不严格次小生成树。

注意图可能不连通。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;

const int maxn = 505;
const int INF = 1e7;
bool vis[maxn];
int d[maxn];
int pre[maxn];
int Max[maxn][maxn];
int g[maxn][maxn];
int n, m;

void init()
{
    int u, v, c;
    scanf("%d%d", &n, &m);
    for(int i=1; i<=n; ++i) for(int j=1; j<=n; ++j) g[i][j] = INF;
    for(int i=1; i<=m; ++i) {
        scanf("%d%d%d", &u, &v, &c);
        g[u][v] = g[v][u] = c;
    }
}

int Prim()
{
    for(int i=2; i<=n; ++i) {
        pre[i]=1;
        d[i] = g[1][i];
    }
    memset(vis, 0, sizeof vis );
    vis[1] = 1; d[1] = 0; pre[1] = -1;
    int ans = 0;
    for(int i=1; i<n; ++i) {
        int Mn = INF, k = -1;
        for(int j=1; j<=n; ++j)
            if(!vis[j] && Mn>d[j]){ Mn = d[k=j];}
        if(-1==k) return INF;
        ans += Mn;
        g[k][pre[k]] = g[pre[k]][k] = INF;
        for(int j=1; j<=n; ++j) if(vis[j])
                Max[j][k] = Max[k][j] = max(Mn, Max[pre[k]][j]);
        vis[k] = 1;
        for(int j=1; j<=n; ++j)
            if(!vis[j]&&d[j]>g[j][k]) {
                d[j] = g[j][k];
                pre[j] = k;
            }
    }
    return ans;
}

void solve()
{
    int ans1 = Prim();
    if(ans1==INF) {
        printf("Cost: -1\n");
    } else {
        printf("Cost: %d\n", ans1);
    }
    int ans2 = INF;
    for(int i=1; i<=n; ++i)
        for(int j=i+1; j<=n; ++j)
            if(g[i][j]!=INF) {
                ans2 = min(ans2, ans1+g[i][j]-Max[i][j]);
            }
    if(ans2==INF){
        printf("Cost: -1\n");
    } else {
        printf("Cost: %d\n", ans2);
    }

}

int main()
{
    init();
    solve();
    return 0;
}

Ural 1416 Confidential，次小生成树