使用 kruskal 算法查找最小生成树 所有边应按权重非降序排列。
选择最小的边。如果未形成环，则包含该边。
应执行步骤 2，直到生成树具有 (v-1) 条边。
在这种情况下，我们被告知要使用贪婪方法。贪心选项是选择权重最小的边。举例来说：该图的最小生成树为 (9-1)= 8 条边。
after sorting:weight src dest21 27 2622 28 2222 26 2524 20 2124 22 2526 28 2627 22 2327 27 2828 20 2728 21 2229 23 2430 25 2431 21 2734 23 25
现在我们需要根据排序选取所有边。
包含边 26-27->，因为没有形成环
边包括 28-22->，因为没有形成环路
包括边缘 26-25->，因为没有形成环路。
包括边缘 20-21->，因为没有形成环路
边 22-25-> 被包含，因为没有形成环路。
边 28-26-> 因环路形成而被丢弃
边 22-23-> > 包括，因为没有形成环路
边 27-28-> 因环路形成而被丢弃
边线 20-27-> 包括，因为没有形成环路
边21-22->因形成环而被丢弃
边23-24->因未形成环而被包括
由于边的数量为(v-1)，所以算法到此结束。
示例#include <stdio.h>#include <stdlib.h>#include <string.h>struct edge { int src, dest, weight;};struct graph { int v, e; struct edge* edge;};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(sizeof( struct edge)*e); return graph;}struct subset { int parent; int rank;};int find(struct subset subsets[], int i){ if (subsets[i].parent != i) subsets[i].parent = find(subsets, subsets[i].parent); return subsets[i].parent;}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++; }}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;}void kruskalmst(struct graph* graph){ int v = graph->v; struct edge result[v]; int e = 0; int i = 0; qsort(graph->edge, graph->e, sizeof(graph->edge[0]), mycomp); struct subset* subsets = (struct subset*)malloc(v * sizeof(struct subset)); for (int v = 0; v < v; ++v) { subsets[v].parent = v; subsets[v].rank = 0; } while (e < v - 1 && i < graph->e) { struct edge next_edge = graph->edge[i++]; int x = find(subsets, next_edge.src); int y = find(subsets, next_edge.dest); if (x != y) { result[e++] = next_edge; union(subsets, x, y); } } printf("following are the edges in the constructed mst\n"); int minimumcost = 0; for (i = 0; i < e; ++i){ printf("%d -- %d == %d\n", result[i].src, result[i].dest, result[i].weight); minimumcost += result[i].weight; } printf("minimum cost spanning tree : %d",minimumcost); return;}int main(){ /* let us create the following weighted graph 30 0--------1 | \ | 26| 25\ |15 | \ | 22--------23 24 */ int v = 24; int e = 25; struct graph* graph = creategraph(v, e); graph->edge[0].src = 20; graph->edge[0].dest = 21; graph->edge[0].weight = 30; graph->edge[1].src = 20; graph->edge[1].dest = 22; graph->edge[1].weight = 26; graph->edge[2].src = 20; graph->edge[2].dest = 23; graph->edge[2].weight = 25; graph->edge[3].src = 21; graph->edge[3].dest = 23; graph->edge[3].weight = 35; graph->edge[4].src = 22; graph->edge[4].dest = 23; graph->edge[4].weight = 24; kruskalmst(graph); return 0;}
输出following are the edges in the constructed mst22 -- 23 == 2420 -- 23 == 2520 -- 21 == 30minimum cost spanning tree : 79
结论本教程演示了如何使用 kruskal 的最小生成树算法-贪心法和 c++ 代码来解决此问题。我们还可以用java、python和其他语言编写这段代码。它是根据克鲁斯卡尔的概念建模的。该程序查找给定图中的最短生成树。我们希望本教程对您有所帮助。
以上就是kruskal的最小生成树算法-贪婪算法在c++中的详细内容。