用Kruskal 算法实现最小生成树-优快云博客

本文链接：https://blog.youkuaiyun.com/xxxx2022D/article/details/135971531

本文介绍了如何使用C语言实现Kruskal算法，通过并查集数据结构来找到带权无向图的最小生成树，包括输入顶点和边的数量、边的权重以及输出构成最小生成树的边的过程。

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Krucskal代码：

void kruskal(struct Edge edges[], int n, int m) {
    qsort(edges, m, sizeof(struct Edge), cmp);

    for (int i = 0; i < n; i++) {
        parent[i] = i;
    }

    int count = 0;
    for (int i = 0; i < m; i++) {
        struct Edge edge = edges[i];
        if (find(edge.u) != find(edge.v)) {
            unionSet(edge.u, edge.v);
            printf("(%d, %d) ", edge.u, edge.v); // 输出构成最小生成树的边
            count++;
            if (count == n - 1) {
                break;
            }
        }
    }
}

最小生成树结果：

源码：

#include <stdio.h>
#include <stdlib.h>

#define MAX_VERTEX 100

int parent[MAX_VERTEX];

int find(int p) {
    while (p != parent[p]) {
        p = parent[p];
    }
    return parent[p];
}

void unionSet(int p, int q) {
    int pRoot = find(p);
    int qRoot = find(q);
    if (pRoot == qRoot) {
        return;
    }
    parent[pRoot] = qRoot;
}

struct Edge {
    int u;
    int v;
    int weight;
};

int cmp(const void* a, const void* b) {
    struct Edge* edgeA = (struct Edge*)a;
    struct Edge* edgeB = (struct Edge*)b;
    return edgeA->weight - edgeB->weight;
}

void kruskal(struct Edge edges[], int n, int m) {
    qsort(edges, m, sizeof(struct Edge), cmp);

    for (int i = 0; i < n; i++) {
        parent[i] = i;
    }

    int count = 0;
    for (int i = 0; i < m; i++) {
        struct Edge edge = edges[i];
        if (find(edge.u) != find(edge.v)) {
            unionSet(edge.u, edge.v);
            printf("(%d, %d) ", edge.u, edge.v); // 输出构成最小生成树的边
            count++;
            if (count == n - 1) {
                break;
            }
        }
    }
}

int main() {
    int n, m;
    printf("请输入顶点和边的数量:\n");
    scanf("%d%d", &n, &m);

    struct Edge* edges = (struct Edge*)malloc(m * sizeof(struct Edge));
    printf("请输入边的权重:\n");
    for (int i = 0; i < m; i++) {
        scanf("%d%d%d", &edges[i].u, &edges[i].v, &edges[i].weight);
    }

    printf("最小生成树中的边:\n");
    kruskal(edges, n, m);

    free(edges);

    return 0;
}