分析
设 z = l c a ( x , y ) ; z = lca(x,y); z=lca(x,y);
三种情况
1. 1. 1.从 z z z点前买入, z z z点后卖出
2. 2. 2.从 z z z点前买入, z z z点前卖出
3. 3. 3.从 z z z点后买入, z z z点后卖出
所以我们需要倍增维护每个点的 2 i 2 ^ i 2i的各种信息即可
代码
#include <iostream>
#include <cstring>
#include <algorithm>
#include <cstdio>
using namespace std;
const int N = 1e5 + 10,INF = 0x3f3f3f3f;
int h[N],ne[N * 2],e[N * 2],idx;
int d[N],f[N][20];
int maxv[N][20],minv[N][20];
int up[N][20],down[N][20];
int a[N];
int n,q;
void add(int x,int y){
ne[idx] = h[x],e[idx] = y,h[x] = idx++;
}
void dfs(int u,int fa){
for(int i = h[u];~i;i = ne[i]){
int j = e[i];
if(j == fa) continue;
f[j][0] = u;
d[j] = d[u] + 1;
maxv[j][0] = max(a[u],a[j]);
minv[j][0] = min(a[u],a[j]);
up[j][0] = max(0,a[u] - a[j]);
down[j][0] = max(0,a[j] - a[u]);
dfs(j,u);
}
}
void init(){
memset(f,-1,sizeof f);
d[1] = 1;
dfs(1,0);
for(int i = 1;i < 20;i++)
for(int u = 1;u <= n;u++){
if(~f[u][i - 1]){
int k = f[u][i - 1];
f[u][i] = f[k][i - 1];
maxv[u][i] = max(maxv[u][i - 1],maxv[k][i - 1]);
minv[u][i] = min(minv[u][i - 1],minv[k][i - 1]);
int a = max(0,maxv[k][i - 1] - minv[u][i - 1]);
int b = max(up[u][i - 1],up[k][i - 1]);
up[u][i] = max(a,b);
a = max(0,maxv[u][i - 1] - minv[k][i - 1]);
b = max(down[u][i - 1],down[k][i - 1]);
down[u][i] = max(a,b);
}
}
}
int lca(int a,int b){
if(d[a] < d[b]) swap(a,b);
for(int i = 19;i >= 0;i--)
if(d[f[a][i]] >= d[b])
a = f[a][i];
if(a == b) return a;
for(int i = 19;i >= 0;i--)
if(f[a][i] != f[b][i])
a = f[a][i],b = f[b][i];
return f[a][0];
}
int Query_up(int x,int depth,int &l){
int ans = 0;
for(int i = 19;~i;i--){
if(depth & (1 << i)){
ans = max(ans,up[x][i]);
ans = max(ans,maxv[x][i] - l);
l = min(l,minv[x][i]);
x = f[x][i];
}
}
return ans;
}
int Query_down(int x,int depth,int &r){
int ans = 0;
for(int i = 19;~i;i--){
if(depth & (1 << i)){
ans = max(ans,down[x][i]);
ans = max(ans,r - minv[x][i]);
r = max(r,maxv[x][i]);
x = f[x][i];
}
}
return ans;
}
int main(){
scanf("%d",&n);
for(int i = 1;i <= n;i++){
d[i] = INF,h[i] = -1;
scanf("%d",&a[i]);
}
for(int i = 1;i < n;i++){
int x,y;
scanf("%d%d",&x,&y);
add(x,y),add(y,x);
}
init();
scanf("%d",&q);
while(q--){
int x,y;
scanf("%d%d",&x,&y);
int z = lca(x,y);
// cout << z << endl;
int l = INF,r = -INF,a,b;
a = Query_up(x,d[x] - d[z],l);
b = Query_down(y,d[y] - d[z],r);
int res = max(max(a,b),max(0,r - l));
// cout << r << ' ' << << ' ' << res << endl;
printf("%d\n",res);
}
return 0;
}
/**
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* ┏┛┻━━━┛┻┓ + +
* ┃ ┃
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* ████━████+
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* ┃ ┃ + + + +Code is far away from
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* ┃ ┗━━━┓ 神兽保佑,代码无bug
* ┃ ┣┓
* ┃ ┏┛
* ┗┓┓┏━┳┓┏┛ + + + +
* ┃┫┫ ┃┫┫
* ┗┻┛ ┗┻┛+ + + +
*/