Verify/LC_chromatic_number.test.cpp

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Last update: 2024-04-26 03:18:17+09:00
Problem: https://judge.yosupo.jp/problem/chromatic_number

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/chromatic_number"

#include "Template/template.hpp"

#include "Graph/chromatic.hpp"


int main(){
    int n,m;
    cin>>n>>m;
    Chromatic g(n);
    rep(i,0,m){
        int x,y;
        cin>>x>>y;
        g.add_edge(x,y);
    }
    cout<<g.run()<<'\n';
    return 0;
}

#line 1 "Verify/LC_chromatic_number.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/chromatic_number"

#line 1 "Template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b-1); i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())

using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
    return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}

#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
    cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
    for (; a[i] != ',' && a[i] != '\0'; i++)
        cerr << a[i];
    cerr << ":" << b << " ";
    _show(i + 1, a, c...);
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "P(" << p.first << ", " << p.second << ")";
    return os;
}
template <typename T, template <class> class C>
ostream &operator<<(ostream &os, const C<T> &v) {
    os << "[";
    for (auto d : v)
        os << d << ", ";
    os << "]";
    return os;
}
#line 2 "Graph/chromatic.hpp"

struct Chromatic{
    const int n;
    vector<ll> es;
    Chromatic(int _n):n(_n),es(n){}
    void add_edge(int u,int v){
        es[u]|=1<<v;
        es[v]|=1<<u;
    }
    int run(){
        vector<int> dp(1<<n),sign(1<<n);
        dp[0]=1;
        rep(mask,0,1<<n){
            if(mask){
                int v=__builtin_ctz(mask);
                dp[mask]=dp[mask^(1<<v)]+dp[(mask^(1<<v))&(~es[v])];
            }
            sign[mask]=((n-__builtin_popcountll(mask))&1?-1:1);
        }
        int ret=n;
        auto calc=[&](int md)->void{
            vector<ll> cur(ALL(sign));
            rep(k,1,ret){
                int cnt=0;
                rep(mask,0,1<<n){
                    cur[mask]=(cur[mask]*dp[mask])%md;
                    if(cur[mask]<0)cur[mask]+=md;
                    cnt=(cnt+cur[mask])%md;
                }
                if(cnt!=0){
                    ret=k;
                    break;
                }
            }
        };
        for(auto& md:{998244353,1000000007,1000000011}){
            calc(md);
        }
        return ret;
    }
};

/**
 * @brief Chromatic Number
 */
#line 5 "Verify/LC_chromatic_number.test.cpp"

int main(){
    int n,m;
    cin>>n>>m;
    Chromatic g(n);
    rep(i,0,m){
        int x,y;
        cin>>x>>y;
        g.add_edge(x,y);
    }
    cout<<g.run()<<'\n';
    return 0;
}