kruskal算法的c++实现

kruskal 算法的思想是将图中所有的顶点，都看作不同的连通分支，也就是他们每一个都是一个树。之后，从所有边中选权重最小的边，每次判断该边的两个顶点是否属于不同的连通分支，如果不属于，将此边加入，并修改两个顶点为一个连通分支 ; 若属于则继续选下一个权重最小的边进行上述判断，直到选中的边的个数等于N-1（N为顶点个数），算法结束，此时所有选中的边和所有的点为原图的最小生成树。

c++ 实现如下：

#include <iostream>

#include <algorithm>

#include <cstdio>

#include <vector>

#include <unordered_map>

struct edges{

edges(int s ,int d , int w):source(s),dist(d),weight(w){}

int source;

int dist;

int weight;

};

bool comp(edges &a , edges &b){

return a.weight < b.weight;

}

int main(){

std::vector<edges> edge_array;

int graph[][6] = {

{0,1,4,0,0,0},

{1,0,1,0,4,0},

{4,1,0,3,0,0},

{0,0,3,0,4,5},

{0,4,0,4,0,0},

{0,0,0,5,0,0}

};

std::unordered_map<int,int> vTree;

for(int i =0 ; i < 6 ; i++){

vTree.insert(std::make_pair(i,i));

}

for(int i =0 ; i < 6 ; i++){

for(int j = i+1 ; j <6 ; j++){

if(graph[i][j] != 0){

edge_array.push_back(edges(i,j,graph[i][j]));

edge_array.push_back(edges(j,i,graph[i][j]));

}

}

}

std::sort(edge_array.begin(),edge_array.end(),comp);

//krusal algorithm begin

int weight_sum = 0;

int i = 0;

for(auto iter = edge_array.begin(); iter != edge_array.end() ; iter++){

if(i >= 5){

break;

}else{

if( vTree.find(iter->source)->second == vTree.find(iter->dist)->second ){

continue;

}else{

i++;

weight_sum += iter->weight;

if(iter->source < iter->dist){

vTree.find(iter->dist)->second = vTree.find(iter->source)->second;

}else{

vTree.find(iter->source)->second = vTree.find(iter->dist)->second;

}

std::cout << "edge: " << iter->source <<" -> " << iter->dist <<" = " << iter->weight << std::endl;

}

}

}

std::cout << "the MST result is : " << weight_sum << std::endl;

return 0;

}