LCA的入門題，我用的是ST線上演算法和Tarjan離線演算法。

ST：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <cmath>

using namespace std;

const int maxn = 10010;
int t, n, cnt;
vector<int> son[maxn];
int parent[maxn];
bool vis[maxn];
int e[maxn<<1]; // e[]: dfs後的節點序列，
int r[maxn];    // r[i]: 節點i在e中第一次出現的位置 
int d[maxn<<1];    // d[]: e[]中相應節點的深度 
int dp[maxn<<1][16];

inline int _min(int i, int j)
{
    if (d[i] < d[j]) return i;
    return j;
}

void initRMQ()
{
    int nn = 2 * n - 1;
    for (int i = 0; i < nn; ++i)
        dp[i][0] = i;
    int k = (int)(log(nn * 1.0) / log(2.0));
    for (int j = 1; j <= k; ++j)
    {
        for (int i = 0; i + (1 << j) - 1 < nn; ++i)
            dp[i][j] = _min(dp[i][j-1],  dp[i+(1<<(j-1))][j-1]);
    }
}

inline int query(int l, int r)
{
    int k = (int)(log(r * 1.0 - l + 1) / log(2.0));
    return _min(dp[l][k], dp[r-(1<<k)+1][k]);
}

/*主要過程，求e, r, d陣列*/ 
void dfs(int u, int depth)
{
    vis[u] = true;
    e[cnt] = u;
    d[cnt] = depth;
    r[u] = cnt;
    ++cnt;
    for (int i = 0; i < son[u].size(); ++i)
    {
        if (!vis[son[u][i]])
        {
            dfs(son[u][i], depth + 1);
            e[cnt] = u;
            d[cnt++] = depth;
        }
    }
}

int main()
{
    scanf("%d", &t);
    while (t--)
    {
        scanf("%d", &n);
        for (int i = 0; i <= n; ++i)
        {
            parent[i] = -1;
            vis[i] = false; 
            son[i].clear(); 
        }
        int u, v, root;
        for (int i = 1; i < n; ++i)
        {
            scanf("%d %d", &u, &v);
            son[u].push_back(v);
            parent[v] = u;
        }
        for (int i = 1; i <= n; ++i)
        {
            if (parent[i] == -1)
            {
                root = i;
                break;
            }
        }
        cnt = 0;
        dfs(root, 0);
        initRMQ();
        scanf("%d %d", &u, &v);
        if (r[u] <= r[v])
            printf("%d\n", e[query(r[u], r[v])]);
        else printf("%d\n", e[query(r[v], r[u])]);
    }
    return 0;
}
 

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>

using namespace std;

const int maxn = 10010;
int t, n;
bool vis[maxn];
int set[maxn], pre[maxn], an[maxn];
vector<int> son[maxn];
vector<int> ask[maxn];

int find(int x)
{
    if (x != set[x])
        set[x] = find(set[x]);
    return set[x];
}

void Union(int x, int y)
{
    x = find(x);
    y = find(y);
    set[x] = y;
}

void lca(int x)
{
    set[x] = x;
    an[x] = x;
    int size = son[x].size();
    for (int i = 0; i < size; ++i)
    {
        lca(son[x][i]);
        Union(x, son[x][i]);
        an[find(x)] = x;
    }
    
    vis[x] = true;
    
    size = ask[x].size();
    for (int i = 0; i < size; ++i)
    {
        if (vis[ask[x][i]])
            printf("%d\n", an[find(ask[x][i])]);
    }
}

int main()
{
    scanf("%d", &t);
    while (t--)
    {
        scanf("%d", &n);
        for (int i = 0; i <= n; ++i)
        {
            pre[i] = -1;
            vis[i] = false;
            son[i].clear();
            ask[i].clear();
        }
        int u, v, root;
        for (int i = 1; i < n; ++i)
        {
            scanf("%d %d", &u, &v);
            son[u].push_back(v);
            pre[v] = u;
        }
        for (int i = 1; i <= n; ++i)
        {
            if (pre[i] == -1)
            {
                root = i;
                break;
            }
        }
        scanf("%d %d", &u, &v);
        ask[u].push_back(v);
        ask[v].push_back(u);
        lca(root);
    }
    return 0;
}