图的最小生成树(MST)之Kruskal算法

来源：互联网发布：java程序设计实验编辑：程序博客网时间：2024/05/29 09:24

克鲁斯卡尔（Kruskal）算法（只与边相关）

Kruskal算法通过每次向当前最小代价生成树T中加入一条边的方法构造最终的最小生成树T。算法按照边的权值非递减顺序选取边，并将其加入T中。如果所选取的边与T中的边不形成环路，则这条边加入T中。由于图G是联通的，且具有n个顶点（n>0），所以最终恰好选取n-1条边加入T中。

实现代码：

#include<iostream>#include<cstring>#include<string>#include<cstdio>#include<algorithm>using namespace std;#define MAX 50int parent[MAX], family[MAX];int vertex_num, edge_num;typedef struct Edge //Edge info storage{int a;int b;int weight;};bool cmp(const Edge & a, const Edge & b){return a.weight < b.weight;}int find(int x) {/* if vertex x is single : parent[x] = x family[x] = 1if vertex x is attached to another vertex y: parent[x] = y  , family[y] = family[y] + family[x]   */for(;parent[x]!=x;x=parent[x]);return x; }bool join(int x, int y) //join two vertex set{/* vertex set join : if parent[x] = parent[y]vertex x and vertex y are in the same set  */int root1, root2;root1 = find(x);root2 = find(y);if(root1 == root2) //in the same vertex setreturn false;else if(family[root1] >= family[root2]){parent[root2] = root1;family[root1] += family[root2];}else{parent[root1] = root2;family[root2] += family[root1];}return true;}int main(){int ltotal, sum, flag;Edge edge[MAX];scanf("%d%d", &vertex_num, &edge_num);ltotal = 0, sum = 0, flag = 0;for(int i = 1; i <= vertex_num; ++i) //initialize parent[] and family[] {parent[i] = i;family[i] = 1;}for(int i = 1; i <= edge_num ; ++i){scanf("%d%d%d", &edge[i].a, &edge[i].b, &edge[i].weight);}sort(edge + 1, edge + 1 + edge_num, cmp); //sort edge by weight of each edgefor(int i = 1; i <= edge_num; ++i){if(join(edge[i].a, edge[i].b)){ltotal++; // edge num increment by 1sum += edge[i].weight; //total weight cout<<edge[i].a<<"->"<<edge[i].b<<endl;}if(ltotal == vertex_num - 1) //MST if edge num = vertex num - 1{flag = 1;break;}}if(flag) printf("%d\n", sum);else printf("data error.\n");return 0;}

输入数据：

7 91 2 281 6 102 3 162 7 143 4 124 5 224 7 185 6 255 7 24

输入数据代表的图及Kruskal算法的结果图：

输出数据：

1->63->42->72->34->55->699

REF：

1，http://blog.csdn.net/niushuai666/article/details/6689285

2，数据结构（C语言版） Ellis Horowitz

0 0