一、最小生成树

二、代码

1、Prim算法

#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

const int N = 510, INF = 0x3f3f3f3f;

int n, m;
int g[N][N];
int dist[N];
bool st[N];

int prim()
{
	memset(dist, 0x3f, sizeof dist);

	int res = 0;
	for(int i = 0; i < n; i++){
		int t = -1;
		for(int j = 1; j <= n; j++)
			if(!st[j] && (t == -1 || dist[t] > dist[j]))
				t = j;
		
		if(i && dist[t] == INF)
			return INF;
		if(i)
			res += dist[t];
		
		for(int j = 1; j <= n; j++)
			dist[j] = min(dist[j], g[t][j]);
		
		st[t] = true;
	}
	return res;
}


int main()
{
	scanf("%d%d", &n, &m);

	memset(g, 0x3f, sizeof g);

	while(m--){
		int a, b, c;
		scanf("%d%d%d", &a, &b, &c);
		g[a][b] = g[b][a] = min(g[a][b], c);
	}

	int t = prim();

	if(t == INF)
		puts("impossible");
	else
		printf("%d\n", t);

	return 0;
}

2、Kruskal算法

#include <iostream>
#include <algorithm>

using namespace std;

const int N = 200010;

int n, m;
int p[N];

struct Edge
{
	int a, b, w;

	bool operator< (const Edge &W) const{
		return w < W.w;
	}
}edges[N];

int find(int x)
{
	if(p[x] != x)
		p[x] = find(p[x]);
	return p[x];
}

int main()
{
	scanf("%d%d", &n, &m);

	for(int i = 0; i < m; i++){
		int a, b, w;
		scanf("%d%d%d", &a, &b, &w);
		edges[i] = {a, b, w};
	}

	sort(edges, edges + m);

	for(int i = 1; i <= n; i++)
		p[i] = i;
	
	int res = 0, cnt = 0;
	for(int i = 0; i < m; i++){
		int a = edges[i].a, b = edges[i].b, w = edges[i].w;

		a = find(a), b = find(b);
		if(a != b){
			p[a] = b;
			res += w;
			cnt++;
		}
	}

	if(cnt < n - 1)
		puts("impossible");
	else
		printf("%d\n", res);
	
	return 0;
}