結果

問題 No.803 Very Limited Xor Subset
ユーザー pazzle1230pazzle1230
提出日時 2019-04-05 20:35:43
言語 C++14
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 6,407 bytes
コンパイル時間 1,584 ms
コンパイル使用メモリ 172,088 KB
実行使用メモリ 4,384 KB
最終ジャッジ日時 2023-09-03 23:20:39
合計ジャッジ時間 3,535 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge14
このコードへのチャレンジ（β）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
4,380 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 AC 1 ms
4,380 KB
testcase_03 AC 1 ms
4,380 KB
testcase_04 AC 1 ms
4,376 KB
testcase_05 AC 1 ms
4,376 KB
testcase_06 AC 2 ms
4,380 KB
testcase_07 AC 2 ms
4,380 KB
testcase_08 AC 2 ms
4,384 KB
testcase_09 AC 2 ms
4,380 KB
testcase_10 AC 2 ms
4,376 KB
testcase_11 AC 1 ms
4,380 KB
testcase_12 AC 2 ms
4,380 KB
testcase_13 AC 2 ms
4,376 KB
testcase_14 AC 2 ms
4,380 KB
testcase_15 AC 2 ms
4,376 KB
testcase_16 AC 2 ms
4,376 KB
testcase_17 AC 2 ms
4,380 KB
testcase_18 AC 2 ms
4,384 KB
testcase_19 AC 3 ms
4,376 KB
testcase_20 AC 2 ms
4,384 KB
testcase_21 AC 3 ms
4,380 KB
testcase_22 AC 2 ms
4,380 KB
testcase_23 AC 2 ms
4,380 KB
testcase_24 AC 2 ms
4,376 KB
testcase_25 AC 2 ms
4,380 KB
testcase_26 AC 3 ms
4,384 KB
testcase_27 AC 3 ms
4,376 KB
testcase_28 AC 3 ms
4,380 KB
testcase_29 AC 2 ms
4,380 KB
testcase_30 AC 3 ms
4,380 KB
testcase_31 AC 2 ms
4,376 KB
testcase_32 AC 2 ms
4,384 KB
testcase_33 AC 3 ms
4,376 KB
testcase_34 AC 2 ms
4,380 KB
testcase_35 AC 2 ms
4,384 KB
testcase_36 AC 2 ms
4,376 KB
testcase_37 AC 2 ms
4,384 KB
testcase_38 AC 2 ms
4,380 KB
testcase_39 AC 2 ms
4,384 KB
testcase_40 AC 3 ms
4,380 KB
testcase_41 AC 2 ms
4,380 KB
testcase_42 AC 3 ms
4,376 KB
testcase_43 AC 2 ms
4,376 KB
testcase_44 AC 1 ms
4,376 KB
testcase_45 AC 1 ms
4,376 KB
testcase_46 AC 2 ms
4,380 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

#define INF_LL (int64)1e18
#define INF (int32)1e9
#define REP(i, n) for(int64 i = 0;i < (n);i++)
#define FOR(i, a, b) for(int64 i = (a);i < (b);i++)
#define all(x) x.begin(),x.end()
#define fs first
#define sc second

using int32 = int_fast32_t;
using uint32 = uint_fast32_t;
using int64 = int_fast64_t;
using uint64 = uint_fast64_t;
using PII = pair<int32, int32>;
using PLL = pair<int64, int64>;

const double eps = 1e-10;

template<typename A, typename B>inline void chmin(A &a, B b){if(a > b) a = b;}
template<typename A, typename B>inline void chmax(A &a, B b){if(a < b) a = b;}

template<typename T>
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 U,typename... V>
typename enable_if<is_same<T, U>::value!=0>::type
fill_v(U &u,const V... v){u=U(v...);}

template<typename T,typename U,typename... V>
typename enable_if<is_same<T, U>::value==0>::type
fill_v(U &u,const V... v){
  for(auto &e:u) fill_v<T>(e,v...);
}

template<::std::size_t Column>
class BinaryMatrix {
public:
	using size_type = ::std::size_t;
	using value_type = ::std::uint64_t;
	using Row = ::std::bitset<Column>;
	using Mat = ::std::vector<Row>;

private:
	size_type R, C;
	Mat A;

	void add_row_to_another(size_type r1, size_type r2){ // Row(r1) += Row(r2)
		A[r1] = A[r1] ^ A[r2];
	}


public:
	BinaryMatrix() {}
	BinaryMatrix(size_type R_, size_type C_) : R(R_), C(C_), A(Mat(R_)) {}
	BinaryMatrix(const Mat& A_) : R(A_.size()), C(A_[0].size()), A(A_) {}
	BinaryMatrix(const Mat&& A_) : R(A_.size()), C(A_[0].size()), A(A_) {}
	BinaryMatrix(const BinaryMatrix& m) : R(m.R), C(m.C), A(m.A) {}
	BinaryMatrix(const BinaryMatrix&& m) : R(m.R), C(m.C), A(m.A) {}

	BinaryMatrix &operator=(const BinaryMatrix &m){
 		R = m.R; C = m.C; A = m.A;
		return *this;
	}
	BinaryMatrix &operator=(const BinaryMatrix &&m){
 		R = m.R; C = m.C; A = m.A;
		return *this;
	}
	static BinaryMatrix I(const size_type N){
		BinaryMatrix m(N, N);
		for(size_type i = 0;i < N;i++) m[i][i] = 1;
		return m;
	}

	const Row& operator[](size_type k) const& { return A.at(k); }
	Row& operator[](size_type k) & { return A.at(k); }
	Row operator[](size_type k) const&& { return ::std::move(A.at(k)); }

	size_type row() const { return R; } // the number of rows
	size_type column() const { return C; }

