LG1505 [国家集训队]旅游 树链剖分

问题描述

LG1505

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题解

边化点权。

超级多操作的树剖板子...

以后就拿这个当树剖板子复习吧...

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\(\mathrm{Code}\)

#include<bits/stdc++.h>
using namespace std;

template <typename Tp>
void read(Tp &x){
	x=0;char ch=1;int fh;
	while(ch!='-'&&(ch>'9'||ch<'0')) ch=getchar();
	if(ch=='-') ch=getchar(),fh=-1;
	else fh=1;
	while(ch>='0'&&ch<='9') x=(x<<1)+(x<<3)+ch-'0',ch=getchar();
	x*=fh;
}

template <typename Tp>
void fr(Tp &x){
	char ch=1;
	while(ch!='C'&&ch!='N'&&ch!='S'&&ch!='M') ch=getchar();
	if(ch=='M'){
		ch=1;while(ch!='A'&&ch!='I') ch=getchar();
	}
	if(ch=='C') x=1;
	else if(ch=='N') x=2;
	else if(ch=='S') x=3;
	else if(ch=='A') x=4;
	else x=5;
}

const int maxn=40007;
const int INF=0x3f3f3f3f;

int n;
int Head[maxn],to[maxn],Next[maxn],tot=1,w[maxn];

int size[maxn],fa[maxn],dep[maxn];
int New[maxn],pre[maxn],ind,top[maxn];
int son[maxn];

//edge id i  ->  2*i-1,2*i

void add(int x,int y,int z){
	to[++tot]=y,Next[tot]=Head[x],Head[x]=tot,w[tot]=z;
}

void dfs1(int x,int f,int dp){
	size[x]=1,fa[x]=f,dep[x]=dp;
	int mxx=-1;
	for(int i=Head[x];i;i=Next[i]){
		int y=to[i];
		if(y==f) continue;
		dfs1(y,x,dp+1);
		size[x]+=size[y];
		if(size[y]>mxx) mxx=size[y],son[x]=y;
	}
}

void dfs2(int x,int tp){
	New[x]=++ind,pre[ind]=x,top[x]=tp;
	if(!son[x]) return;
	dfs2(son[x],tp);
	for(int i=Head[x];i;i=Next[i]){
		int y=to[i];
		if(y==fa[x]||y==son[x]) continue;
		dfs2(y,y);
	}
}

int val[maxn],f[maxn];

void preprocess(){
	for(int i=2;i<=tot;i+=2){//错误笔记：tot一开始等于1，则第一条边从2开始
		int x=to[i xor 1],y=to[i];
		if(dep[x]>dep[y]) val[x]=w[i],f[i]=f[i xor 1]=x;//错误笔记：边化点权，要记录每个边化到哪个点上了。
		else val[y]=w[i],f[i]=f[i xor 1]=y;
	}
}

#define lfc (x<<1)
#define rgc ((x<<1)|1)
#define mid ((l+r)>>1)

int mx[maxn<<1],mi[maxn<<1],sum[maxn<<1];
int lazy[maxn<<1];

void pushup(int x){
	mx[x]=max(mx[lfc],mx[rgc]);
	mi[x]=min(mi[lfc],mi[rgc]);
	sum[x]=sum[lfc]+sum[rgc];
}

void pushdown(int x){
	if(!lazy[x]) return;
	lazy[lfc]^=1,lazy[rgc]^=1;
	sum[lfc]=-sum[lfc],sum[rgc]=-sum[rgc];
	int lf=mx[lfc],rg=mx[rgc];
	mx[lfc]=-mi[lfc],mx[rgc]=-mi[rgc];
	mi[lfc]=-lf,mi[rgc]=-rg;
	lazy[x]=0;//错误笔记：lazy标记有没有清空
}

void build(int x,int l,int r){
	if(l==r){
		mx[x]=mi[x]=sum[x]=val[pre[l]];
		return;
	}
	build(lfc,l,mid);build(rgc,mid+1,r);
	pushup(x);
}

int L,R,need;

void dd_change(int x,int l,int r){
	if(l==r&&L==l){
		sum[x]=mx[x]=mi[x]=need;return;
	}
	pushdown(x);
	if(L<=mid) dd_change(lfc,l,mid);
	else dd_change(rgc,mid+1,r);
	pushup(x);
}

