結果

問題 No.2236 Lights Out On Simple Graph
ユーザー ecottea
提出日時 2023-03-03 22:44:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3,953 ms / 4,000 ms
コード長 9,931 bytes
コンパイル時間 4,988 ms
コンパイル使用メモリ 261,904 KB
最終ジャッジ日時 2025-02-11 03:30:25
ジャッジサーバーID
(参考情報)
judge5 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 57
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ソースコード

diff #
プレゼンテーションモードにする

#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
const vi DX = { 1, 0, -1, 0 }; // 4
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004004004004004LL;
double EPS = 1e-12;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // mod
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
//
template <class T> inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
// Visual Studio
#ifdef _MSC_VER
#include "local.hpp"
// gcc
#else
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_list2D(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
using mint = modint1000000007;
//using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);
istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>;
#endif
//
/*
*
*
* Bit_matrix<N>(int m, int n) : O(m N / 64)
* m * n
* n <= N
*
* Bit_matrix<N>(int n) : O(n N / 64)
* n * n
*
* Bit_matrix<N>(vector<bitset<N>> a, int n) : O(m N / 64)
* a
*
* Bit_matrix<N>(vi[vl] a, int n) : O(m N / 64)
* a[i] j v[i][j]
*
* push_back(bitset<N> col) : O(N / 64)
* col
*
* A * x : O(m N / 64)
* m * n A n x
* m <= N
*
* A * B : O(l m n)
* l * m A m * n B
*
* Bit_matrix<N> pow(ll d) : O(n^3 log d)
* d
*
* Bit_matrix<N> transpose() : O(m n)
* N
*/
template <int N>
struct Bit_matrix {
int m, n; // , m * n
vector<bitset<N>> v; //
//
Bit_matrix() : m(0), n(0) {}
Bit_matrix(int m, int n) : m(m), n(n), v(m) {}
Bit_matrix(int n) : m(n), n(n), v(m) { rep(i, n) v[i][i] = 1; }
Bit_matrix(const vector<bitset<N>>& a, int n) : m(sz(a)), n(n), v(a) {}
Bit_matrix(const vi& a, int n) : m(sz(a)), n(n), v(m) { rep(i, m) v[i] = bitset<N>(a[i]); }
Bit_matrix(const vl& a, int n) : m(sz(a)), n(n), v(m) { rep(i, m) v[i] = bitset<N>(a[i]); }
//
Bit_matrix(const Bit_matrix& old) = default;
Bit_matrix& operator=(const Bit_matrix& other) = default;
//
bool operator==(const Bit_matrix& g) const { return m == g.m && n == g.n && v == g.v; }
bool operator!=(const Bit_matrix& g) const { return !(*this == g); }
//
bitset<N> const& operator[](int i) const { return v[i]; }
bitset<N>& operator[](int i) { return v[i]; }
//
void push_back(const bitset<N>& col) { v.push_back(col); m++; }
//
bitset<N> operator*(const bitset<N>& x) const {
bitset<N> y;
rep(i, m) y[i] = (v[i] & x).count() % 2;
return y;
}
//
Bit_matrix operator*(const Bit_matrix& b) const {
Bit_matrix res(m, b.n);
rep(i, res.m) rep(j, res.n) rep(k, n) res[i][j] = res[i][j] ^ (v[i][k] & b[k][j]);
return res;
}
Bit_matrix& operator*=(const Bit_matrix& b) { *this = *this * b; return *this; }
//
Bit_matrix pow(ll d) const {
Bit_matrix res(n), pow2 = *this;
while (d > 0) {
if ((d & 1) != 0) res *= pow2;
pow2 *= pow2;
d /= 2;
}
return res;
}
// A^T
Bit_matrix transpose() const {
Bit_matrix res(n, m);
rep(i, res.m) rep(j, res.n) res[i][j] = v[j][i];
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Bit_matrix& a) {
rep(i, a.m) {
os << "[";
rep(j, a.n) os << a.v[i][j] << (j < a.n - 1 ? " " : "]");
if (i < a.m - 1) os << "\n";
}
return os;
}
#endif
};
mt19937_64 mt;
vi p, q;
//O(m n min(m, n) / 64)
/*
* m×(n+1) mat 1 sol
* false
*
* solve_eq<N> gcc
*/
template <int N>
bool solve_eq(Bit_matrix<N>& mat, bitset<N>* sol = nullptr) {
// verify : https://onlinejudge.u-aizu.ac.jp/problems/1308
int m = mat.m, n = mat.n - 1;
auto& v = mat.v;
shuffle(all(p), mt);
shuffle(q.begin(), q.begin() + n, mt);
//
vector<pii> pivots;
//
list<int> rmd;
repi(j, 0, n) rmd.push_back(j);
rep(i, m) {
// i 1
auto it = rmd.begin();
for (; it != rmd.end(); it++) {
if (v[p[i]][q[*it]] == 1) break;
}
// 0
if (it == rmd.end()) continue;
int j = *it;
rmd.erase(it);
// 1
if (j == n) return false;
// j j 1 XOR
pivots.push_back({ i, j });
rep(i2, m) {
if (v[p[i2]][q[j]] && i2 != i) v[p[i2]] ^= v[p[i]];
}
}
//
if (sol != nullptr) {
sol->reset();
repe(pv, pivots) {
(*sol)[pv.second] = v[p[pv.first]][q[n]];
}
}
return true;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
auto start = chrono::system_clock::now();
mt = mt19937_64((int)time(NULL));
int n, m;
cin >> n >> m;
p.resize(n); iota(all(p), 0);
q.resize(m + 1); iota(all(q), 0);
const int N = 64;
Bit_matrix<N> mat0(n, m + 1);
rep(i, m) {
int a, b;
cin >> a >> b;
a--; b--;
mat0[a][i] = 1;
mat0[b][i] = 1;
}
rep(i, n) {
int c;
cin >> c;
mat0[i][m] = c;
}
dump(mat0);
int res = INF;
while (1) {
Bit_matrix<N> mat(mat0);
bitset<N> sol;
bool ex = solve_eq<N>(mat, &sol);
dump(sol);
if (!ex) EXIT(-1);
chmin(res, (int)sol.count());
auto now = chrono::system_clock::now();
auto msec = chrono::duration_cast<std::chrono::milliseconds>(now - start).count();
if (msec >= 3950) break;
}
cout << res << endl;
}
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