CSES-solutions/CSES Problem Set/New Roads Queries.cpp

/* Problem URL: https://cses.fi/problemset/task/2101/ */

#include <bits/stdc++.h>

#include <algorithm>

using namespace std;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (size_t i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (size_t i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m, q;
    cin >> n >> m >> q;

    V<tuple<int, int, int>> edges;

    rep(i, m) {
        int a, b;
        cin >> a >> b;
        a--, b--;
        edges.emplace_back(i, a, b);
    }

    vi dsu(n);
    rep(i, n) {
        dsu[i] = i;
    }

    function<int(int)> find_p = [&](int i){
        if (dsu[i] == i) {
            return i;
        }
        return dsu[i] = find_p(dsu[i]);
    };

    auto make_pair = [&](int a, int b) {
        a = find_p(a);
        b = find_p(b);

        if (a == b) {
            return false;
        }

        dsu[b] = a;

        return true;
    };

    V<V<pair<int, int>>> graph(n);

    for (auto [i, a, b] : edges) {
        if (make_pair(a, b)) {
            graph[a].emplace_back(b, i + 1);
            graph[b].emplace_back(a, i + 1);
        }
    }

    vvi par(n, vi(20, 0));
    vvi maximus(n, vi(20, 0));
    vi depth(n, 0);

    function<void(int, int, int)> dfs = [&](int i, int p, int big){
        par[i][0] = p;
        maximus[i][0] = big;
        depth[i] = depth[p] + 1;

        nrep(j, 1, 20) {
            par[i][j] = par[par[i][j - 1]][j - 1];
            maximus[i][j] = max(maximus[i][j - 1], maximus[par[i][j - 1]][j - 1]);
        }

        for (auto [u, v] : graph[i]) {
            if (u == p) {
                continue;
            }

            dfs(u, i, v);
        }
    };

    auto lca = [&](int a, int b){
        if (depth[a] > depth[b]) {
            swap(a, b);
        }

        int ans = 0;

        int diff = depth[b] - depth[a];

        for (int i = 19; i >= 0; i--) {
            if (diff & (1 << i)) {
                rmax(ans, maximus[b][i]);
                b = par[b][i];
            }
        }

        if (a == b) {
            return ans;
        }

        for (int i = 19; i >= 0; i--) {
            if (par[a][i] != par[b][i]) {
                rmax(ans, maximus[a][i]);
                rmax(ans, maximus[b][i]);
                a = par[a][i];
                b = par[b][i];
            }
        }

        return max({ans, maximus[a][0], maximus[b][0]});
    };

    rep(i, n) {
        if (dsu[i] == i) {
            fill(all(par[i]), i);
            dfs(i, i, 0);
        }
    }

    while (q--) {
        int a, b;
        cin >> a >> b;
        a--, b--;

        if (find_p(a) != find_p(b)) {
            cout << "-1\n";
            continue;
        }

        cout << lca(a, b) << '\n';
    }
}