bipartite
(src/graph/bipartite.hpp)

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• Last update: 2024-11-09 01:34:39+09:00
• Include: #include "src/graph/bipartite.hpp"

bipartite

vector<int> bipartite(Graph<T> g)

$n$ 頂点 $m$ 辺の無向グラフ g が二部グラフかどうか判定します．

g が二部グラフである場合， g の各頂点を $0$ と $1$ で彩色した配列を返します．
二部グラフでない場合は空の配列を返します．

計算量

• $O(n + m)$

Depends on

• Graph (src/graph/graph_template.hpp)
• template (src/template/template.hpp)

Verified with

• verify/unit_test/graph/bipartite.test.cpp

Code

#pragma once
#include "../template/template.hpp"
#include "./graph_template.hpp"
template <typename T>
vector<int> bipartite(const Graph<T>& g) {
    const int n = g.size();
    vector<int> color(n, -1);
    auto dfs = [&](const auto& dfs, const int cur, const int col) -> bool {
        color[cur] = col;
        for(const Edge<T>& e : g[cur]) {
            if(color[e.to] == col) return false;
            if(color[e.to] == -1 and !dfs(dfs, e.to, 1 - col)) return false;
        }
        return true;
    };
    for(int i = 0; i < n; ++i) {
        if(color[i] != -1) continue;
        if(!dfs(dfs, i, 0)) return {};
    }
    return color;
}

#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 4 "src/graph/bipartite.hpp"
template <typename T>
vector<int> bipartite(const Graph<T>& g) {
    const int n = g.size();
    vector<int> color(n, -1);
    auto dfs = [&](const auto& dfs, const int cur, const int col) -> bool {
        color[cur] = col;
        for(const Edge<T>& e : g[cur]) {
            if(color[e.to] == col) return false;
            if(color[e.to] == -1 and !dfs(dfs, e.to, 1 - col)) return false;
        }
        return true;
    };
    for(int i = 0; i < n; ++i) {
        if(color[i] != -1) continue;
        if(!dfs(dfs, i, 0)) return {};
    }
    return color;
}

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