洛谷 [P3398] 仓鼠找sugar

树剖求LCA

我们可以发现,两条路径ab,cd相交,当且仅当 dep[lca(a,b)]>=dep[lca(c,d)]&(lca(lca(a,b),c)lca(a,b)||lca(lca(a,b),d)lca(a,b))或把abcd交换一下即可

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstdlib>
using namespace std;
const int MAXN=200005;
int init(){
	int rv=0,fh=1;
	char c=getchar();
	while(c<'0'||c>'9'){
		if(c=='-') fh=-1;
		c=getchar();
	}
	while(c>='0'&&c<='9'){
		rv=(rv<<1)+(rv<<3)+c-'0';
		c=getchar();
	}
	return rv*fh;
}
int head[MAXN],dep[MAXN],fa[MAXN],siz[MAXN],son[MAXN],n,m,nume,top[MAXN],id[MAXN],ind;
struct edge{
	int to,nxt;
}e[MAXN<<1];
void adde(int from,int to){
	e[++nume].to=to;
	e[nume].nxt=head[from];
	head[from]=nume;
}
void dfs1(int u,int rt){
	fa[u]=rt;
	dep[u]=dep[rt]+1;
	siz[u]=1;
	int ma=0;
	for(int i=head[u];i;i=e[i].nxt){
		int v=e[i].to;
		if(v==rt) continue;
		dfs1(v,u);
		siz[u]+=siz[v];
		if(ma<siz[v]){
			ma=siz[v];
			son[u]=v;
		}
	}
}
void dfs2(int u,int topf){
	top[u]=topf;
	id[u]=++ind;
	if(!son[u]) return;
	dfs2(son[u],topf);
	for(int i=head[u];i;i=e[i].nxt){
		int v=e[i].to;
		if(v==fa[u]||v==son[u]) continue;
		dfs2(v,v);
	}
}
int LCA(int a,int b){
	while(top[a]!=top[b]){
		if(dep[top[a]]>dep[top[b]]) a=fa[top[a]];
		else b=fa[top[b]];
	}
	return dep[a]>dep[b]?b:a;
}
int main(){
	n=init();m=init();
	for(int i=1;i<n;i++){
		int u=init(),v=init();
		adde(u,v);adde(v,u);
	}
	dep[1]=1;
	dfs1(1,0);
	dfs2(1,1);
	for(int i=1;i<=m;i++){
		int a=init(),b=init(),c=init(),d=init();
		int r1=LCA(a,b),r2=LCA(c,d);
		if(dep[r1]<dep[r2]){
			swap(r1,r2);
			swap(a,c);
			swap(b,d);
		}
		if(LCA(r1,c)==r1||LCA(r1,d)==r1) cout<<"Y"<<endl;
		else cout<<"N"<<endl;
	}
	return 0;
}