This documentation is automatically generated by online-judge-tools/verification-helper
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/chromatic_number
#include "../../template/template.hpp"
#include "../../graph/others/chromatic-number.hpp"
#include "../../math/matrix/square-matrix.hpp"
int main() {
int N, M;
cin >> N >> M;
SquareMatrix< bool, 20 > g;
for(int i = 0; i < M; i++) {
int u, v;
cin >> u >> v;
g[u][v] = g[v][u] = true;
}
cout << chromatic_number(g) << "\n";
}
#line 1 "test/verify/yosupo-chromatic-number.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/chromatic_number
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (T &in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
for (auto &e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F &&f) : F(forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args &&...args) const {
return F::operator()(*this, forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F &&f) {
return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-chromatic-number.test.cpp"
#line 2 "graph/others/chromatic-number.hpp"
/**
* @brief Chromatic Number(彩色数)
*
* @see https://www.slideshare.net/wata_orz/ss-12131479
*/
template <typename Matrix>
int chromatic_number(Matrix &g) {
int N = (int)g.size();
vector<int> es(N);
for (int i = 0; i < (int)g.size(); i++) {
for (int j = 0; j < (int)g.size(); j++) {
if (g[i][j] != 0) es[i] |= 1 << j;
}
}
vector<int> ind(1 << N);
ind[0] = 1;
for (int S = 1; S < (1 << N); S++) {
int u = __builtin_ctz(S);
ind[S] = ind[S ^ (1 << u)] + ind[(S ^ (1 << u)) & ~es[u]];
}
vector<int> cnt((1 << N) + 1);
for (int i = 0; i < (1 << N); i++) {
cnt[ind[i]] += __builtin_parity(i) ? -1 : 1;
}
vector<pair<unsigned, int> > hist;
for (int i = 1; i <= (1 << N); i++) {
if (cnt[i]) hist.emplace_back(i, cnt[i]);
}
constexpr int mods[] = {1000000007, 1000000011, 1000000021};
int ret = N;
for (int k = 0; k < 3; k++) {
auto buf = hist;
for (int c = 1; c < ret; c++) {
int64_t sum = 0;
for (auto &[i, x] : buf) {
sum += (x = int64_t(x) * i % mods[k]);
}
if (sum % mods[k]) ret = c;
}
}
return ret;
}
#line 1 "math/matrix/square-matrix.hpp"
/**
* @brief Square-Matrix(正方行列)
*/
template <class T, size_t N>
struct SquareMatrix {
array<array<T, N>, N> A;
SquareMatrix() : A{{}} {}
size_t size() const { return N; }
inline const array<T, N> &operator[](int k) const { return (A.at(k)); }
inline array<T, N> &operator[](int k) { return (A.at(k)); }
static SquareMatrix add_identity() { return SquareMatrix(); }
static SquareMatrix mul_identity() {
SquareMatrix mat;
for (size_t i = 0; i < N; i++) mat[i][i] = 1;
return mat;
}
SquareMatrix &operator+=(const SquareMatrix &B) {
for (size_t i = 0; i < N; i++) {
for (size_t j = 0; j < N; j++) {
(*this)[i][j] += B[i][j];
}
}
return *this;
}
SquareMatrix &operator-=(const SquareMatrix &B) {
for (size_t i = 0; i < N; i++) {
for (size_t j = 0; j < N; j++) {
(*this)[i][j] -= B[i][j];
}
}
return *this;
}
SquareMatrix &operator*=(const SquareMatrix &B) {
array<array<T, N>, N> C;
for (size_t i = 0; i < N; i++) {
for (size_t j = 0; j < N; j++) {
for (size_t k = 0; k < N; k++) {
C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
