cplib-cpp

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:heavy_check_mark: flow/b-flow.hpp

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#pragma once
#include "maxflow.hpp"
#include "mcf_costscaling.hpp"
#include <algorithm>
#include <vector>

// CUT begin
template <typename CAP, typename COST> struct B_Flow {
    int N, E;
    COST cost_bias;
    bool infeasible;
    mf_graph<CAP> mf;
    mcf_costscaling<CAP, COST> mcf;
    std::vector<CAP> b;
    std::vector<CAP> fbias;
    std::vector<int> fdir;
    std::vector<CAP> f;
    std::vector<COST> potential;

    B_Flow(int N = 0) : N(N), E(0), cost_bias(0), infeasible(false), mf(N + 2), mcf(N + 2), b(N) {}

    void add_supply(int v, CAP supply) { b[v] += supply; }
    void add_demand(int v, CAP demand) { b[v] -= demand; }
    void add_edge(int s, int t, CAP lower_cap, CAP upper_cap, COST cost) {
        assert(s >= 0 and s < N);
        assert(t >= 0 and t < N);
        if (lower_cap > upper_cap) {
            infeasible = true;
            return;
        }
        E++;
        if (s == t) {
            if (cost > 0) {
                upper_cap = lower_cap;
            } else {
                lower_cap = upper_cap;
            }
        }
        if (cost < 0) {
            fbias.emplace_back(lower_cap);
            fdir.emplace_back(-1);
            cost_bias += cost * upper_cap;
            b[s] -= upper_cap;
            b[t] += upper_cap;
            mf.add_edge(t, s, upper_cap - lower_cap);
            mcf.add_edge(t, s, upper_cap - lower_cap, -cost);
        } else {
            fbias.emplace_back(upper_cap);
            fdir.emplace_back(1);
            if (lower_cap < 0) {
                cost_bias += cost * lower_cap, b[s] -= lower_cap, b[t] += lower_cap;
                upper_cap -= lower_cap, lower_cap = 0;
            }
            if (lower_cap > 0) {
                cost_bias += cost * lower_cap;
                b[s] -= lower_cap;
                b[t] += lower_cap;
                upper_cap -= lower_cap;
            }
            mf.add_edge(s, t, upper_cap);
            mcf.add_edge(s, t, upper_cap, cost);
        }
    }

    std::pair<bool, COST> solve() {
        if (infeasible) return std::make_pair(false, 0);
        CAP bsum = 0, bsum_negative = 0;
        for (int i = 0; i < N; i++) {
            if (b[i] > 0) {
                mf.add_edge(N, i, b[i]), mcf.add_edge(N, i, b[i], 0), bsum += b[i];
            } else {
                mf.add_edge(i, N + 1, -b[i]), mcf.add_edge(i, N + 1, -b[i], 0),
                    bsum_negative -= b[i];
            }
        }
        if (bsum != bsum_negative or mf.flow(N, N + 1) < bsum) return std::make_pair(false, 0);
        std::fill(b.begin(), b.end(), 0);
        mcf.add_supply(N, bsum);
        mcf.add_demand(N + 1, bsum);
        COST ret = mcf.solve();
        potential = mcf.potential(), potential.resize(N);
        COST cost_ret = cost_bias + ret;
        cost_bias = 0;
        f = fbias;
        auto edges = mcf.edges();
        for (int e = 0; e < E; e++) f[e] -= fdir[e] * (edges[e].cap - edges[e].flow);
        return std::make_pair(true, cost_ret);
    }
};
#line 2 "flow/maxflow.hpp"

#include <algorithm>
#include <cassert>
#include <fstream>
#include <limits>
#include <string>
#include <vector>

