P3379 【模板】最近公共祖先（LCA）

倍增查祖先
[题目]：(https://www.luogu.com.cn/problem/P3379)

#include <bits/stdc++.h>
using namespace std;
#define int long long
vector<int> ve[(int)5e5+7];
int lg[(int)5e5+7];
int fa[(int)5e5+7][30], depth[(int)5e5+7];
int vis[(int)5e5+7];int n, m, s, x, y;
void DFS(int now, int fath) //子节点和父节点
{
    vis[now] = 1;
    if (now!=s) fa[now][0] = fath;
    else fa[now][0] = 0;
    depth[now] = depth[fath] + 1; //更新深度
    for (int i = 1; i <= lg[depth[now]] - 1; i++)
    {
        fa[now][i] = fa[fa[now][i - 1]][i - 1]; //一节一节网上搜
    }
    for (int i = 0; i < ve[now].size(); i++)
        if (!vis[ve[now][i]])
            DFS(ve[now][i], now);
}
int LCK(int x, int y)
{
    if (depth[x] < depth[y])
        swap(x, y);
    while (depth[x] > depth[y])
        x = fa[x][lg[depth[x] - depth[y]] - 1];
    if (x == y)
        return x;
    for (int k = lg[depth[x]] - 1; k >= 0; k--)
    {
        if (fa[x][k] != fa[y][k])
            x = fa[x][k], y = fa[y][k];
    }
    return fa[x][0];
}
signed main()
{
    
    scanf("%lld%lld%lld",&n,&m,&s);
    for (int i = 1; i < n; i++)
    {
        scanf("%lld%lld",&x,&y);
        ve[x].push_back(y);
        ve[y].push_back(x);
    }
    for (int i = 1; i <= n; i++)
        lg[i] = lg[i - 1] + (1 << lg[i - 1] == i);
    DFS(s, s); //从树根开始
    for (int i = 0; i < m; i++)
    {
        scanf("%lld%lld",&x,&y);
        int sum = LCK(x, y);
        cout << sum << endl;
    }
}