うしさんからパクってきた最小費用流
(graph_tree/min_cost_flow_ei.hpp)

#pragma once

/**
 * @brief うしさんからパクってきた最小費用流
 */

template <typename flow_t, typename cost_t>
struct PrimalDual{
    const cost_t INF;
    struct edge{
        int to;
        flow_t cap;
        cost_t cost;
        int rev;
        bool isrev;
    };
    vector<vector<edge>> graph;
    vector<cost_t> potential, min_cost;
    vector<int> prevv, preve;

    PrimalDual(int V) : graph(V), INF(numeric_limits<cost_t>::max()) {}

    void add_edge(int from, int to, flow_t cap, cost_t cost){
        graph[from].emplace_back((edge){to, cap, cost, (int)graph[to].size(), false});
        graph[to].emplace_back((edge){from, 0, -cost, (int)graph[from].size() - 1, true});
    }

    cost_t min_cost_flow(int s, int t, flow_t f){
        int V = (int)graph.size();
        cost_t ret = 0;
        using Pi = pair<cost_t, int>;
        priority_queue<Pi, vector<Pi>, greater<Pi>> que;
        potential.assign(V, 0);
        preve.assign(V, -1);
        prevv.assign(V, -1);

        while (f > 0)
        {
            min_cost.assign(V, INF);
            que.emplace(0, s);
            min_cost[s] = 0;
            while (!que.empty()){
                Pi p = que.top();
                que.pop();
                if (min_cost[p.second] < p.first)
                    continue;
                for (int i = 0; i < int(graph[p.second].size()); i++){
                    edge &e = graph[p.second][i];
                    cost_t nextCost = min_cost[p.second] + e.cost + potential[p.second] - potential[e.to];
                    if (e.cap > 0 && min_cost[e.to] > nextCost){
                        min_cost[e.to] = nextCost;
                        prevv[e.to] = p.second, preve[e.to] = i;
                        que.emplace(min_cost[e.to], e.to);
                    }
                }
            }
            if (min_cost[t] == INF)return -1;
            for (int v = 0; v < V; v++)potential[v] += min_cost[v];
            flow_t addflow = f;
            for (int v = t; v != s; v = prevv[v]){
                addflow = min(addflow, graph[prevv[v]][preve[v]].cap);
            }
            f -= addflow;
            ret += addflow * potential[t];
            for (int v = t; v != s; v = prevv[v]){
                edge &e = graph[prevv[v]][preve[v]];
                e.cap -= addflow;
                graph[v][e.rev].cap += addflow;
            }
        }
        return ret;
    }

    void output(){
        for (int i = 0; i < graph.size(); i++){
            for (auto &e : graph[i]){
                if (e.isrev) continue;
                auto &rev_e = graph[e.to][e.rev];
                cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/" << rev_e.cap + e.cap << ")" << endl;
            }
        }
    }
};

#line 2 "graph_tree/min_cost_flow_ei.hpp"

/**
 * @brief うしさんからパクってきた最小費用流
 */

template <typename flow_t, typename cost_t>
struct PrimalDual{
    const cost_t INF;
    struct edge{
        int to;
        flow_t cap;
        cost_t cost;
        int rev;
        bool isrev;
    };
    vector<vector<edge>> graph;
    vector<cost_t> potential, min_cost;
    vector<int> prevv, preve;

    PrimalDual(int V) : graph(V), INF(numeric_limits<cost_t>::max()) {}

    void add_edge(int from, int to, flow_t cap, cost_t cost){
        graph[from].emplace_back((edge){to, cap, cost, (int)graph[to].size(), false});
        graph[to].emplace_back((edge){from, 0, -cost, (int)graph[from].size() - 1, true});
    }

    cost_t min_cost_flow(int s, int t, flow_t f){
        int V = (int)graph.size();
        cost_t ret = 0;
        using Pi = pair<cost_t, int>;
        priority_queue<Pi, vector<Pi>, greater<Pi>> que;
        potential.assign(V, 0);
        preve.assign(V, -1);
        prevv.assign(V, -1);

        while (f > 0)
        {
            min_cost.assign(V, INF);
            que.emplace(0, s);
            min_cost[s] = 0;
            while (!que.empty()){
                Pi p = que.top();
                que.pop();
                if (min_cost[p.second] < p.first)
                    continue;
                for (int i = 0; i < int(graph[p.second].size()); i++){
                    edge &e = graph[p.second][i];
                    cost_t nextCost = min_cost[p.second] + e.cost + potential[p.second] - potential[e.to];
                    if (e.cap > 0 && min_cost[e.to] > nextCost){
                        min_cost[e.to] = nextCost;
                        prevv[e.to] = p.second, preve[e.to] = i;
                        que.emplace(min_cost[e.to], e.to);
                    }
                }
            }
            if (min_cost[t] == INF)return -1;
            for (int v = 0; v < V; v++)potential[v] += min_cost[v];
            flow_t addflow = f;
            for (int v = t; v != s; v = prevv[v]){
                addflow = min(addflow, graph[prevv[v]][preve[v]].cap);
            }
            f -= addflow;
            ret += addflow * potential[t];
            for (int v = t; v != s; v = prevv[v]){
                edge &e = graph[prevv[v]][preve[v]];
                e.cap -= addflow;
                graph[v][e.rev].cap += addflow;
            }
        }
        return ret;
    }

    void output(){
        for (int i = 0; i < graph.size(); i++){
            for (auto &e : graph[i]){
                if (e.isrev) continue;
                auto &rev_e = graph[e.to][e.rev];
                cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/" << rev_e.cap + e.cap << ")" << endl;
            }
        }
    }
};