// CUT begin
// MaxFlow based and AtCoder Library, single class, no namespace, no private variables, compatible
// with C++11 Reference: <https://atcoder.github.io/ac-library/production/document_ja/maxflow.html>
template <class Cap> struct mf_graph {
    struct simple_queue_int {
        std::vector<int> payload;
        int pos = 0;
        void reserve(int n) { payload.reserve(n); }
        int size() const { return int(payload.size()) - pos; }
        bool empty() const { return pos == int(payload.size()); }
        void push(const int &t) { payload.push_back(t); }
        int &front() { return payload[pos]; }
        void clear() {
            payload.clear();
            pos = 0;
        }
        void pop() { pos++; }
    };

    mf_graph() : _n(0) {}
    mf_graph(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap});
        g[to].push_back(_edge{from, from_id, 0});
        return m;
    }

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

    edge get_edge(int i) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
    }
    std::vector<edge> edges() {
        int m = int(pos.size());
        std::vector<edge> result;
        for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); }
        return result;
    }
    void change_edge(int i, Cap new_cap, Cap new_flow) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        assert(0 <= new_flow && new_flow <= new_cap);
        auto &_e = g[pos[i].first][pos[i].second];
        auto &_re = g[_e.to][_e.rev];
        _e.cap = new_cap - new_flow;
        _re.cap = new_flow;
    }

    std::vector<int> level, iter;
    simple_queue_int que;

    void _bfs(int s, int t) {
        std::fill(level.begin(), level.end(), -1);
        level[s] = 0;
        que.clear();
        que.push(s);
        while (!que.empty()) {
            int v = que.front();
            que.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;
                que.push(e.to);
            }
        }
    }
    Cap _dfs(int v, int s, Cap up) {
        if (v == s) return up;
        Cap res = 0;
        int level_v = level[v];
        for (int &i = iter[v]; i < int(g[v].size()); i++) {
            _edge &e = g[v][i];
            if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
            Cap d = _dfs(e.to, s, std::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;
    }

    Cap flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); }
    Cap flow(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);

        level.assign(_n, 0), iter.assign(_n, 0);
        que.clear();

        Cap flow = 0;
        while (flow < flow_limit) {
            _bfs(s, t);
            if (level[t] == -1) break;
            std::fill(iter.begin(), iter.end(), 0);
            Cap f = _dfs(t, s, flow_limit - flow);
            if (!f) break;
            flow += f;
        }
        return flow;
    }

    std::vector<bool> min_cut(int s) {
        std::vector<bool> visited(_n);
        simple_queue_int que;
        que.push(s);
        while (!que.empty()) {
            int p = que.front();
            que.pop();
            visited[p] = true;
            for (auto e : g[p]) {
                if (e.cap && !visited[e.to]) {
                    visited[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        return visited;
    }

    void dump_graphviz(std::string filename = "maxflow") const {
        std::ofstream ss(filename + ".DOT");
        ss << "digraph{\n";
        for (int i = 0; i < _n; i++) {
            for (const auto &e : g[i]) {
                if (e.cap > 0) ss << i << "->" << e.to << "[label=" << e.cap << "];\n";
            }
        }
        ss << "}\n";
        ss.close();
        return;
    }

    int _n;
    struct _edge {
        int to, rev;
        Cap cap;
    };
    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};
#line 4 "flow/mcf_costscaling.hpp"

// Cost scaling
// https://people.orie.cornell.edu/dpw/orie633/
template <class Cap, class Cost, int SCALING = 1, int REFINEMENT_ITER = 20>
struct mcf_costscaling {
    mcf_costscaling() = default;
    mcf_costscaling(int n) : _n(n), to(n), b(n), p(n) {}

    int _n;
    std::vector<Cap> cap;
    std::vector<Cost> cost;
    std::vector<int> opposite;
    std::vector<std::vector<int>> to;
    std::vector<Cap> b;
    std::vector<Cost> p;

