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");elseprintf("%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");elseprintf("%d\n", res);return 0;
}