void qj_change(int x,int l,int r){
	if(l>R||r<L) return;
	if(L<=l&&r<=R){
		lazy[x]^=1;int temp=mx[x];
		sum[x]=-sum[x],mx[x]=-mi[x],mi[x]=-temp;
		return;
	}
	pushdown(x);
	qj_change(lfc,l,mid);qj_change(rgc,mid+1,r);
	pushup(x);
}

int sum_query(int x,int l,int r){
	if(l>R||r<L) return 0;
	if(L<=l&&r<=R) return sum[x];
	pushdown(x);
	return sum_query(lfc,l,mid)+sum_query(rgc,mid+1,r);
}

int max_query(int x,int l,int r){
	if(l>R||r<L) return -INF;
	if(L<=l&&r<=R) return mx[x];
	pushdown(x);
	return max(max_query(lfc,l,mid),max_query(rgc,mid+1,r));
}

int min_query(int x,int l,int r){
	if(l>R||r<L) return INF;
	if(L<=l&&r<=R) return mi[x];
	pushdown(x);
	return min(min_query(lfc,l,mid),min_query(rgc,mid+1,r));
}

int T,op;

void cz1(){
	int x;
	read(x);read(need);
	x=New[f[x<<1]],L=x;//错误笔记：双向存边，在数组中编号要*2
	dd_change(1,1,n);
}

void cz2(){
	int x,y;
	read(x);read(y);
	++x,++y;
	while(top[x]!=top[y]){
		if(dep[top[x]]<dep[top[y]]) swap(x,y);
		L=New[top[x]],R=New[x];//错误笔记：写作L=New[x],R=New[y]
		qj_change(1,1,n);
		x=fa[top[x]];
	}
	if(dep[x]>dep[y]) swap(x,y);
	L=New[x]+1,R=New[y];
	if(L<=R) qj_change(1,1,n);
}

void cz3(){
	int x,y,res=0;
	read(x);read(y);
	++x,++y;
	while(top[x]!=top[y]){
		if(dep[top[x]]<dep[top[y]]) swap(x,y);
		L=New[top[x]],R=New[x];
		res+=sum_query(1,1,n);
		x=fa[top[x]];
	}
	if(dep[x]>dep[y]) swap(x,y);
	L=New[x]+1,R=New[y];
	if(L<=R) res+=sum_query(1,1,n);
	printf("%d\n",res);
}

void cz4(){
	int x,y,res=-INF;
	read(x);read(y);
	++x,++y;
	while(top[x]!=top[y]){
		if(dep[top[x]]<dep[top[y]]) swap(x,y);
		L=New[top[x]],R=New[x];
		res=max(res,max_query(1,1,n));
		x=fa[top[x]];
	}
	if(dep[x]>dep[y]) swap(x,y);
	L=New[x]+1,R=New[y];
	if(L<=R) res=max(res,max_query(1,1,n));
	printf("%d\n",res);
}

void cz5(){
	int x,y,res=INF;
	read(x);read(y);
	++x,++y;
	while(top[x]!=top[y]){
		if(dep[top[x]]<dep[top[y]]) swap(x,y);
		L=New[top[x]],R=New[x];
		res=min(res,min_query(1,1,n));
		x=fa[top[x]];
	}
	if(dep[x]>dep[y]) swap(x,y);
	L=New[x]+1,R=New[y];
	if(L<=R) res=min(res,min_query(1,1,n));
	printf("%d\n",res);
}

int main(){
	#ifndef ONLINE_JUDGE
		freopen("travel.in","r",stdin);
	#endif
	read(n);
	for(int i=1,x,y,z;i<n;i++){
		read(x);read(y);read(z);
		++x,++y;
		add(x,y,z);add(y,x,z);
	}
	dfs1(1,0,1);dfs2(1,1);
	preprocess();build(1,1,n);
	read(T);
	while(T--){
		fr(op);
		if(op==1) cz1();
		else if(op==2) cz2();
		else if(op==3) cz3();
		else if(op==4) cz4();
		else cz5();
	}
	return 0;
}