EZOJ #386 最小生成树

分析

先建出最小生成树

之后每次倍增找环即可

代码

#include<bits/stdc++.h>
using namespace std;
#define int long long
struct node {
    int x,y,z,is,id;
};
node d[];
int head[],nxt[],to[],w[],cnt,res,dep[];
int pr[][],sum[][],n,m,ans[],fa[],tot;
inline void add(int x,int y,int z){
    nxt[++cnt]=head[x];
    head[x]=cnt;
    to[cnt]=y;
    w[cnt]=z;
    nxt[++cnt]=head[y];
    head[y]=cnt;
    to[cnt]=x;
    w[cnt]=z;
}
inline void dfs(int x,int fa){
    dep[x]=dep[fa]+;
    pr[x][]=fa;
    for(int i=head[x];i;i=nxt[i])
      if(to[i]!=fa)sum[to[i]][]=w[i],dfs(to[i],x);
}
inline int lca(int x,int y){
    if(dep[x]<dep[y])swap(x,y);
    int len=dep[x]-dep[y],wh=;
    for(int i=;i<=;i++)
      if((<<i)&len)wh=max(wh,sum[x][i]),x=pr[x][i];
    if(x==y)return wh;
    for(int i=;i>=;i--)
      if(pr[x][i]!=pr[y][i]){
          wh=max(wh,max(sum[x][i],sum[y][i]));
          x=pr[x][i];
          y=pr[y][i];
      }
    wh=max(wh,max(sum[x][],sum[y][]));
    return wh;
}
inline bool cmp(const node a,const node b){return a.z<b.z;}
inline int sf(int x){return fa[x]==x?x:fa[x]=sf(fa[x]);}
signed main(){
    int i,j,k;
    scanf("%lld%lld",&n,&m);
    for(i=;i<=m;i++){
      scanf("%lld%lld%lld",&d[i].x,&d[i].y,&d[i].z);
      d[i].id=i;
    }
    for(i=;i<=n;i++)fa[i]=i;
    sort(d+,d+m+,cmp);
    for(i=;i<=m;i++){
      int x=d[i].x,y=d[i].y;
      if(sf(x)==sf(y))continue;
      fa[sf(y)]=sf(x);
      add(x,y,d[i].z);
      res+=d[i].z;
      tot++;
      d[i].is=;
      if(tot==n-)break;
    }
    dfs(,);
    for(i=;i<=;i++)
      for(j=;j<=n;j++)
        pr[j][i]=pr[pr[j][i-]][i-],
        sum[j][i]=max(sum[j][i-],sum[pr[j][i-]][i-]);
    for(i=;i<=m;i++){
      if(d[i].is)ans[d[i].id]=res;
        else ans[d[i].id]=res+d[i].z-lca(d[i].x,d[i].y);
    }
    for(i=;i<=m;i++)printf("%lld\n",ans[i]);
    return ;
}