【BZOJ】【P1758】【Wc2010】【重建计划】【题解】【点分治+二分+单调队列】

传送门:http://www.lydsy.com/JudgeOnline/problem.php?id=1758

二分答案

把边权减去mid,点分治判断是否有>=0,长度在[L,U]的路径

单调队列优化

Code:

#include<bits/stdc++.h>using namespace std;const double eps=1e-5;const int maxn=1e5+5;int dcmp(double x){return (x>eps)-(x<-eps);}int n,L,U;double lim;int getint(){int res=0;char c=getchar();while(!isdigit(c))c=getchar();while(isdigit(c))res=res*10+c-'0',c=getchar();return res;}double ans;struct edge{int u,v,w;};vector<edge>G[maxn];int root,All;short cant[maxn];int siz[maxn],f[maxn],fa[maxn];void makert(int u,int &root){siz[u]=1;f[u]=0;for(int i=0;i<G[u].size();i++){edge e=G[u][i];if(cant[e.v]||e.v==fa[u])continue;fa[e.v]=u;makert(e.v,root);siz[u]+=siz[e.v];f[u]=max(f[u],siz[e.v]);}f[u]=max(f[u],All-f[u]);if(f[root]>f[u])root=u;}double mx[maxn],d[maxn];int data[maxn],dep[maxn];bool ok(int u,double mid){int size=0;for(int i=0;i<G[u].size();i++){edge e=G[u][i];if(cant[e.v])continue;data[0]=0;fa[e.v]=u;queue<int>q;q.push(e.v);d[e.v]=e.w-mid;dep[e.v]=1;while(!q.empty()){int u=q.front();q.pop();data[++data[0]]=u;for(int i=0;i<G[u].size();i++){edge e=G[u][i];if(cant[e.v]||fa[u]==e.v)continue;fa[e.v]=u;dep[e.v]=dep[u]+1;q.push(e.v);d[e.v]=d[u]+e.w-mid;}}deque<int>dq;int now=size;for(int j=1;j<=data[0];j++){int u=data[j];while(now>=0&&dep[u]+now>=L){while(dq.size()&&mx[dq.back()]<mx[now])dq.pop_back();dq.push_back(now--);}while(dq.size()&&dq.front()+dep[u]>U)dq.pop_front();if(dq.size()&&d[u]+mx[dq.front()]>=0)return 1;}for(int j=size+1;j<=dep[data[data[0]]];j++)mx[j]=-1e10;for(int j=1;j<=data[0];j++){int u=data[j];mx[dep[u]]=max(mx[dep[u]],d[u]);}size=max(size,dep[data[data[0]]]);}return 0;}void calc(int u){double l=ans,r=lim;while(dcmp(l-r)){double mid=(l+r)*.5;if(ok(u,mid))l=mid;else r=mid;}ans=l;}void solve(int u){calc(u);cant[u]=1;for(int i=0;i<G[u].size();i++){edge e=G[u][i];if(cant[e.v]||siz[e.v]<L)continue;f[root=0]=n+1;All=siz[e.v];makert(e.v,root);solve(root);}}int main(){n=getint();L=getint();U=getint();All=n;for(int i=1;i<n;i++){int u=getint(),v=getint(),w=getint();lim=max(lim,double(w));G[u].push_back((edge){u,v,w});G[v].push_back((edge){v,u,w});}f[root=0]=n+1;makert(1,root);solve(root);cout<<fixed<<setprecision(3)<<ans<<endl;return 0;}