贪心算法(2)-Kruskal最小生成树

// Kruskal 最小生成树算法
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

// 带有权重的边
struct Edge
{
    int src, dest, weight;
};

// 无向图
struct Graph
{
    // V-> 顶点个数, E->边的个数
    int V, E;
    // 由于是无向图，从 src 到 dest的边，同时也是 dest到src的边，按一条边计算
    struct Edge* edge;
};

//构建一个V个顶点 E条边的图
struct Graph* createGraph(int V, int E)
{
    struct Graph* graph = (struct Graph*) malloc( sizeof(struct Graph) );
    graph->V = V;
    graph->E = E;
    graph->edge = (struct Edge*) malloc( graph->E * sizeof( struct Edge ) );
    return graph;
}

//并查集的结构体
struct subset
{
    int parent;
    int rank;
};

// 使用路径压缩查找元素i
int find(struct subset subsets[], int i)
{
    if (subsets[i].parent != i)
        subsets[i].parent = find(subsets, subsets[i].parent);

    return subsets[i].parent;
}

// 按秩合并 x，y
void Union(struct subset subsets[], int x, int y)
{
    int xroot = find(subsets, x);
    int yroot = find(subsets, y);
    if (subsets[xroot].rank < subsets[yroot].rank)
        subsets[xroot].parent = yroot;
    else if (subsets[xroot].rank > subsets[yroot].rank)
        subsets[yroot].parent = xroot;
    else
    {
        subsets[yroot].parent = xroot;
        subsets[xroot].rank++;
    }
}

// 很据权重比较两条边
int myComp(const void* a, const void* b)
{
    struct Edge* a1 = (struct Edge*)a;
    struct Edge* b1 = (struct Edge*)b;
    return a1->weight > b1->weight;
}

// Kruskal 算法
void KruskalMST(struct Graph* graph)
{
    int V = graph->V;
    struct Edge result[V];  //存储结果
    int e = 0;  //result[] 的index
    int i = 0;  // 已排序的边的 index

    //第一步排序
    qsort(graph->edge, graph->E, sizeof(graph->edge[0]), myComp);

    // 为并查集分配内存
    struct subset *subsets =
        (struct subset*) malloc( V * sizeof(struct subset) );

    // 初始化并查集
    for (int v = 0; v < V; ++v)
    {
        subsets[v].parent = v;
        subsets[v].rank = 0;
    }

    // 边的数量到V-1结束
    while (e < V - 1)
    {
        // Step 2: 先选最小权重的边
        struct Edge next_edge = graph->edge[i++];

        int x = find(subsets, next_edge.src);
        int y = find(subsets, next_edge.dest);

        // 如果此边不会引起环
        if (x != y)
        {
            result[e++] = next_edge;
            Union(subsets, x, y);
        }
        // 否则丢弃，继续
    }

    // 打印result[]
    printf("Following are the edges in the constructed MST\n");
    for (i = 0; i < e; ++i)
        printf("%d -- %d == %d\n", result[i].src, result[i].dest,
                                                   result[i].weight);
    return;
}

// 测试
int main()
{
    /* 创建下面的图：
             10
        0--------1
        |  \     |
       6|   5\   |15
        |      \ |
        2--------3
            4       */
    int V = 4;  // 顶点个数
    int E = 5;  //边的个数
    struct Graph* graph = createGraph(V, E);
    // 添加边 0-1
    graph->edge[0].src = 0;
    graph->edge[0].dest = 1;
    graph->edge[0].weight = 10;

    graph->edge[1].src = 0;
    graph->edge[1].dest = 2;
    graph->edge[1].weight = 6;

    graph->edge[2].src = 0;
    graph->edge[2].dest = 3;
    graph->edge[2].weight = 5;

    graph->edge[3].src = 1;
    graph->edge[3].dest = 3;
    graph->edge[3].weight = 15;

    graph->edge[4].src = 2;
    graph->edge[4].dest = 3;
    graph->edge[4].weight = 4;

    KruskalMST(graph);

    return 0;
}

Following are the edges in the constructed MST
2 -- 3 == 4
0 -- 3 == 5
0 -- 1 == 10