\(\color{purple}{1.暴力}\)

#include <iostream>
#include <bits/stdc++.h>

using namespace std;
const int maxn = 5e5 + 10;

vector <int> vec[maxn];

int f[maxn];
int dep[maxn];

void dfs(int now, int fa);
int gt(int a, int b);

int main()
{
    int n, m, s;
    cin >> n >> m >> s;
    
    for (int i = 1; i < n; ++i)
    {
        int x, y;
        cin >> x >> y;
        vec[x].push_back(y);
        vec[y].push_back(x);
    }

    dfs(s, 0);

    for (int i = 1; i <= m; ++i)
    {
        int x, y;
        cin >> x >> y;
        cout << gt(x, y) << '\n';
    }
    return 0;
}

void dfs(int now, int fa)
{
    dep[now] = dep[fa] + 1;
    f[now] = fa;

    for (auto i : vec[now])
    {
        if (i != fa)
            dfs(i, now);
    }
}

int gt(int a, int b)
{
    if (a == b)
    {
        return a;
    }

    if (dep[a] > dep[b])
    {
        swap(a, b);
    }

    while (dep[a] != dep[b])
    {
        b = f[b];
    }

    if (a == b)
        return a;

    while (f[a] != f[b])
    {
        a = f[a];
        b = f[b];
    }

    return f[a];
}

\(\color{purple}{2.倍增}\)

#include <iostream>
#include <bits/stdc++.h>

using namespace std;
const int maxn = 5e5 + 10;

vector<int> vec[maxn];

int f[maxn][25];
int dep[maxn];

void dfs(int now, int fa);
int gt(int a, int b);

int main()
{
    int n, m, s;
    cin >> n >> m >> s;

    for (int i = 1; i < n; ++i)
    {
        int x, y;
        cin >> x >> y;
        vec[x].push_back(y);
        vec[y].push_back(x);
    }

    dfs(s, 0);

    for (int i = 1; i <= m; ++i)
    {
        int x, y;
        cin >> x >> y;
        cout << gt(x, y) << '\n';
    }
    return 0;
}

void dfs(int now, int fa)
{
    dep[now] = dep[fa] + 1;
    f[now][0] = fa;

    for (int i = 1; i <= 20; ++i)
    {
        f[now][i] = f[f[now][i - 1]][i - 1];
    }

    for (auto i : vec[now])
    {
        if (i != fa)
            dfs(i, now);
    }
}

int gt(int x, int y)
{
    if (dep[x] < dep[y])
        swap(x, y);
    for (int i = 20; i >= 0; --i)
    {
        if (dep[f[x][i]] >= dep[y])
            x = f[x][i];
        if (x == y)
            return x;
    }
    for (int i = 20; i >= 0; --i)
    {
        if (f[x][i] != f[y][i])
        {
            x = f[x][i];
            y = f[y][i];
        }
    }
    return f[x][0];
}