}
}
}
A.swap(C);
return (*this);
}
SquareMatrix &operator^=(uint64_t k) {
SquareMatrix B = SquareMatrix::mul_identity();
while (k > 0) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return *this;
}
SquareMatrix operator+(const SquareMatrix &B) const {
return SquareMatrix(*this) += B;
}
SquareMatrix operator-(const SquareMatrix &B) const {
return SquareMatrix(*this) -= B;
}
SquareMatrix operator*(const SquareMatrix &B) const {
return SquareMatrix(*this) *= B;
}
SquareMatrix operator^(uint64_t k) const { return SquareMatrix(*this) ^= k; }
friend ostream &operator<<(ostream &os, SquareMatrix &p) {
for (int i = 0; i < N; i++) {
os << "[";
for (int j = 0; j < N; j++) {
os << p[i][j] << (j + 1 == N ? "]\n" : ",");
}
}
return os;
}
};
#line 7 "test/verify/yosupo-chromatic-number.test.cpp"
int main() {
int N, M;
cin >> N >> M;
SquareMatrix< bool, 20 > g;
for(int i = 0; i < M; i++) {
int u, v;
cin >> u >> v;
g[u][v] = g[v][u] = true;
}
cout << chromatic_number(g) << "\n";
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | big_00 | AC | 12 ms | 12 MB |
g++ | big_01 | AC | 12 ms | 12 MB |
g++ | big_02 | AC | 11 ms | 11 MB |
g++ | big_03 | AC | 12 ms | 12 MB |
g++ | big_04 | AC | 12 ms | 12 MB |
g++ | big_05 | AC | 12 ms | 12 MB |
g++ | big_06 | AC | 12 ms | 12 MB |
g++ | big_07 | AC | 11 ms | 11 MB |
g++ | big_08 | AC | 12 ms | 12 MB |
g++ | big_09 | AC | 11 ms | 12 MB |
g++ | clique_cycle_00 | AC | 12 ms | 11 MB |
g++ | clique_cycle_01 | AC | 12 ms | 11 MB |
g++ | clique_cycle_02 | AC | 11 ms | 12 MB |
g++ | clique_cycle_03 | AC | 12 ms | 11 MB |
g++ | example_00 | AC | 12 ms | 11 MB |
g++ | example_01 | AC | 12 ms | 11 MB |
g++ | random_00 | AC | 11 ms | 12 MB |
g++ | random_01 | AC | 11 ms | 11 MB |
g++ | random_02 | AC | 11 ms | 11 MB |
g++ | random_03 | AC | 11 ms | 11 MB |
g++ | random_04 | AC | 11 ms | 12 MB |
g++ | random_05 | AC | 11 ms | 12 MB |
g++ | random_06 | AC | 12 ms | 11 MB |
g++ | random_07 | AC | 12 ms | 11 MB |
g++ | random_08 | AC | 12 ms | 12 MB |
g++ | random_09 | AC | 12 ms | 11 MB |
clang++ | big_00 | AC | 15 ms | 12 MB |
clang++ | big_01 | AC | 15 ms | 11 MB |
clang++ | big_02 | AC | 15 ms | 11 MB |
clang++ | big_03 | AC | 15 ms | 12 MB |
clang++ | big_04 | AC | 15 ms | 12 MB |
clang++ | big_05 | AC | 15 ms | 12 MB |
clang++ | big_06 | AC | 15 ms | 12 MB |
clang++ | big_07 | AC | 15 ms | 11 MB |
clang++ | big_08 | AC | 15 ms | 12 MB |
clang++ | big_09 | AC | 15 ms | 12 MB |
clang++ | clique_cycle_00 | AC | 15 ms | 11 MB |
clang++ | clique_cycle_01 | AC | 15 ms | 11 MB |
clang++ | clique_cycle_02 | AC | 15 ms | 12 MB |
clang++ | clique_cycle_03 | AC | 15 ms | 11 MB |
clang++ | example_00 | AC | 15 ms | 11 MB |
clang++ | example_01 | AC | 15 ms | 11 MB |
clang++ | random_00 | AC | 15 ms | 12 MB |
clang++ | random_01 | AC | 15 ms | 11 MB |
clang++ | random_02 | AC | 15 ms | 11 MB |
clang++ | random_03 | AC | 15 ms | 11 MB |
clang++ | random_04 | AC | 15 ms | 12 MB |
clang++ | random_05 | AC | 15 ms | 12 MB |
clang++ | random_06 | AC | 15 ms | 11 MB |
clang++ | random_07 | AC | 15 ms | 11 MB |
clang++ | random_08 | AC | 15 ms | 12 MB |
clang++ | random_09 | AC | 15 ms | 11 MB |