倍增求LCA

LCA:(Least Common Ancestors),即最近公共祖先节点。

const int maxn = 100003;
const int maxl = 19;

struct Edge {
    int t;
    Edge *ne;
};

int dep[maxn], up[maxn][maxl];
Edge *head[maxn];

void DFS(int u) {
    for (int i = 1; i < maxl; ++ i) {
        up[u][i] = up[up[u][i - 1]][i - 1];
    }
    for (Edge* e = head[u]; e; e = e->ne) { // 枚举儿子
        if (!dep[e->t]) {
            dep[e->t] = dep[u] + 1;
            up[e->t][0] = u;
            DFS(e->t);
        }
    }
}

int LCA(int u, int v) {
    if (dep[u] < dep[v]) {
        swap(u, v);
    }
    for (int i = maxl - 1; i >= 0; -- i) {
        if (dep[up[u][i]] >= dep[v]) {
            u = up[u][i];
        }
    }//保证深度相同 
    if (u == v) {
        return u;
    }
    for (int i = maxl - 1; i >= 0; -- i) {
        if (up[u][i] != up[v][i]) {
            u = up[u][i];
            v = up[v][i];
        }
    }
    return up[u][0];
}

int main() {
    memset(dep, -1, sizeof(dep));
    dep[1] = 0;
    up[1][0] = 0;
    DFS(1);
    while (q --) {
        int u, v;
        cin >> u >> v;
        cout << LCA(u, v) << endl;
    }
}