        int i = chx - 'A' + 1, j = chy - 'A' + 1;        graph[i][j] = weight;        graph[j][i] = weight;    }    printf("Total: %d\n", Prim(graph, m));    return 0;}