CSES-solutions/CSES Problem Set/Distinct Routes.cpp

/* Problem URL: https://cses.fi/problemset/task/1711 */

#include <bits/stdc++.h>

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;
    cin >> n >> m;

    vvi graph(n);
    V<tuple<int, ll, ll>> edges;

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

        graph[a].push_back(edges.size());
        edges.emplace_back(b, 1, 0);
        graph[b].push_back(edges.size());
        edges.emplace_back(a, 0, 0);
    }

    int inf = INT32_MAX >> 1;

    vi level(n);
    auto bfs = [&](){
        level[0] = 0;
        queue<int> q;
        q.push(0);

        while (!q.empty()) {
            auto a = q.front();
            q.pop();

            for (auto id : graph[a]) {
                auto [b, c, u] = edges[id];

                if (level[b] > level[a] + 1 && c != u) {
                    level[b] = level[a] + 1;
                    q.push(b);
                }
            }
        }

        return level[n - 1] != inf;
    };

    V<bool> vis(n);

    function<ll(int, ll)> dfs = [&](int i, ll flux){
        if (flux == 0) {
            return 0LL;
        }

        if (i == n - 1) {
            return flux;
        }

        for (auto id : graph[i]) {
            auto &[j, c, u] = edges[id];

            if (level[j] <= level[i] || vis[j]) {
                continue;
            }

            ll ans = dfs(j, min(flux, c - u));

            if (ans == 0) {
                continue;
            }

            auto &[_, __, ud] = edges[id ^ 1];
        
            u += ans;
            ud -= ans;

            return ans;
        }

        vis[i] = true;
        return 0LL;
    };

    ll ans = 0;
    while (true) {
        fill(all(level), inf);

        if (!bfs()) {
            break;
        }

        fill(all(vis), false);

        ll count = 0;
        while ((count = dfs(0, inf))) {
            ans += count;
        }
    }

    cout << ans << '\n';

    while (ans--) {
        vi tmp;

        function<void(int)> dfs = [&](int i){
            tmp.push_back(i + 1);

            for (auto id : graph[i]) {
                auto &[j, c, u] = edges[id];

                if (u == 1) {
                    u--;
                    dfs(j);
                    return;
                }
            }
        };

        dfs(0);
        cout << tmp.size() << '\n';
        cout << tmp;
        tmp.clear();
    }
}