Graph/MaxFlow/MinCostMaxFlowSPFA.h

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• Last update: 2022-01-10 00:42:12+08:00
• Link: http://codeforces.com/gym/100213
• Link: http://codeforces.com/gym/100216
• Link: http://codeforces.com/gym/100222
• Link: http://www.infoarena.ro/problema/fmcm
• Link: https://codeforces.com/blog/entry/70740
• Link: https://codeforces.com/contest/277/problem/E
• Link: https://open.kattis.com/problems/mincostmaxflow

Verified with

• Graph/tests/aizu_grl_6_b_mincost_maxflow_spfa.test.cpp

Code

// Min Cost Max Flow - SPFA
// Index from 0
// edges cap changed during find flow
// Lots of double comparison --> likely to fail for double
// Example:
// MinCostFlow mcf(n);
// mcf.addEdge(u, v, cap, cost);
// cout << mcf.minCostFlow() << endl;
// Tested:
// - ***TLE*** https://codeforces.com/blog/entry/70740
// - ***TLE*** http://www.infoarena.ro/problema/fmcm
// - https://open.kattis.com/problems/mincostmaxflow
// - http://codeforces.com/gym/100213 - A
// - http://codeforces.com/gym/100216 - A
// - http://codeforces.com/gym/100222 - D
// - ACM Regional Daejeon 2014 - L (negative weights)
// - https://codeforces.com/contest/277/problem/E

template<class Flow=int, class Cost=int>
struct MinCostFlow {
    const Flow INF_FLOW = 1000111000;
    const Cost INF_COST = 1000111000111000LL;

    int n, t, S, T;
    Flow totalFlow;
    Cost totalCost;
    vector<int> last, visited;
    vector<Cost> dis;
    struct Edge {
        int to;
        Flow cap;
        Cost cost;
        int next;
        Edge(int _to, Flow _cap, Cost _cost, int _next) :
                to(_to), cap(_cap), cost(_cost), next(_next) {}
    };
    vector<Edge> edges;

    MinCostFlow(int _n) : n(_n), t(0), totalFlow(0), totalCost(0), last(n, -1), visited(n, 0), dis(n, 0) {
        edges.clear();
    }

    int addEdge(int from, int to, Flow cap, Cost cost) {
        edges.push_back(Edge(to, cap, cost, last[from]));
        last[from] = t++;
        edges.push_back(Edge(from, 0, -cost, last[to]));
        last[to] = t++;
        return t - 2;
    }

    pair<Flow, Cost> minCostFlow(int _S, int _T) {
        S = _S; T = _T;
        SPFA();
        while (1) {
            while (1) {
                std::fill(visited.begin(), visited.end(), 0);
                if (!findFlow(S, INF_FLOW)) break;
            }
            if (!modifyLabel()) break;
        }
        return make_pair(totalFlow, totalCost);
    }

private:
    void SPFA() {
        std::fill(dis.begin(), dis.end(), INF_COST);
        priority_queue< pair<Cost,int> > Q;
        Q.push(make_pair(dis[S]=0, S));
        while (!Q.empty()) {
            int x = Q.top().second;
            Cost d = -Q.top().first;
            Q.pop();
            // For double: dis[x] > d + EPS
            if (dis[x] != d) continue;
            for(int it = last[x]; it >= 0; it = edges[it].next)
                if (edges[it].cap > 0 && dis[edges[it].to] > d + edges[it].cost)
                    Q.push(make_pair(-(dis[edges[it].to] = d + edges[it].cost), edges[it].to));
        }
        Cost disT = dis[T];
        for (int i = 0; i < n; i++) {
            dis[i] = disT - dis[i];
        }
    }

    Flow findFlow(int x, Flow flow) {
        if (x == T) {
            totalCost += dis[S] * flow;
            totalFlow += flow;
            return flow;
        }
        visited[x] = 1;
        Flow now = flow;
        for(int it = last[x]; it >= 0; it = edges[it].next)
            // For double: fabs(dis[edges[it].to] + edges[it].cost - dis[x]) < EPS
            if (edges[it].cap && !visited[edges[it].to] && dis[edges[it].to] + edges[it].cost == dis[x]) {
                Flow tmp = findFlow(edges[it].to, min(now, edges[it].cap));
                edges[it].cap -= tmp;
                edges[it ^ 1].cap += tmp;
                now -= tmp;
                if (!now) break;
            }
        return flow - now;
    }

    bool modifyLabel() {
        Cost d = INF_COST;
        for (int i = 0; i < n; i++) if (visited[i])
            for(int it = last[i]; it >= 0; it = edges[it].next)
                if (edges[it].cap && !visited[edges[it].to])
                    d = min(d, dis[edges[it].to] + edges[it].cost - dis[i]);

