graph/flow/ford-fulkerson.hpp

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• Last update: 2024-10-04 14:05:18+02:00
• Include: #include "graph/flow/ford-fulkerson.hpp"

Verified with

• test/aoj-grl-6-a-2.test.cpp

Code

#include <bits/stdc++.h>
using namespace std;

template <typename flow_t>
struct FordFulkerson {
    struct edge {
        int to;
        flow_t cap;
        int rev;
        bool isrev;
        int idx;
    };

    const flow_t INF;
    vector<vector<edge> > graph;
    vector<int> used;
    int timestamp;

    explicit FordFulkerson(int V)
        : INF(numeric_limits<flow_t>::max()),
          graph(V),
          used(V, -1),
          timestamp(0) {}

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

    flow_t find_augment_path(int idx, const int t, flow_t flow) {
        if (idx == t) return flow;
        used[idx] = timestamp;
        for (auto &e : graph[idx]) {
            if (e.cap > 0 && used[e.to] != timestamp) {
                flow_t d = find_augment_path(e.to, t, min(flow, e.cap));
                if (d > 0) {
                    e.cap -= d;
                    graph[e.to][e.rev].cap += d;
                    return d;
                }
            }
        }
        return 0;
    }

    flow_t max_flow(int s, int t) {
        flow_t flow = 0;
        for (flow_t f; (f = find_augment_path(s, t, INF)) > 0; timestamp++) {
            flow += f;
        }
        timestamp++;
        return flow;
    }

    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 << "/"
                     << e.cap + rev_e.cap << ")" << endl;
            }
        }
    }
};

#line 1 "graph/flow/ford-fulkerson.hpp"
#include <bits/stdc++.h>
using namespace std;

template <typename flow_t>
struct FordFulkerson {
    struct edge {
        int to;
        flow_t cap;
        int rev;
        bool isrev;
        int idx;
    };

    const flow_t INF;
    vector<vector<edge> > graph;
    vector<int> used;
    int timestamp;

    explicit FordFulkerson(int V)
        : INF(numeric_limits<flow_t>::max()),
          graph(V),
          used(V, -1),
          timestamp(0) {}

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

    flow_t find_augment_path(int idx, const int t, flow_t flow) {
        if (idx == t) return flow;
        used[idx] = timestamp;
        for (auto &e : graph[idx]) {
            if (e.cap > 0 && used[e.to] != timestamp) {
                flow_t d = find_augment_path(e.to, t, min(flow, e.cap));
                if (d > 0) {
                    e.cap -= d;
                    graph[e.to][e.rev].cap += d;
                    return d;
                }
            }
        }
        return 0;
    }

    flow_t max_flow(int s, int t) {
        flow_t flow = 0;
        for (flow_t f; (f = find_augment_path(s, t, INF)) > 0; timestamp++) {
            flow += f;
        }
        timestamp++;
        return flow;
    }

    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 << "/"
                     << e.cap + rev_e.cap << ")" << endl;
            }
        }
    }
};

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