CSES-solutions/CSES Problem Set/Planets Queries II.cpp

/* Problem URL: https://cses.fi/problemset/task/1160 */

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

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

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int 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, q;
    cin >> n >> q;

    vi parent(n);
    rep(i, n) {
        int a;
        cin >> a;

        parent[i] = a - 1;
    }

    V<bool> loop(n);
    vi group(n);
    vi cyclepos(n);

    V<bool> vis(n);
    V<bool> frame(n);
    vi groupsize;
    vi cyclechoice(n);
    int g = 0;

    auto func = [&](int i) {
        set<int> used;
        while (!vis[i] && !frame[i]) {
            vis[i] = true;
            frame[i] = true;
            used.insert(i);
            i = parent[i];
        }

        if (frame[i]) {
            loop[i] = true;
            group[i] = g;
            cyclechoice[i] = i;

            int now = 1;

            int j = parent[i];

            while (j != i) {
                cyclepos[j] = now;
                now++;
                loop[j] = true;
                group[j] = g;
                cyclechoice[j] = j;
                j = parent[j];
            }

            g++;
            groupsize.push_back(now);
        }

        for (auto j : used) {
            frame[j] = false;
        }
    };

    rep(i, n) {
        if (vis[i]) {
            continue;
        }

        func(i);
    }

    fill(all(vis), false);
    vi pos(n);

    function<void(int)> dfs = [&](int i) {
        vis[i] = true;

        if (!vis[parent[i]] && !loop[parent[i]]) {
            dfs(parent[i]);
        }

        pos[i] = pos[parent[i]] + 1;
        cyclechoice[i] = cyclechoice[parent[i]];
    };

    rep(i, n) {
        if (!loop[i] && !vis[i]) {
            dfs(i);
        }
    }

    vvi lift(17, vi(n));

    vi valids;
    rep(i, n) {
        if (!loop[i]) {
            valids.push_back(i);
            lift[0][i] = parent[i];
        }
    }

    nrep(i, 1, 17) {
        repv(j, valids) {
            lift[i][j] = lift[i - 1][lift[i - 1][j]];
        }
    }

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

        if (loop[a] && loop[b]) {
            if (group[a] != group[b]) {
                cout << "-1\n";
                continue;
            }

            int g = group[a];

            cout << ((cyclepos[b] - cyclepos[a]) % groupsize[g] + groupsize[g]) % groupsize[g] << '\n';
            continue;
        }

        if (loop[a] && !loop[b]) {
            cout << "-1\n";
            continue;
        }

        if (!loop[a] && loop[b]) {
            int choice = cyclechoice[a];

            if (group[choice] != group[b]) {
                cout << "-1\n";
                continue;
            }

            int g = group[choice];

            cout << pos[a] + ((cyclepos[b] - cyclepos[choice]) % groupsize[g] + groupsize[g]) % groupsize[g] << '\n';
            continue;
        }

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

        if (diff < 0) {
            cout << "-1\n";
            continue;
        }

        rep(i, 17) {
            if ((diff >> i) & 1) {
                a = lift[i][a];
            }
        }

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

        cout << diff << '\n';
    }
}