[国家集训队2]Tree I

题面

https://www.luogu.org/problem/P2619

题解

注意可行解的区间性质

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#define ri register int
#define N 200050
#define M 400050
using namespace std;

int n,m,k,cnt;
int f[N],L[M];

struct edge {
  int u,v,l;
  int w;
} e[M];

bool cmp(int x,int y){return L[x]<L[y] || (L[x]==L[y] && e[x].w>e[y].w);}

int id[N];
bool used[N];
int findroot(int x){
  if (f[x]==x) return x;
  return f[x]=findroot(f[x]);
}

int check(int mid) {
  for (ri i=1;i<=m;i++) if (e[i].w) L[i]=e[i].l-mid; else L[i]=e[i].l;
  for (ri i=1;i<=n;i++) f[i]=i;
  for (ri i=1;i<=m;i++) used[i]=0;
  sort(id+1,id+m+1,cmp);
  int cc=0; cnt=0;
  for (ri i=1;i<=m;i++) {
    int r1=findroot(e[id[i]].u),r2=findroot(e[id[i]].v);
    if (r1==r2) continue;
    f[r1]=r2;
    cnt++;
    used[id[i]]=1;
    if (e[id[i]].w) cc++;
    if (cnt==n-1) return cc;
  }
}

int main(){
  scanf("%d %d %d",&n,&m,&k);
  for (ri i=1;i<=m;i++) {
    scanf("%d %d %d %d",&e[i].u,&e[i].v,&e[i].l,&e[i].w);
    e[i].u++;
    e[i].v++;
    e[i].w^=1;
  }
  int lb=-101,rb=101,ans;
  for (ri i=1;i<=m;i++) id[i]=i;
  while (lb<=rb) {
    int mid=(lb+rb)/2;
    if (check(mid)>=k) ans=mid,rb=mid-1; else lb=mid+1;
  }
  check(ans);
  int ret=0; cnt=0;
  for (ri i=1;i<=n;i++) f[i]=i;
  for (ri i=1;i<=m;i++) {
    int r1=findroot(e[id[i]].u),r2=findroot(e[id[i]].v);
    if (r1==r2) continue;
    f[r1]=r2;
    cnt++;
    ret+=L[id[i]];
    if (cnt==n-1) break;
  }
  cout<<ret+k*ans<<endl;
  return 0;
}