結果

問題 No.803 Very Limited Xor Subset
ユーザー pazzle1230
提出日時 2019-04-05 20:35:43
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4 ms / 2,000 ms
コード長 6,407 bytes
コンパイル時間 2,255 ms
コンパイル使用メモリ 173,320 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-06-13 03:53:10
合計ジャッジ時間 3,350 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 43
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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

#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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