        // For double: if (d > INF_COST / 10)     INF_COST = 1e20
        if (d == INF_COST) return false;
        for (int i = 0; i < n; i++) if (visited[i])
            dis[i] += d;
        return true;
    }
};

#line 1 "Graph/MaxFlow/MinCostMaxFlowSPFA.h"
// Min Cost Max Flow - SPFA
// Index from 0
// edges cap changed during find flow
// Lots of double comparison --> likely to fail for double
// Example:
// MinCostFlow mcf(n);
// mcf.addEdge(u, v, cap, cost);
// cout << mcf.minCostFlow() << endl;
// Tested:
// - ***TLE*** https://codeforces.com/blog/entry/70740
// - ***TLE*** http://www.infoarena.ro/problema/fmcm
// - https://open.kattis.com/problems/mincostmaxflow
// - http://codeforces.com/gym/100213 - A
// - http://codeforces.com/gym/100216 - A
// - http://codeforces.com/gym/100222 - D
// - ACM Regional Daejeon 2014 - L (negative weights)
// - https://codeforces.com/contest/277/problem/E

template<class Flow=int, class Cost=int>
struct MinCostFlow {
    const Flow INF_FLOW = 1000111000;
    const Cost INF_COST = 1000111000111000LL;

    int n, t, S, T;
    Flow totalFlow;
    Cost totalCost;
    vector<int> last, visited;
    vector<Cost> dis;
    struct Edge {
        int to;
        Flow cap;
        Cost cost;
        int next;
        Edge(int _to, Flow _cap, Cost _cost, int _next) :
                to(_to), cap(_cap), cost(_cost), next(_next) {}
    };
    vector<Edge> edges;

    MinCostFlow(int _n) : n(_n), t(0), totalFlow(0), totalCost(0), last(n, -1), visited(n, 0), dis(n, 0) {
        edges.clear();
    }

    int addEdge(int from, int to, Flow cap, Cost cost) {
        edges.push_back(Edge(to, cap, cost, last[from]));
        last[from] = t++;
        edges.push_back(Edge(from, 0, -cost, last[to]));
        last[to] = t++;
        return t - 2;
    }

    pair<Flow, Cost> minCostFlow(int _S, int _T) {
        S = _S; T = _T;
        SPFA();
        while (1) {
            while (1) {
                std::fill(visited.begin(), visited.end(), 0);
                if (!findFlow(S, INF_FLOW)) break;
            }
            if (!modifyLabel()) break;
        }
        return make_pair(totalFlow, totalCost);
    }

private:
    void SPFA() {
        std::fill(dis.begin(), dis.end(), INF_COST);
        priority_queue< pair<Cost,int> > Q;
        Q.push(make_pair(dis[S]=0, S));
        while (!Q.empty()) {
            int x = Q.top().second;
            Cost d = -Q.top().first;
            Q.pop();
            // For double: dis[x] > d + EPS
            if (dis[x] != d) continue;
            for(int it = last[x]; it >= 0; it = edges[it].next)
                if (edges[it].cap > 0 && dis[edges[it].to] > d + edges[it].cost)
                    Q.push(make_pair(-(dis[edges[it].to] = d + edges[it].cost), edges[it].to));
        }
        Cost disT = dis[T];
        for (int i = 0; i < n; i++) {
            dis[i] = disT - dis[i];
        }
    }

    Flow findFlow(int x, Flow flow) {
        if (x == T) {
            totalCost += dis[S] * flow;
            totalFlow += flow;
            return flow;
        }
        visited[x] = 1;
        Flow now = flow;
        for(int it = last[x]; it >= 0; it = edges[it].next)
            // For double: fabs(dis[edges[it].to] + edges[it].cost - dis[x]) < EPS
            if (edges[it].cap && !visited[edges[it].to] && dis[edges[it].to] + edges[it].cost == dis[x]) {
                Flow tmp = findFlow(edges[it].to, min(now, edges[it].cap));
                edges[it].cap -= tmp;
                edges[it ^ 1].cap += tmp;
                now -= tmp;
                if (!now) break;
            }
        return flow - now;
    }

    bool modifyLabel() {
        Cost d = INF_COST;
        for (int i = 0; i < n; i++) if (visited[i])
            for(int it = last[i]; it >= 0; it = edges[it].next)
                if (edges[it].cap && !visited[edges[it].to])
                    d = min(d, dis[edges[it].to] + edges[it].cost - dis[i]);

        // For double: if (d > INF_COST / 10)     INF_COST = 1e20
        if (d == INF_COST) return false;
        for (int i = 0; i < n; i++) if (visited[i])
            dis[i] += d;
        return true;
    }
};

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