BZOJ 4326 NOIP2015 运输计划

Posted 2020-10-24 zzyer

题解：二分答案，标记长度>mid的路径，找到最长的被所有标记路径覆盖的边，如果maxpath-maxedge<=mid就符合

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn=300009;
const int oo=1000000000;

int n,m;

int cntedge;
int head[maxn];
int to[maxn<<1],nex[maxn<<1],dist[maxn<<1];
void Addedge(int x,int y,int z){
	nex[++cntedge]=head[x];
	to[cntedge]=y;
	dist[cntedge]=z;
	head[x]=cntedge;
}

int f[maxn][20];
int fdist[maxn];
int dep[maxn];
int d[maxn];
void Dfs(int now,int fa){
	f[now][0]=fa;
	dep[now]=dep[fa]+1;
	for(int i=head[now];i;i=nex[i]){
		if(to[i]==fa)continue;
		fdist[to[i]]=dist[i];
		d[to[i]]=d[now]+dist[i];
		Dfs(to[i],now);
	}
}

void LCAinit(){
	for(int j=1;j<=19;++j){
		for(int i=1;i<=n;++i){
			f[i][j]=f[f[i][j-1]][j-1];
		}
	}
}
int Getlca(int u,int v){
	if(dep[u]<dep[v])swap(u,v);
	for(int j=19;j>=0;--j){
		if(dep[f[u][j]]>=dep[v])u=f[u][j];
	}
	if(u==v)return u;
	for(int j=19;j>=0;--j){
		if(f[u][j]!=f[v][j]){
			u=f[u][j];v=f[v][j];
		}
	}
	return f[u][0];
}

int g[maxn];
void Dp(int x,int fa){
	for(int i=head[x];i;i=nex[i]){
		if(to[i]==fa)continue;
		Dp(to[i],x);
		g[x]+=g[to[i]];
	}
}

int rx[maxn],ry[maxn],lca[maxn],rd[maxn];
int maxlength;
int l,r,mid,ans;

void minit(){
	maxlength=0;
	memset(d,0,sizeof(d));
	memset(dep,0,sizeof(dep));
	memset(f,0,sizeof(f));
	memset(fdist,0,sizeof(fdist));
	memset(head,0,sizeof(head));
	cntedge=0;
}
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n-1;++i){
		int x,y,z;
		scanf("%d%d%d",&x,&y,&z);
		Addedge(x,y,z);
		Addedge(y,x,z);
	}
	
	Dfs(1,0);
	LCAinit();
	
	for(int i=1;i<=m;++i){
		scanf("%d%d",&rx[i],&ry[i]);
		lca[i]=Getlca(rx[i],ry[i]);
		rd[i]=d[rx[i]]+d[ry[i]]-2*d[lca[i]];
		maxlength=max(maxlength,rd[i]);
	}
	
	l=0;r=oo;
	while(l<=r){
		mid=(l+r)>>1;
		
		memset(g,0,sizeof(g));
		int invedge=0;
		for(int i=1;i<=m;++i){
			if(rd[i]>mid){
				g[rx[i]]++;g[ry[i]]++;g[lca[i]]-=2;++invedge;
			}
		}
		Dp(1,0);
		int maxedge=0;
		for(int i=2;i<=n;++i){
			if(g[i]==invedge)maxedge=max(maxedge,fdist[i]);
		}
		if(maxlength-maxedge<=mid){
			ans=mid;r=mid-1;
		}else{
			l=mid+1;
		}
	}
	cout<<ans<<endl;
	return 0;
}