CSES-Solutions/Graph Algorithms/DistinctRoutes.cpp at main · Avuvos/CSES-Solutions · GitHub

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#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

const int MOD = 1e9 + 7;
const ll INF = 1e18;

struct FlowEdge {
    int v, u;
    ll cap, flow = 0;

    FlowEdge(int v, int u, ll cap) : v(v), u(u), cap(cap) {}
};

struct Dinic {
    const ll flow_inf = 1e18;
    vector<FlowEdge> edges;
    vector<vector<int>> adj;
    int n, m = 0;
    int s, t;
    vector<int> level, ptr;
    vector<vector<int>> paths;
    queue<int> q;

    Dinic(int n, int s, int t) : n(n), s(s), t(t) {
        adj.resize(n);
        level.resize(n);
        ptr.resize(n);
    }

    void add_edge(int v, int u, ll cap) {
        edges.emplace_back(v, u, cap);
        edges.emplace_back(u, v, 0);
        adj[v].push_back(m);
        adj[u].push_back(m + 1);
        m += 2;
    }

    bool bfs() {
        while (!q.empty()) {
            int v = q.front();
            q.pop();
            for (int id: adj[v]) {
                if (edges[id].cap - edges[id].flow < 1)
                    continue;
                if (level[edges[id].u] != -1)
                    continue;
                level[edges[id].u] = level[v] + 1;
                q.push(edges[id].u);
            }
        }
        return level[t] != -1;
    }

    ll dfs(int v, ll pushed) {
        if (pushed == 0)
            return 0;
        if (v == t)
            return pushed;
        for (int &cid = ptr[v]; cid < (int) adj[v].size(); cid++) {
            int id = adj[v][cid];
            int u = edges[id].u;
            if (level[v] + 1 != level[u] || edges[id].cap - edges[id].flow < 1)
                continue;
            ll tr = dfs(u, min(pushed, edges[id].cap - edges[id].flow));
            if (tr == 0)
                continue;
            edges[id].flow += tr;
            edges[id ^ 1].flow -= tr;
            return tr;
        }
        return 0;
    }

    ll flow() {
        ll f = 0;
        while (true) {
            fill(level.begin(), level.end(), -1);
            level[s] = 0;
            q.push(s);
            if (!bfs())
                break;
            fill(ptr.begin(), ptr.end(), 0);
            while (ll pushed = dfs(s, flow_inf)) {
                f += pushed;
            }
        }
        return f;
    }

    void path_dfs(int v) {
        if (v == t) {
            return;
        }
        for (auto id: adj[v]) {
            if (edges[id].flow && edges[id].cap) {
                edges[id].flow = 0;
                paths.back().push_back(edges[id].u);
                path_dfs(edges[id].u);
                return;
            }
        }
    }
};


void solve() {
    int n, m;
    cin >> n >> m;
    int source = 0;
    int target = n - 1;
    Dinic dinic(n, source, target);
    for (int i = 0; i < m; i++) {
        int u, v;
        cin >> u >> v;
        u--, v--;
        dinic.add_edge(u, v, 1);
    }

    int k = dinic.flow();
    cout << k << endl;
    for (int i = 0; i < k; i++) {
        dinic.paths.push_back({source});
        dinic.path_dfs(source);
    }

    for (auto &path: dinic.paths) {
        cout << path.size() << endl;
        for (auto &node: path) {
            cout << node + 1 << " ";
        }
        cout << endl;
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int T = 1;
//    cin >> T;
    while (T--) {
        solve();
    }
    return 0;
}