LCA/RMQ预处理

以HDU 3078 为例。通过LCA/RMQ，找到u,v之间的第K大值即可。

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <cstring>
#include <cmath>
#include <vector>
#include <queue>
#include <algorithm>
#include <map>
using namespace std;

const int maxn = 80010;
int weight[maxn];

int n, Q;
vector <int> Tree[maxn];

bool vis[maxn];
int fa[maxn];

int d[maxn*2][20];
int top;
int dfn[maxn*2], euler[maxn*2], pos[maxn];

void init()
{
	top = 0;
}

void dfs(int u)
{
	vis[u] = 1;
	for(int i = 0; i < Tree[u].size(); i++)
	{
		int v = Tree[u][i];
		if(vis[v]) continue;
		fa[v] = u;
		dfs(v);
	}
}

void DFS(int u, int dep)
{
	vis[u] = 1;
	dfn[top] = dep;
	euler[top] = u;
	pos[u] = top;
	++top;
	for(int i = 0; i < Tree[u].size(); i++)
	{
		int v = Tree[u][i];
		if(vis[v]) continue;
		DFS(v, dep+1);
		dfn[top] = dep;
		euler[top] = u;
		++top;
	}
}

void RMQ_init(int n)
{
	for(int i = 1; i <= n; i++) d[i][0] = i;
	for(int j = 1; (1<<j) <= n; j++)
		for(int i = 1; i + (1<<j)-1 <= n; i++)
		{
			if(dfn[d[i][j-1]] < dfn[d[i + (1<<(j-1))][j-1]]) d[i][j] = d[i][j-1];
			else d[i][j] = d[i + (1<<(j-1))][j-1];
		}
}

int RMQ(int L, int R)
{
	int k = 0;
	while(1<<(k+1) <= R-L+1) k++;
	if(dfn[d[L][k]] < dfn[d[R-(1<<k)+1][k]]) return d[L][k];
	return d[R-(1<<k)+1][k];
}

int LCA(int u, int v)
{
	if(pos[u] > pos[v])  swap(u, v);
	return euler[RMQ(pos[u], pos[v])];
}

void read_case()
{
	top = 0;
	
	scanf("%d%d", &n, &Q);
	for(int i = 1; i <= n; i++) scanf("%d", &weight[i]);
	
	for(int i = 1; i < n; i++)
	{
		int u, v;
		scanf("%d%d", &u, &v);
		Tree[u].push_back(v);
		Tree[v].push_back(u);
	}
}

vector<int> res;

int cmp(int a, int b) { return a > b; }

int cal(int u, int v, int k, int lca)
{
	res.clear();
	res.push_back(weight[u]);
	while(u != lca)
	{
		u = fa[u];
		res.push_back(weight[u]);
	}
	if(v != lca) res.push_back(weight[v]);
	while(v != lca)
	{
		v = fa[v];
		if(v == lca) break;
		res.push_back(weight[v]);
	}
	if(res.size() < k) return -1;
	sort(res.begin(), res.end(), cmp);
	return res[k-1];
}

void solve()
{
	read_case();
	fa[1] = 1;
	DFS(1, 0);
	RMQ_init(top);
	
	memset(vis, 0, sizeof(vis));
	dfs(1);
	while(Q--)
	{
		int k, u, v;
		scanf("%d%d%d", &k, &u, &v);
		if(k != 0)
		{
			int lca = LCA(u, v);
			int ans;
			if((ans = cal(u, v, k, lca)) < 0) printf("invalid request!\n");
			else printf("%d\n", ans);
		}
		else weight[u] = v;
	}
}

int main()
{
	solve();
	system("pause");
	return 0;
}