Fu_L's Library

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:heavy_check_mark: max_matching
(src/graph/max_matching.hpp)

max_matching

Edges<T> max_matching(int n, Edges<T> es)

$n$ 頂点無向グラフの辺集合 es からグラフの最大マッチングを計算します．
返り値は採用された辺集合です．

注: #include "graph/max_matching.hpp" を #include "template/template.hpp" の上に書かないとCompile Errorが起こります．

制約

計算量

頂点数，辺数をそれぞれ $V, E$ として，

Depends on

Verified with

Code

#pragma once
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/max_cardinality_matching.hpp>
#include "../template/template.hpp"
#include "../graph/graph_template.hpp"
template <typename T>
Edges<T> max_matching(const int n, const Edges<T>& es) {
    using namespace boost;
    using G = adjacency_list<vecS, vecS, undirectedS>;
    using V = graph_traits<G>::vertex_descriptor;
    G g(n);
    for(const Edge<T>& e : es) {
        assert(e.cost == 1);
        add_edge(e.from, e.to, g);
    }
    vector<V> mate(n);
    edmonds_maximum_cardinality_matching(g, &mate[0]);
    Edges<T> res;
    for(V v = 0; v < num_vertices(g); ++v) {
        if(mate[v] != graph_traits<G>::null_vertex() and v < mate[v]) {
            res.push_back({(int)v, (int)mate[v], 1});
        }
    }
    return res;
}
#line 2 "src/graph/max_matching.hpp"
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/max_cardinality_matching.hpp>
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/graph/graph_template.hpp"
template <typename T>
struct Edge {
    int from, to;
    T cost;
    int idx;
    Edge()
        : from(-1), to(-1), cost(-1), idx(-1) {}
    Edge(const int from, const int to, const T& cost = 1, const int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}
    operator int() const {
        return to;
    }
};
template <typename T>
struct Graph {
    Graph(const int N)
        : n(N), es(0), g(N) {}
    int size() const {
        return n;
    }
    int edge_size() const {
        return es;
    }
    void add_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }
    void add_directed_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es++);
    }
    inline vector<Edge<T>>& operator[](const int& k) {
        assert(0 <= k and k < n);
        return g[k];
    }
    inline const vector<Edge<T>>& operator[](const int& k) const {
        assert(0 <= k and k < n);
        return g[k];
    }

   private:
    int n, es;
    vector<vector<Edge<T>>> g;
};
template <typename T>
using Edges = vector<Edge<T>>;
#line 7 "src/graph/max_matching.hpp"
template <typename T>
Edges<T> max_matching(const int n, const Edges<T>& es) {
    using namespace boost;
    using G = adjacency_list<vecS, vecS, undirectedS>;
    using V = graph_traits<G>::vertex_descriptor;
    G g(n);
    for(const Edge<T>& e : es) {
        assert(e.cost == 1);
        add_edge(e.from, e.to, g);
    }
    vector<V> mate(n);
    edmonds_maximum_cardinality_matching(g, &mate[0]);
    Edges<T> res;
    for(V v = 0; v < num_vertices(g); ++v) {
        if(mate[v] != graph_traits<G>::null_vertex() and v < mate[v]) {
            res.push_back({(int)v, (int)mate[v], 1});
        }
    }
    return res;
}
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