	BinaryMatrix& operator+=(const BinaryMatrix &B){
		assert(column() == B.column() && row() == B.row());
		for(size_type i = 0;i < R;i++)
			(*this)[i] ^= B[i];
		return *this;
	}

	BinaryMatrix& operator-=(const BinaryMatrix &B){
		assert(column() == B.column() && row() == B.row());
		for(size_type i = 0;i < R;i++)
			(*this)[i] ^= B[i];
		return *this;
	}

	BinaryMatrix& operator*=(const BinaryMatrix &B){
		assert(column() == B.row());
		BinaryMatrix M(R, B.column());
		for(size_type i = 0;i < R;i++) {
			for(size_type j = 0;j < B.column();j++) {
				M[i][j] = 0;
				for(size_type k = 0;k < C;k++) {
					M[i][j] ^= ((*this)[i][k] & B[k][j]);
				}
			}
		}
		swap(M, *this);
		return *this;
	}

	void gaussian_elimination() {
		size_type last_row = 0;
		for (size_type i = 0; i < C && last_row < R; i++) {
			for (size_type j = last_row; j < R; j++) {
				if (A[j][i]) {
					swap(A[j], A[last_row]);
					break;
				}
			}

			for (size_type j = 0; j < R; j++) {
				if (last_row == j) continue;
				if (A[last_row][i] & A[j][i]) {
					add_row_to_another(j, last_row);
				}
			}
			if (A[last_row][i]) last_row++;
		}
	}

	size_type rank() {
		Mat tmp = A;
		gaussian_elimination();
		swap(tmp, A);
		for (size_type i = 0; i < R; i++) {
			size_type cnt = 0;
			for (size_type j = 0; j < C; j++) {
				if (tmp[i][j]) cnt++;
			}
			if (cnt == 0) return i;
		}
		return R;
	}
};

template<::std::uint_fast64_t mod>
class ModInt{
private:
	using value_type = ::std::uint_fast64_t;
	value_type n;
public:
	ModInt() : n(0) {}
	ModInt(value_type n_) : n(n_ % mod) {}
	ModInt(const ModInt& m) : n(m.n) {}

	template<typename T>
	explicit operator T() const { return static_cast<T>(n); }
	value_type get() const { return n; }

	friend ::std::ostream& operator<<(::std::ostream &os, const ModInt<mod> &a) {
		return os << a.n;
	}

	friend ::std::istream& operator>>(::std::istream &is, ModInt<mod> &a) {
		value_type x;
		is >> x;
		a = ModInt<mod>(x);
		return is;
	}

	bool operator==(const ModInt& m) const { return n == m.n; }
	bool operator!=(const ModInt& m) const { return n != m.n; }
	ModInt& operator*=(const ModInt& m){ n = n * m.n % mod; return *this; }

	ModInt pow(value_type b) const{
		ModInt ans = 1, m = ModInt(*this);
		while(b){
			if(b & 1) ans *= m;
			m *= m;
			b >>= 1;
		}
		return ans;
	}

	ModInt inv() const { return (*this).pow(mod-2); }
	ModInt& operator+=(const ModInt& m){ n += m.n; n = (n < mod ? n : n - mod); return *this; }
	ModInt& operator-=(const ModInt& m){ n += mod - m.n; n = (n < mod ? n : n - mod); return *this; }
	ModInt& operator/=(const ModInt& m){ *this *= m.inv(); return *this; }
	ModInt operator+(const ModInt& m) const { return ModInt(*this) += m; }
	ModInt operator-(const ModInt& m) const { return ModInt(*this) -= m; }
	ModInt operator*(const ModInt& m) const { return ModInt(*this) *= m; }
	ModInt operator/(const ModInt& m) const { return ModInt(*this) /= m; }
	ModInt& operator++(){ n += 1; return *this; }
	ModInt& operator--(){ n -= 1; return *this; }
	ModInt operator++(int){
		ModInt old(n);
		n += 1;
		return old;
	}
	ModInt operator--(int){
		ModInt old(n);
		n -= 1;
		return old;
	}
	ModInt operator-() const { return ModInt(mod-n); }
};

const int64 mod = 1e9+7;

int main(void){
	cin.tie(0);
	ios::sync_with_stdio(false);
	int64 N, M, X;
	bitset<360> to, now;
	cin >> N >> M >> X;
	BinaryMatrix<360> bm(N, 60+M);
	REP(i, 60) {
		if (X >> i & 1) to[i] = 1;
	}
	REP(i, N) {
		int64 A;
		cin >> A;
		REP(j, 60)
			if (A >> j & 1) bm[i][j] = 1;
	}

	REP(i, M) {
		int64 t, l, r;
		cin >> t >> l >> r;
		FOR(j, l-1, r) {
			bm[j][i+60] = 1;
		}
		to[i+60] = t;
	}
	bm.gaussian_elimination();
	REP(i, N) {
		REP(j, 360) {
			if (now[j] == to[j] && bm[i][j]) break;
			if (now[j] != to[j] && bm[i][j]) {
				now ^= bm[i];
				break;
			}
		}
	}
	if (now != to) {
		cout << 0 << endl;
	} else {
		ModInt<mod> res = 2;
		res = res.pow(N-bm.rank());
		cout << res << endl;
	}
}
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