[二分答案 树链剖分] BZOJ 4326 NOIP2015 运输计划

考虑二分

把所有超过mid的链取交集，然后取交集上最长的边权赋0，判断

#include<cstdio>
#include<cstdlib>
#include<algorithm>
#define V G[p].v
using namespace std;

inline char nc()
{
	static char buf[100000],*p1=buf,*p2=buf;
	if (p1==p2) { p2=(p1=buf)+fread(buf,1,100000,stdin); if (p1==p2) return EOF; }
	return *p1++;
}

inline void read(int &x)
{
	char c=nc(),b=1;
	for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;
	for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;
}

struct Seg_SUM{
	int M,TH;
	int T[400005],H[400005];
	inline void Build (int n)
	{
		for (M=1,TH=0;M<n+2;M<<=1,TH++);
	}
	inline void Add(int s,int t,int c)
	{
		for (s+=M-1,t+=M+1;s^t^1;s>>=1,t>>=1)
		{
			if (~s&1) T[s^1]+=c;
			if ( t&1) T[t^1]+=c;
		}
	}
	inline int Query(int s)
	{
		int ret=0;
		ret+=T[s+=M];
		while (s>>=1)
			ret+=T[s];
		return ret;
	}
}Seg;

const int N=300005;

struct edge{
	int u,v,w,next;
};

edge G[2*N];
int head[N],inum;

inline void add(int u,int v,int w,int p){
	G[p].u=u; G[p].v=v; G[p].w=w; G[p].next=head[u]; head[u]=p;
}

int size[N],depth[N],fat[N],dis[N];
int clk,tid[N],top[N];

void dfs(int u,int fa){
	fat[u]=fa; depth[u]=depth[fa]+1; size[u]=1;
	for (int p=head[u];p;p=G[p].next)
		if (V!=fa)
		{
			dis[V]=dis[u]+G[p].w;
			dfs(V,u),size[u]+=size[V];
		}
}

void find(int u,int fa,int z){
	tid[u]=++clk; top[u]=z;
	int maximum=0,son=0;
	for (int p=head[u];p;p=G[p].next)
		if (V!=fa && size[V]>maximum)
			maximum=size[son=V];
	if (son) find(son,u,z);
	for (int p=head[u];p;p=G[p].next)
		if (V!=fa && V!=son)
			find(V,u,V);
}

inline int LCA(int u,int v){
	for (;top[u]!=top[v];u=fat[top[u]])
		if (depth[top[u]]<depth[top[v]]) 
			swap(u,v);
	if (depth[u]>depth[v]) swap(u,v);
	return u;
}

int n,m;

struct event{
	int u,v,lca,dis;
}eve[N];

inline void Modify(int u,int v,int r){
	for (;top[u]!=top[v];u=fat[top[u]])
	{
		if (depth[top[u]]<depth[top[v]]) swap(u,v);
		Seg.Add(tid[top[u]],tid[u],r);
	}
	if (depth[u]>depth[v]) swap(u,v);
	Seg.Add(tid[u],tid[v],r);
}

inline bool Check(int mid){
	int maxd=0,cnt=0;
	for (int i=1;i<=m;i++)
		if (eve[i].dis>mid)
		{
			++cnt;
			Modify(eve[i].u,eve[i].v,1);
			maxd=max(maxd,eve[i].dis);
		}
	int maxl=0;
	for (int i=1;i<=n;i++)
		if (i!=1 && Seg.Query(tid[i])==cnt && Seg.Query(tid[fat[i]])==cnt)
			maxl=max(maxl,dis[i]-dis[fat[i]]);
	for (int i=1;i<=m;i++)
		if (eve[i].dis>mid)
			Modify(eve[i].u,eve[i].v,-1);
	return maxd-maxl<=mid;
}

int maxd=0;

inline void Bin()
{
	Seg.Build(n);
	int L=0,R=maxd,MID;
	while (L+1<R)
		if (Check(MID=(L+R)>>1))
			R=MID;
		else
			L=MID;
	printf("%d\n",R);
}

int main()
{
	int iu,iv,iw;
	freopen("t.in","r",stdin);
	freopen("t.out","w",stdout);
	read(n); read(m);
	for (int i=1;i<n;i++)
		read(iu),read(iv),read(iw),add(iu,iv,iw,++inum),add(iv,iu,iw,++inum);
	dfs(1,0); find(1,0,1);
	for (int i=1;i<=m;i++)
	{
		read(iu),read(iv);
		eve[i].u=iu; eve[i].v=iv;
		eve[i].lca=LCA(iu,iv); eve[i].dis=dis[iu]+dis[iv]-2*dis[eve[i].lca];
		maxd=max(maxd,eve[i].dis);
	}
	Bin();
	return 0;
}