POJ3728：LCA

POJ3728

题意：从a到b的路径上，找权值差最大的两点，并且后一点比前一点大。输出最大权值差。

题解

• 暴力倍增LCA。

代码

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <vector>
using namespace std;
int const inf = 0x7f7f7f7f;
int const N = 50000 + 10;
int const M = 20;
int first[N],ne[N<<1],to[N<<1],lg[N];
int tot,n,q;
int fa[N][M],dep[N],val[N],up[N][M],down[N][M],maxx[N][M],minn[N][M];
void pre(){
	lg[1] = 0;
	for(int i=2;i<N;i++)
		lg[i] = lg[i/2] + 1;
}
void add(int u,int v){
	ne[tot] = first[u];
	to[tot] = v;
	first[u] = tot++;
}
void dfs(int u,int f){
	dep[u] = dep[f] + 1;	fa[u][0] = f;
	maxx[u][0] = max(val[u],val[f]);	minn[u][0] = min(val[u],val[f]);
	up[u][0] = max(0,val[f] - val[u]);	down[u][0] = max(0,val[u] - val[f]);
	for(int i=1;(1<<i)<=dep[u];i++){	
		int k = fa[u][i-1];
		fa[u][i] = fa[k][i-1];
		maxx[u][i] = max(maxx[u][i-1],maxx[k][i-1]);	
		minn[u][i] = min(minn[u][i-1],minn[k][i-1]);	
		up[u][i] = max(max(0,maxx[k][i-1]-minn[u][i-1]),max(up[u][i-1],up[k][i-1]));
		down[u][i] = max(max(0,maxx[u][i-1]-minn[k][i-1]),max(down[u][i-1],down[k][i-1]));
	}
	for(int i=first[u];~i;i=ne[i]){
		int v = to[i];
		if(v == f)	continue;
		dfs(v,u);
	}
}
int lca(int x,int y){
	if(dep[x] < dep[y])		swap(x,y);
	while(dep[x] > dep[y])
		x = fa[x][lg[dep[x]-dep[y]]];
	if(x == y)	return x;
	for(int i=lg[dep[x]];i>=0;i--)
		if(fa[x][i] != fa[y][i])
			x = fa[x][i],	y = fa[y][i];
	return fa[x][0];
}
void solve(){
	scanf("%d",&q);
	while(q--){
		int u,v;
		scanf("%d%d",&u,&v);
		int t = lca(u,v);
		int MAX = 0,MIN = inf,upmax = 0,downmax = 0;
		for(int depth=18;depth>=0;depth--){  //深度由许多个二进制组成
			if((dep[u]-dep[t])&(1<<depth)){
				upmax = max(upmax,up[u][depth]);
				upmax = max(upmax,maxx[u][depth]-MIN);
				MIN = min(MIN,minn[u][depth]);
				u = fa[u][depth];
			}
		}
		for(int depth=18;depth>=0;depth--){
			if((dep[v]-dep[t])&(1<<depth)){
				int depth = lg[dep[v] - dep[t]];
				downmax = max(downmax,down[v][depth]);
				downmax = max(downmax,MAX - minn[v][depth]);
				MAX = max(MAX,maxx[v][depth]);
				v = fa[v][depth];
			}
		}
		printf("%d\n",max(max(0,MAX-MIN),max(upmax,downmax)));
	}
}	
int main(){
	pre();
	memset(first,-1,sizeof(first));
	scanf("%d",&n);
	for(int i=1;i<=n;i++)	scanf("%d",&val[i]);
	for(int i=1;i<=n-1;i++){
		int u,v;
		scanf("%d%d",&u,&v);
		add(u,v);
		add(v,u);
	}
	dfs(1,0);
	solve();
	return 0;
}