graph/bipartite-graph.hpp

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• Last update: 2022-07-12 17:31:52+03:00
• Include: #include "graph/bipartite-graph.hpp"

Depends on

• ds/queue.hpp
• graph/maxflow.hpp

Required by

• graph/vertex-cover-small-ans.hpp

Code

#pragma once

#include "maxflow.hpp"

struct BipartiteGraph: MaxFlow<ll> {
    int L, R, s, t;
    bool was_flow;

    explicit BipartiteGraph(int N, int M)
        : MaxFlow<ll>(N + M + 2),
          L(N),
          R(M),
          s(N + M),
          t(N + M + 1),
          was_flow(false) {
        for (int i = 0; i < L; i++) {
            MaxFlow<ll>::add_edge(s, i, 1); 
        }
        for (int i = 0; i < R; i++) {
            MaxFlow<ll>::add_edge(i + L, t, 1);
        }
    }

    int add_edge(int a, int b, ll c = 1) {
        assert(0 <= a && a < L);
        assert(0 <= b && b < R);
        return MaxFlow<ll>::add_edge(a, b + L, c);
    }

    ll flow() {
        was_flow = true;
        return MaxFlow<ll>::flow(s, t);
    }

    pair<vector<int>, vector<int>> minimumVertexCover() {
        if (!was_flow)
            flow();
        vector<bool> used = dfsUsed();
        vector<int> lv, rv;
        for (int i = 0; i < L; i++) {
            if (!used[i]) {
                lv.push_back(i);
            }
        }
        for (int i = 0; i < R; i++) {
            if (used[i + L]) {
                rv.push_back(i);
            }
        }
        return {lv, rv};
    }

    private:
    vector<bool> dfsUsed() {
        vector<vector<int>> g(L + R);
        vector<bool> matched(L);
        for (auto &e : MaxFlow<ll>::edges()) {
            if (e.from == s || e.to == t)
                continue;
            if (e.flow > 0) {
                g[e.to].push_back(e.from);
                matched[e.from] = true;
            } else {
                g[e.from].push_back(e.to);
            }
        }
        vector<bool> used(L + R);
        auto dfs = [&](auto dfs, int v) -> void {
            used[v] = 1;
            for (int u : g[v])
                if (!used[u])
                    dfs(dfs, u);
        };
        for (int i = 0; i < L; i++) {
            if (!matched[i] && !used[i]) {
                dfs(dfs, i);
            }
        }
        return used;
    }
};

#line 2 "graph/bipartite-graph.hpp"

#line 2 "ds/queue.hpp"

template<typename T>
struct simple_queue {
    vector<T> arr;
    int pos = 0;
    void reserve(int n) { arr.reserve(n); }
    int size() const { return sz(arr) - pos; }
    bool empty() { return pos == sz(arr); }
    void push(const T& t) { arr.push_back(t); }
    T& front() {
        return arr[pos];
    }
    void clear() {
        arr.clear();
        pos = 0;
    }
    void pop() { pos++; }
};
#line 3 "graph/maxflow.hpp"

template<typename T>
struct MaxFlow {
    explicit MaxFlow(int n) : n(n), g(n) {}

    int add_edge(int from, int to, T cap) {
        assert(0 <= from && from < n);
        assert(0 <= to && to < n);
        assert(0 <= cap);
        int m = sz(pos);
        pos.push_back({from, sz(g[from])});
        int sz_from = sz(g[from]);
        int sz_to = sz(g[to]);
        if (from == to) {
            sz_to++;
        }
        g[from].push_back({to, sz_to, cap});
        g[to].push_back({from, sz_from, 0});
        return m;
    }

    struct edge {
        int from, to;
        T cap, flow;
    };

    edge get_edge(int i) {
        assert(0 <= i && i < sz(pos));
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return {_re.to, _e.to, _e.cap + _re.cap, _re.cap};
    }

    vector<edge> edges() {
        int m = sz(pos);
        vector<edge> ans;
        for (int i = 0; i < m; i++) {
            ans.push_back(get_edge(i));
        }
        return ans;
    }