    int add_edge(int from_, int to_, Cap cap_, Cost cost_) {
        assert(0 <= from_ and from_ < _n);
        assert(0 <= to_ and to_ < _n);
        assert(0 <= cap_);
        cost_ *= (_n + 1);
        const int e = int(cap.size());
        to[from_].push_back(e);
        cap.push_back(cap_);
        cost.push_back(cost_);
        opposite.push_back(to_);

        to[to_].push_back(e + 1);
        cap.push_back(0);
        cost.push_back(-cost_);
        opposite.push_back(from_);
        return e / 2;
    }
    void add_supply(int v, Cap supply) { b[v] += supply; }
    void add_demand(int v, Cap demand) { add_supply(v, -demand); }

    template <typename RetCost = Cost> RetCost solve() {
        Cost eps = 1;
        std::vector<int> que;
        for (const auto c : cost) {
            while (eps <= -c) eps <<= SCALING;
        }
        for (; eps >>= SCALING;) {
            auto no_admissible_cycle = [&]() -> bool {
                for (int i = 0; i < _n; i++) {
                    if (b[i]) return false;
                }
                std::vector<Cost> pp = p;
                for (int iter = 0; iter < REFINEMENT_ITER; iter++) {
                    bool flg = false;
                    for (int e = 0; e < int(cap.size()); e++) {
                        if (!cap[e]) continue;
                        int i = opposite[e ^ 1], j = opposite[e];
                        if (pp[j] > pp[i] + cost[e] + eps)
                            pp[j] = pp[i] + cost[e] + eps, flg = true;
                    }
                    if (!flg) return p = pp, true;
                }
                return false;
            };
            if (no_admissible_cycle()) continue; // Refine

            for (int e = 0; e < int(cap.size()); e++) {
                const int i = opposite[e ^ 1], j = opposite[e];
                const Cost cp_ij = cost[e] + p[i] - p[j];
                if (cap[e] and cp_ij < 0)
                    b[i] -= cap[e], b[j] += cap[e], cap[e ^ 1] += cap[e], cap[e] = 0;
            }
            que.clear();
            int qh = 0;
            for (int i = 0; i < _n; i++) {
                if (b[i] > 0) que.push_back(i);
            }
            std::vector<int> iters(_n);
            while (qh < int(que.size())) {
                const int i = que[qh++];
                for (; iters[i] < int(to[i].size()) and b[i]; ++iters[i]) { // Push
                    int e = to[i][iters[i]];
                    if (!cap[e]) continue;
                    int j = opposite[e];
                    Cost cp_ij = cost[e] + p[i] - p[j];
                    if (cp_ij >= 0) continue;
                    Cap f = b[i] > cap[e] ? cap[e] : b[i];
                    if (b[j] <= 0 and b[j] + f > 0) que.push_back(j);
                    b[i] -= f, b[j] += f, cap[e] -= f, cap[e ^ 1] += f;
                }

                if (b[i] > 0) { // Relabel
                    bool flg = false;
                    for (int e : to[i]) {
                        if (!cap[e]) continue;
                        Cost x = p[opposite[e]] - cost[e] - eps;
                        if (!flg or x > p[i]) flg = true, p[i] = x;
                    }
                    que.push_back(i), iters[i] = 0;
                }
            }
        }
        RetCost ret = 0;
        for (int e = 0; e < int(cap.size()); e += 2) ret += RetCost(cost[e]) * cap[e ^ 1];
        return ret / (_n + 1);
    }
    std::vector<Cost> potential() const {
        std::vector<Cost> ret = p, c0 = cost;
        for (auto &x : ret) x /= (_n + 1);
        for (auto &x : c0) x /= (_n + 1);
        while (true) {
            bool flg = false;
            for (int i = 0; i < _n; i++) {
                for (const auto e : to[i]) {
                    if (!cap[e]) continue;
                    int j = opposite[e];
                    auto y = ret[i] + c0[e];
                    if (ret[j] > y) ret[j] = y, flg = true;
                }
            }
            if (!flg) break;
        }
        return ret;
    }
    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };
    edge get_edge(int e) const {
        int m = cap.size() / 2;
        assert(e >= 0 and e < m);
        return {opposite[e * 2 + 1], opposite[e * 2], cap[e * 2] + cap[e * 2 + 1], cap[e * 2 + 1],
                cost[e * 2] / (_n + 1)};
    }
    std::vector<edge> edges() const {
        int m = cap.size() / 2;
        std::vector<edge> result(m);
        for (int i = 0; i < m; i++) result[i] = get_edge(i);
        return result;
    }
};
#line 6 "flow/b-flow.hpp"

