最近公共祖先 LCA 模板

（以洛谷P3379为例）

其中：

dep[u]：表示结点u的深度
dp[u][k]:表示结点u的2^k祖先

代码：

#include<iostream>
#include<cstdio>
#include<cstring>

const int maxn = 500000 + 10;
int nxt[maxn << 1], to[maxn << 1], head[maxn << 1], cnt;
int dep[maxn << 1];
int dp[maxn << 1][21];//dp[u][k]表示结点u的2^k祖先,2^21
int n, m, s;

inline void add(int a, int b) {
    to[++cnt] = b;
    nxt[cnt] = head[a];
    head[a] = cnt;
}

inline void dfs1(int u, int fa) {//预处理dp[u][k]倍增
    dep[u] = dep[fa] + 1;
    for (int i = 1; i <= 20; i++)
        dp[u][i] = dp[dp[u][i - 1]][i - 1];//u的2^i祖先=u的2^(i-1)祖先的2^(i-1)祖先
    for (int i = head[u]; i; i = nxt[i]) {
        int v = to[i];
        if (v == fa) continue;
        dp[v][0] = u;
        dfs1(v, u);
    }
}

inline int LCA(int x, int y) {
    if (dep[x] < dep[y]) std::swap(x, y);
    for (int i = 20; i >= 0; i--) {
        if (dep[dp[x][i]] >= dep[y]) x = dp[x][i];
        if (x == y) return x;
    }
    for (int i = 20; i >= 0; i--) {
        if (dp[x][i] != dp[y][i]) {
            x = dp[x][i];
            y = dp[y][i];
        }
    }//倍增查找LCA
    return dp[x][0];
}

inline int read() {
    int x = 0, w = 0;
    char ch = 0;
    while (!isdigit(ch)) w |= ch == '-', ch = getchar();
    while (isdigit(ch)) x = (x << 1) + (x << 3) + (ch ^ 48), ch = getchar();
    return w ? -x : x;
}

int main() {
    n = read(), m = read(), s = read();
    for (int i = 1; i <= n - 1; i++) {
        int x, y;
        x = read(), y = read();
        add(x, y);
        add(y, x);
    }
    dfs1(s, 0);
    while (m--) {
        int a = read(), b = read();
        printf("%d\n", LCA(a, b));
    }
    return 0;
}