    T flow(int s, int t) {
        return flow(s, t, numeric_limits<T>::max());
    }

    T flow(int s, int t, T flow_limit) {
        assert(0 <= s && s < n);
        assert(0 <= t && t < n);
        assert(s != t);
        vector<int> level(n), iter(n);
        simple_queue<int> q;

        auto bfs = [&]() {
            fill(all(level), -1);
            level[s] = 0;
            q.clear();
            q.push(s);
            while (!q.empty()) {
                int v = q.front();
                q.pop();
                for (auto e : g[v]) {
                    if (e.cap == 0 || level[e.to] >= 0) continue;
                    level[e.to] = level[v] + 1;
                    if (e.to == t) return;
                    q.push(e.to);
                }
            }
        };
        auto dfs = [&](auto self, int v, T up) {
            if (v == s) {
                return up;
            }
            T res = 0;
            int level_v = level[v];
            for (int& i = iter[v]; i < sz(g[v]); i++) {
                auto &e = g[v][i];
                if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
                T d =
                    self(self, e.to, min(up - res, g[e.to][e.rev].cap));
                if (d <= 0) continue;
                g[v][i].cap += d;
                g[e.to][e.rev].cap -= d;
                res += d;
                if (res == up)
                    return res;
            }
            level[v] = n;
            return res;
        };

        T flow = 0;
        while (flow < flow_limit) {
            bfs();
            if (level[t] == -1)
                break;
            fill(all(iter), 0);
            T f = dfs(dfs, t, flow_limit - flow);
            if (!f)
                break;
            flow += f;
        }
        return flow;
    }

    private:
    int n;
    vector<pair<int, int>> pos;
    struct _edge {
        int to, rev;
        T cap;
    };
    vector<vector<_edge>> g;
};
#line 4 "graph/bipartite-graph.hpp"

struct BipartiteGraph: MaxFlow<ll> {
    int L, R, s, t;
    bool was_flow;

    explicit BipartiteGraph(int N, int M)
        : MaxFlow<ll>(N + M + 2),
          L(N),
          R(M),
          s(N + M),
          t(N + M + 1),
          was_flow(false) {
        for (int i = 0; i < L; i++) {
            MaxFlow<ll>::add_edge(s, i, 1); 
        }
        for (int i = 0; i < R; i++) {
            MaxFlow<ll>::add_edge(i + L, t, 1);
        }
    }

    int add_edge(int a, int b, ll c = 1) {
        assert(0 <= a && a < L);
        assert(0 <= b && b < R);
        return MaxFlow<ll>::add_edge(a, b + L, c);
    }

    ll flow() {
        was_flow = true;
        return MaxFlow<ll>::flow(s, t);
    }

    pair<vector<int>, vector<int>> minimumVertexCover() {
        if (!was_flow)
            flow();
        vector<bool> used = dfsUsed();
        vector<int> lv, rv;
        for (int i = 0; i < L; i++) {
            if (!used[i]) {
                lv.push_back(i);
            }
        }
        for (int i = 0; i < R; i++) {
            if (used[i + L]) {
                rv.push_back(i);
            }
        }
        return {lv, rv};
    }

    private:
    vector<bool> dfsUsed() {
        vector<vector<int>> g(L + R);
        vector<bool> matched(L);
        for (auto &e : MaxFlow<ll>::edges()) {
            if (e.from == s || e.to == t)
                continue;
            if (e.flow > 0) {
                g[e.to].push_back(e.from);
                matched[e.from] = true;
            } else {
                g[e.from].push_back(e.to);
            }
        }
        vector<bool> used(L + R);
        auto dfs = [&](auto dfs, int v) -> void {
            used[v] = 1;
            for (int u : g[v])
                if (!used[u])
                    dfs(dfs, u);
        };
        for (int i = 0; i < L; i++) {
            if (!matched[i] && !used[i]) {
                dfs(dfs, i);
            }
        }
        return used;
    }
};

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