CSES-solutions/CSES Problem Set/Giant Pizza.cpp

/* Problem URL: https://cses.fi/problemset/task/1684 */

#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, m;
    cin >> m >> n;

    n <<= 1;

    vvi graph(n);
    vvi inv(n);

    while (m--) {
        char op1, op2;
        int a, b;
        cin >> op1 >> a >> op2 >> b;

        a--, b--;

        if (op1 == '-') {
            a += n >> 1;
        }

        if (op2 == '-') {
            b += n >> 1;
        }

        graph[a].push_back((b + (n >> 1)) % n);
        graph[b].push_back((a + (n >> 1)) % n);
        inv[(b + (n >> 1)) % n].push_back(a);
        inv[(a + (n >> 1)) % n].push_back(b);
    }

    V<bool> vis(n);
    vi top;

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

        for (auto j : graph[i]) {
            if (vis[j]) {
                continue;
            }

            preorder(j);
        }

        top.push_back(i);
    };

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

        preorder(i);
    }

    reverse(all(top));
    fill(all(vis), false);

    vi group(n);
    vi representant(n);
    int g = 0;

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

        for (auto j : inv[i]) {
            if (vis[j]) {
                continue;
            }

            scc(j);
        }
    };

    repv(i, top) {
        if (vis[i]) {
            continue;
        }

        scc(i);
        representant.push_back(i);
        g++;
    }

    rep(i, n >> 1) {
        if (group[i] == group[i + (n >> 1)]) {
            cout << "IMPOSSIBLE\n";
            return 0;
        }
    }

    fill(all(vis), false);
    reverse(all(representant));

    string ans(n >> 1, ' ');

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

        if (ans[i % (n >> 1)] == ' ') {
            ans[i % (n >> 1)] = i < (n >> 1) ? '-' : '+';
        }

        repv(j, graph[i]) {
            if (vis[j] || group[j] != group[i]) {
                continue;
            }

            getans(j);
        }
    };

    repv(i, representant) {
        if (vis[i]) {
            continue;
        }

        getans(i);
    }

    repv(i, ans) {
        cout << i << ' ';
    }
    cout << '\n';
}