This documentation is automatically generated by online-judge-tools/verification-helper
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/maximum_independent_set
#include "../../template/template.hpp"
#include "../../math/matrix/matrix.hpp"
#include "../../graph/others/maximum-independent-set.hpp"
int main() {
int N, M;
cin >> N >> M;
Matrix< bool > mat(N);
for(int i = 0; i < M; i++) {
int a, b;
cin >> a >> b;
mat[a][b] = true;
mat[b][a] = true;
}
auto ret = maximum_independent_set(mat);
cout << ret.size() << endl;
cout << ret << endl;
}
#line 1 "test/verify/yosupo-maximum-independent-set.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/maximum_independent_set
#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-maximum-independent-set.test.cpp"
#line 1 "math/matrix/matrix.hpp"
template< class T >
struct Matrix {
vector< vector< T > > A;
Matrix() {}
Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}
Matrix(size_t n) : A(n, vector< T >(n, 0)) {};
size_t size() const {
if(A.empty()) return 0;
assert(A.size() == A[0].size());
return A.size();
}
size_t height() const {
return (A.size());
}
size_t width() const {
return (A[0].size());
}
inline const vector< T > &operator[](int k) const {
return (A.at(k));
}
inline vector< T > &operator[](int k) {
return (A.at(k));
}
static Matrix I(size_t n) {
Matrix mat(n);
for(int i = 0; i < n; i++) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
size_t n = height(), m = B.width(), p = width();
assert(p == B.height());
vector< vector< T > > C(n, vector< T >(m, 0));
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
for(int k = 0; k < p; k++)
C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
A.swap(C);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::I(height());
while(k > 0) {
if(k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const {
return (Matrix(*this) += B);
}
Matrix operator-(const Matrix &B) const {
return (Matrix(*this) -= B);
}
Matrix operator*(const Matrix &B) const {
return (Matrix(*this) *= B);
}
Matrix operator^(const long long k) const {
return (Matrix(*this) ^= k);
}
friend ostream &operator<<(ostream &os, Matrix &p) {
size_t n = p.height(), m = p.width();
for(int i = 0; i < n; i++) {
os << "[";
for(int j = 0; j < m; j++) {
os << p[i][j] << (j + 1 == m ? "]\n" : ",");
}
}
return (os);
}
T determinant() {
Matrix B(*this);
assert(width() == height());
T ret = 1;
for(int i = 0; i < width(); i++) {
int idx = -1;
for(int j = i; j < width(); j++) {
if(B[j][i] != 0) idx = j;
}
if(idx == -1) return (0);
if(i != idx) {
ret *= -1;
swap(B[i], B[idx]);
}
ret *= B[i][i];
T vv = B[i][i];
for(int j = 0; j < width(); j++) {
B[i][j] /= vv;
}
for(int j = i + 1; j < width(); j++) {
T a = B[j][i];
for(int k = 0; k < width(); k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return (ret);
}
};
#line 1 "graph/others/maximum-independent-set.hpp"
/**
* @brief Maximum Independent Set(最大独立集合)
*/
template< typename Matrix >
vector< int > maximum_independent_set(const Matrix &g, int trial = 1000000) {
int N = (int) g.size();
vector< uint64_t > bit(N);
assert(N <= 64);
for(int i = 0; i < N; i++) {
for(int j = 0; j < N; j++) {
if(i != j) {
assert(g[i][j] == g[j][i]);
if(g[i][j]) bit[i] |= uint64_t(1) << j;
}
}
}
vector< int > ord(N);
iota(begin(ord), end(ord), 0);
mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int ret = 0;
uint64_t ver = 0;
for(int i = 0; i < trial; i++) {
shuffle(begin(ord), end(ord), mt);
uint64_t used = 0;
int add = 0;
for(int j : ord) {
if(used & bit[j]) continue;
used |= uint64_t(1) << j;
++add;
}
if(ret < add) {
ret = add;
ver = used;
}
}
vector< int > ans;
for(int i = 0; i < N; i++) {
if((ver >> i) & 1) ans.emplace_back(i);
}
return ans;
}
#line 7 "test/verify/yosupo-maximum-independent-set.test.cpp"
int main() {
int N, M;
cin >> N >> M;
Matrix< bool > mat(N);
for(int i = 0; i < M; i++) {
int a, b;
cin >> a >> b;
mat[a][b] = true;
mat[b][a] = true;
}
auto ret = maximum_independent_set(mat);
cout << ret.size() << endl;
cout << ret << endl;
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | example_00 | AC | 76 ms | 4 MB |
g++ | example_01 | AC | 59 ms | 4 MB |
g++ | hack0_00 | AC | 330 ms | 4 MB |
g++ | handmade_00 | AC | 82 ms | 4 MB |
g++ | many_maximals_00 | AC | 305 ms | 4 MB |
g++ | max_random_00 | AC | 243 ms | 4 MB |
g++ | max_random_01 | AC | 293 ms | 4 MB |
g++ | max_random_02 | AC | 340 ms | 4 MB |
g++ | max_random_03 | AC | 300 ms | 4 MB |
g++ | max_random_04 | AC | 262 ms | 4 MB |
g++ | one_two_00 | AC | 302 ms | 4 MB |
g++ | random_00 | AC | 236 ms | 4 MB |
g++ | random_01 | AC | 59 ms | 4 MB |
g++ | random_02 | AC | 189 ms | 4 MB |
g++ | random_03 | AC | 10 ms | 4 MB |
g++ | random_04 | AC | 181 ms | 4 MB |
clang++ | example_00 | AC | 45 ms | 4 MB |
clang++ | example_01 | AC | 38 ms | 4 MB |
clang++ | hack0_00 | AC | 186 ms | 4 MB |
clang++ | handmade_00 | AC | 54 ms | 4 MB |
clang++ | many_maximals_00 | AC | 186 ms | 4 MB |
clang++ | max_random_00 | AC | 186 ms | 4 MB |
clang++ | max_random_01 | AC | 189 ms | 4 MB |
clang++ | max_random_02 | AC | 186 ms | 4 MB |
clang++ | max_random_03 | AC | 186 ms | 4 MB |
clang++ | max_random_04 | AC | 188 ms | 4 MB |
clang++ | one_two_00 | AC | 186 ms | 4 MB |
clang++ | random_00 | AC | 156 ms | 4 MB |
clang++ | random_01 | AC | 36 ms | 4 MB |
clang++ | random_02 | AC | 120 ms | 4 MB |
clang++ | random_03 | AC | 10 ms | 4 MB |
clang++ | random_04 | AC | 103 ms | 4 MB |