competitive-programming-library

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:warning: minimum-cost flow with primal-dual method (old/minimum-cost-flow.inc.cpp)

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Code

template <class T>
struct edge { int to; T cap, cost; int rev; };
template <class T>
void add_edge(vector<vector<edge<T> > > & graph, int from, int to, T cap, T cost) {
    graph[from].push_back((edge<T>) {   to, cap,  cost, int(graph[  to].size())     });
    graph[  to].push_back((edge<T>) { from,  0, - cost, int(graph[from].size()) - 1 });
}
/**
 * @brief minimum-cost flow with primal-dual method
 * @note mainly O(V^2UC) for U is the sum of capacities and C is the sum of costs. and additional O(VE) if negative edges exist
 */
template <class T>
T min_cost_flow_destructive(int src, int dst, T flow, vector<vector<edge<T> > > & graph) {
    T result = 0;
    vector<T> potential(graph.size());
    if (0 < flow) { // initialize potential when negative edges exist (slow). you can remove this if unnecessary
        fill(ALL(potential), numeric_limits<T>::max());
        potential[src] = 0;
        while (true) { // Bellman-Ford algorithm
            bool updated = false;
            REP (e_from, graph.size()) for (auto & e : graph[e_from]) if (e.cap) {
                if (potential[e_from] == numeric_limits<T>::max()) continue;
                if (potential[e.to] > potential[e_from] + e.cost) {
                    potential[e.to] = potential[e_from] + e.cost; // min
                    updated = true;
                }
            }
            if (not updated) break;
        }
    }
    while (0 < flow) {
        // update potential using dijkstra
        vector<T> distance(graph.size(), numeric_limits<T>::max()); // minimum distance
        vector<int> prev_v(graph.size()); // constitute a single-linked-list represents the flow-path
        vector<int> prev_e(graph.size());
        { // initialize distance and prev_{v,e}
            reversed_priority_queue<pair<T, int> > que; // distance * vertex
            distance[src] = 0;
            que.emplace(0, src);
            while (not que.empty()) { // Dijkstra's algorithm
                T d; int v; tie(d, v) = que.top(); que.pop();
                if (potential[v] == numeric_limits<T>::max()) continue; // for unreachable nodes
                if (distance[v] < d) continue;
                // look round the vertex
                REP (e_index, graph[v].size()) {
                    // consider updating
                    edge<T> e = graph[v][e_index];
                    int w = e.to;
                    if (potential[w] == numeric_limits<T>::max()) continue;
                    T d1 = distance[v] + e.cost + potential[v] - potential[w]; // updated distance
                    if (0 < e.cap and d1 < distance[e.to]) {
                        distance[w] = d1;
                        prev_v[w] = v;
                        prev_e[w] = e_index;
                        que.emplace(d1, w);
                    }
                }
            }
        }
        if (distance[dst] == numeric_limits<T>::max()) return -1; // no such flow
        REP (v, graph.size()) {
            if (potential[v] == numeric_limits<T>::max()) continue;
            potential[v] += distance[v];
        }
        // finish updating the potential
        // let flow on the src->dst minimum path
        T delta = flow; // capacity of the path
        for (int v = dst; v != src; v = prev_v[v]) {
            chmin(delta, graph[prev_v[v]][prev_e[v]].cap);
        }
        flow -= delta;
        result += delta * potential[dst];
        for (int v = dst; v != src; v = prev_v[v]) {
            edge<T> & e = graph[prev_v[v]][prev_e[v]]; // reference
            e.cap -= delta;
            graph[v][e.rev].cap += delta;
        }
    }
    return result;
}

#line 1 "old/minimum-cost-flow.inc.cpp"
template <class T>
struct edge { int to; T cap, cost; int rev; };
template <class T>
void add_edge(vector<vector<edge<T> > > & graph, int from, int to, T cap, T cost) {
    graph[from].push_back((edge<T>) {   to, cap,  cost, int(graph[  to].size())     });
    graph[  to].push_back((edge<T>) { from,  0, - cost, int(graph[from].size()) - 1 });
}
/**
 * @brief minimum-cost flow with primal-dual method
 * @note mainly O(V^2UC) for U is the sum of capacities and C is the sum of costs. and additional O(VE) if negative edges exist
 */
template <class T>
T min_cost_flow_destructive(int src, int dst, T flow, vector<vector<edge<T> > > & graph) {
    T result = 0;
    vector<T> potential(graph.size());
    if (0 < flow) { // initialize potential when negative edges exist (slow). you can remove this if unnecessary
        fill(ALL(potential), numeric_limits<T>::max());
        potential[src] = 0;
        while (true) { // Bellman-Ford algorithm
            bool updated = false;
            REP (e_from, graph.size()) for (auto & e : graph[e_from]) if (e.cap) {
                if (potential[e_from] == numeric_limits<T>::max()) continue;
                if (potential[e.to] > potential[e_from] + e.cost) {
                    potential[e.to] = potential[e_from] + e.cost; // min
                    updated = true;
                }
            }
            if (not updated) break;
        }
    }
    while (0 < flow) {
        // update potential using dijkstra
        vector<T> distance(graph.size(), numeric_limits<T>::max()); // minimum distance
        vector<int> prev_v(graph.size()); // constitute a single-linked-list represents the flow-path
        vector<int> prev_e(graph.size());
        { // initialize distance and prev_{v,e}
            reversed_priority_queue<pair<T, int> > que; // distance * vertex
            distance[src] = 0;
            que.emplace(0, src);
            while (not que.empty()) { // Dijkstra's algorithm
                T d; int v; tie(d, v) = que.top(); que.pop();
                if (potential[v] == numeric_limits<T>::max()) continue; // for unreachable nodes
                if (distance[v] < d) continue;
                // look round the vertex
                REP (e_index, graph[v].size()) {
                    // consider updating
                    edge<T> e = graph[v][e_index];
                    int w = e.to;
                    if (potential[w] == numeric_limits<T>::max()) continue;
                    T d1 = distance[v] + e.cost + potential[v] - potential[w]; // updated distance
                    if (0 < e.cap and d1 < distance[e.to]) {
                        distance[w] = d1;
                        prev_v[w] = v;
                        prev_e[w] = e_index;
                        que.emplace(d1, w);
                    }
                }
            }
        }
        if (distance[dst] == numeric_limits<T>::max()) return -1; // no such flow
        REP (v, graph.size()) {
            if (potential[v] == numeric_limits<T>::max()) continue;
            potential[v] += distance[v];
        }
        // finish updating the potential
        // let flow on the src->dst minimum path
        T delta = flow; // capacity of the path
        for (int v = dst; v != src; v = prev_v[v]) {
            chmin(delta, graph[prev_v[v]][prev_e[v]].cap);
        }
        flow -= delta;
        result += delta * potential[dst];
        for (int v = dst; v != src; v = prev_v[v]) {
            edge<T> & e = graph[prev_v[v]][prev_e[v]]; // reference
            e.cap -= delta;
            graph[v][e.rev].cap += delta;
        }
    }
    return result;
}

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