tyvj 2054 [Nescafé29]四叶草魔杖——最小生成树+状压dp

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=20,M=N*(N-1)/2,Lm=(1<<16)+5;
int n,m,a[N],hd[N],c[Lm],lm,v[Lm],cnt,dp[Lm],fa[N];
bool vis[Lm];
struct Ed{
    int x,y,w;
    Ed(int x=0,int y=0,int w=0):x(x),y(y),w(w) {}
}ed[M];
bool cmp(Ed x,Ed y){return x.w<y.w;}
int find(int a){return fa[a]==a?a:fa[a]=find(fa[a]);}
void kruscal(int s,int &k)
{
    for(int i=1;i<=n;i++)fa[i]=i;
    for(int i=1;i<=m;i++)
    {
        int x=ed[i].x,y=ed[i].y;
        if(((1<<(x-1))&s)&&((1<<(y-1))&s)&&find(x)!=find(y))
        {
            fa[(find(x))]=find(y);c[k]+=ed[i].w;
        }
    }
    int tf=0;
    for(int i=0;i<n;i++)
      if((1<<i)&s)
        {
          if(!tf)tf=find(i+1);
          else if(find(i+1)!=tf){v[k]=c[k]=0;k--;return;}
        }
}
void init()
{
    sort(ed+1,ed+m+1,cmp);
    for(int s=1;s<lm;s++)
    {
        int sum=0;
        for(int j=0;j<n;j++) if((1<<j)&s) sum+=a[j+1];
        if(sum)continue;
        v[++cnt]=s;kruscal(s,cnt);
    }
}
void dfs(int s)
{
    if(vis[s])return;vis[s]=1;
    for(int i=1;i<=cnt;i++)
        if((s&v[i])==v[i])
        {
            dfs(s-v[i]);dp[s]=min(dp[s],dp[s-v[i]]+c[i]);
        }
}
int main()
{
    scanf("%d%d",&n,&m);int x,y,z;lm=(1<<n);
    for(int i=1;i<=n;i++)scanf("%d",&a[i]);
    for(int i=1;i<=m;i++)
    {
        scanf("%d%d%d",&x,&y,&z);
        ed[i]=Ed(x+1,y+1,z);
    }
    init();
    memset(dp,0x3f,sizeof dp);dp[0]=0;
    dfs(lm-1);
    if(dp[lm-1]==0x3f3f3f3f)printf("Impossible");
    else printf("%d",dp[lm-1]);
    return 0;
}