// CUT begin
template <typename CAP, typename COST> struct B_Flow {
    int N, E;
    COST cost_bias;
    bool infeasible;
    mf_graph<CAP> mf;
    mcf_costscaling<CAP, COST> mcf;
    std::vector<CAP> b;
    std::vector<CAP> fbias;
    std::vector<int> fdir;
    std::vector<CAP> f;
    std::vector<COST> potential;

    B_Flow(int N = 0) : N(N), E(0), cost_bias(0), infeasible(false), mf(N + 2), mcf(N + 2), b(N) {}

    void add_supply(int v, CAP supply) { b[v] += supply; }
    void add_demand(int v, CAP demand) { b[v] -= demand; }
    void add_edge(int s, int t, CAP lower_cap, CAP upper_cap, COST cost) {
        assert(s >= 0 and s < N);
        assert(t >= 0 and t < N);
        if (lower_cap > upper_cap) {
            infeasible = true;
            return;
        }
        E++;
        if (s == t) {
            if (cost > 0) {
                upper_cap = lower_cap;
            } else {
                lower_cap = upper_cap;
            }
        }
        if (cost < 0) {
            fbias.emplace_back(lower_cap);
            fdir.emplace_back(-1);
            cost_bias += cost * upper_cap;
            b[s] -= upper_cap;
            b[t] += upper_cap;
            mf.add_edge(t, s, upper_cap - lower_cap);
            mcf.add_edge(t, s, upper_cap - lower_cap, -cost);
        } else {
            fbias.emplace_back(upper_cap);
            fdir.emplace_back(1);
            if (lower_cap < 0) {
                cost_bias += cost * lower_cap, b[s] -= lower_cap, b[t] += lower_cap;
                upper_cap -= lower_cap, lower_cap = 0;
            }
            if (lower_cap > 0) {
                cost_bias += cost * lower_cap;
                b[s] -= lower_cap;
                b[t] += lower_cap;
                upper_cap -= lower_cap;
            }
            mf.add_edge(s, t, upper_cap);
            mcf.add_edge(s, t, upper_cap, cost);
        }
    }

    std::pair<bool, COST> solve() {
        if (infeasible) return std::make_pair(false, 0);
        CAP bsum = 0, bsum_negative = 0;
        for (int i = 0; i < N; i++) {
            if (b[i] > 0) {
                mf.add_edge(N, i, b[i]), mcf.add_edge(N, i, b[i], 0), bsum += b[i];
            } else {
                mf.add_edge(i, N + 1, -b[i]), mcf.add_edge(i, N + 1, -b[i], 0),
                    bsum_negative -= b[i];
            }
        }
        if (bsum != bsum_negative or mf.flow(N, N + 1) < bsum) return std::make_pair(false, 0);
        std::fill(b.begin(), b.end(), 0);
        mcf.add_supply(N, bsum);
        mcf.add_demand(N + 1, bsum);
        COST ret = mcf.solve();
        potential = mcf.potential(), potential.resize(N);
        COST cost_ret = cost_bias + ret;
        cost_bias = 0;
        f = fbias;
        auto edges = mcf.edges();
        for (int e = 0; e < E; e++) f[e] -= fdir[e] * (edges[e].cap - edges[e].flow);
        return std::make_pair(true, cost_ret);
    }
};
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