DataStructure/test/aizu_grl_5_c_lca.test.cpp

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Last update: 2022-08-11 17:15:37+08:00
Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C

Depends on

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C"

#include "../../template.h"
#include "../LCA.h"

void solve() {
    ios::sync_with_stdio(0); cin.tie(0);
    int n; cin >> n;
    vector<vector<int>> adj(n);
    REP(i,n) {
        int k; cin >> k;
        while (k--) {
            int j; cin >> j;
            adj[i].push_back(j);
            adj[j].push_back(i);
        }
    }

    LCA lca(n, adj, 0);

    int q; cin >> q;
    while (q--) {
        int u, v; cin >> u >> v;
        cout << lca.lca(u, v) << '\n';
    }
}

#line 1 "DataStructure/test/aizu_grl_5_c_lca.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C"

#line 1 "template.h"
#include <bits/stdc++.h>
using namespace std;

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)
#define EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it)

#define DEBUG(x) { cout << #x << " = "; cout << (x) << endl; }
#define PR(a,n) { cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl; }
#define PR0(a,n) { cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))

// For printing pair, container, etc.
// Copied from https://quangloc99.github.io/2021/07/30/my-CP-debugging-template.html
template<class U, class V> ostream& operator << (ostream& out, const pair<U, V>& p) {
    return out << '(' << p.first << ", " << p.second << ')';
}

template<class Con, class = decltype(begin(declval<Con>()))>
typename enable_if<!is_same<Con, string>::value, ostream&>::type
operator << (ostream& out, const Con& con) {
    out << '{';
    for (auto beg = con.begin(), it = beg; it != con.end(); it++) {
        out << (it == beg ? "" : ", ") << *it;
    }
    return out << '}';
}
template<size_t i, class T> ostream& print_tuple_utils(ostream& out, const T& tup) {
    if constexpr(i == tuple_size<T>::value) return out << ")"; 
    else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); 
}
template<class ...U> ostream& operator << (ostream& out, const tuple<U...>& t) {
    return print_tuple_utils<0, tuple<U...>>(out, t);
}

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
long long get_rand(long long r) {
    return uniform_int_distribution<long long> (0, r-1)(rng);
}

template<typename T>
vector<T> read_vector(int n) {
    vector<T> res(n);
    for (int& x : res) cin >> x;
    return res;
}

void solve();

int main() {
    ios::sync_with_stdio(0); cin.tie(0);
    solve();
    return 0;
}
#line 1 "DataStructure/LCA.h"
// LCA
// Notes:
// - Index from 0
// - Cannot use for queries like min edge in path u -> v
//
// Tested:
// - https://judge.yosupo.jp/problem/lca
#line 1 "DataStructure/RMQ.h"
// RMQ {{{
//
// Sparse table
// Usage:
// RMQ<int, _min> st(v);
//
// Note:
// - doesn't work for empty range
//
// Tested:
// - https://judge.yosupo.jp/problem/staticrmq
template<class T, T (*op) (T, T)> struct RMQ {
    RMQ() = default;
    RMQ(const vector<T>& v) : t{v}, n{(int) v.size()} {
        for (int k = 1; (1<<k) <= n; ++k) {
            t.emplace_back(n - (1<<k) + 1);
            for (int i = 0; i + (1<<k) <= n; ++i) {
                t[k][i] = op(t[k-1][i], t[k-1][i + (1<<(k-1))]);
            }
        }
    }

    // get range [l, r-1]
    // doesn't work for empty range
    T get(int l, int r) const {
        assert(0 <= l && l < r && r <= n);
        int k = __lg(r - l);
        return op(t[k][l], t[k][r - (1<<k)]);
    }

private:
    vector<vector<T>> t;
    int n;
};
template<class T> T _min(T a, T b) { return b < a ? b : a; }
template<class T> T _max(T a, T b) { return a < b ? b : a; }
// }}}
#line 9 "DataStructure/LCA.h"
struct LCA {
    const int n;
    vector<vector<int>> adj;
    const int root;
    using P = pair<int,int>;
    static P f(P x, P y) { return std::min(x, y); }

    LCA(int _n, const vector<vector<int>>& _adj, int _root)
            : n(_n), adj(_adj), root(_root) {
        assert(0 <= root && root < n);
        id.resize(n);
        depth.resize(n);
        order.reserve(2 * n);
        dfs(root, -1, 0);
        rmq = RMQ<P, f>(order);
    }

    int lca(int u, int v) {
        assert(0 <= u && u < n);
        assert(0 <= v && v < n);

        int x = id[u], y = id[v];
        if (x > y) std::swap(x, y);
        return rmq.get(x, y+1).second;
    }

// private:
    vector<int> id, depth;
    vector<P> order;
    RMQ<P, f> rmq;

    void dfs(int u, int fu, int d) {
        id[u] = order.size();
        depth[u] = d;
        order.emplace_back(d, u);
        for (int v : adj[u]) {
            if (v == fu) continue;
            dfs(v, u, d + 1);
            order.emplace_back(d, u);
        }
    }
};
#line 5 "DataStructure/test/aizu_grl_5_c_lca.test.cpp"

void solve() {
    ios::sync_with_stdio(0); cin.tie(0);
    int n; cin >> n;
    vector<vector<int>> adj(n);
    REP(i,n) {
        int k; cin >> k;
        while (k--) {
            int j; cin >> j;
            adj[i].push_back(j);
            adj[j].push_back(i);
        }
    }

    LCA lca(n, adj, 0);

    int q; cin >> q;
    while (q--) {
        int u, v; cin >> u >> v;
        cout << lca.lca(u, v) << '\n';
    }
}