prime算法

参考博客：https://blog.csdn.net/lqcsp/article/details/14118871

复杂度：O(n*n)

#include <iostream>  
#include <string.h>  
  
using namespace std;  
const int MAXN = 2010;  
const int INF = 1 << 30;  
int map[MAXN][MAXN];  
int N, M;  
int lowcost[MAXN];  
  
void init()  
{  
  for(size_t i = 0; i <= N; ++i)  
    for(size_t j = 0; j <= N; ++j)  
      map[i][j] = INF;  
}  
  
int prime()  
{  
  for(size_t i = 1; i <= N; ++i)  
    lowcost[i] = map[1][i];  
  int min;  
  bool visited[N + 1];// index begin from 1 not 0  
  int ans = -1;  
  memset(visited, false, sizeof(visited));  
  lowcost[1] = 0;  
  visited[1] = true;  
  for(size_t i = 1; i < N; ++i)//loop N - 1 times  
  {  
    min = INF;  
    int k;  
    for(size_t j = 1; j <= N; ++j)// find the minimun edge between two edge set  
    {  
      if(!visited[j] && min > lowcost[j])  
      {  
        min = lowcost[j];  
        k = j;  
      }  
    }  
    visited[k] = true;  
    ans = ans > min ? ans : min;   
    for(size_t j = 1; j <= N; ++j)// update the array of lowcost   
    {  
      if(!visited[j] && lowcost[j] > map[k][j])  
        lowcost[j] = map[k][j];  
    }  
  }  
  return ans;  
}  
  
int main()  
{  
  while(cin >> N >> M)  
  {  
    init();  
    int x, y, c;  
    for(size_t i = 0; i < M; ++i)  
    {  
      cin >> x >> y >> c;  
      if(map[x][y] > c)  
        map[x][y] = c;  
      if(map[y][x] > c)  
        map[y][x] = c;  
    }  
    cout << prime() << endl;  
  }  
}