#581306 (C++17) No.803 Very Limited Xor Subset

提出ソース

結果

問題	No.803 Very Limited Xor Subset
ユーザー	minato
提出日時	2020-11-19 20:58:12
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	3 ms / 2,000 ms
コード長	9,727 bytes
コンパイル時間	3,774 ms
コンパイル使用メモリ	232,676 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-23 11:47:28
合計ジャッジ時間	5,218 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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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 6,812 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,944 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	1 ms 6,940 KB
testcase_11	AC	2 ms 6,940 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	2 ms 6,940 KB
testcase_14	AC	3 ms 6,944 KB
testcase_15	AC	2 ms 6,940 KB
testcase_16	AC	3 ms 6,944 KB
testcase_17	AC	2 ms 6,940 KB
testcase_18	AC	2 ms 6,940 KB
testcase_19	AC	2 ms 6,940 KB
testcase_20	AC	2 ms 6,944 KB
testcase_21	AC	2 ms 6,944 KB
testcase_22	AC	2 ms 6,940 KB
testcase_23	AC	3 ms 6,944 KB
testcase_24	AC	3 ms 6,940 KB
testcase_25	AC	3 ms 6,940 KB
testcase_26	AC	3 ms 6,944 KB
testcase_27	AC	2 ms 6,944 KB
testcase_28	AC	2 ms 6,944 KB
testcase_29	AC	2 ms 6,940 KB
testcase_30	AC	2 ms 6,940 KB
testcase_31	AC	3 ms 6,940 KB
testcase_32	AC	3 ms 6,940 KB
testcase_33	AC	3 ms 6,940 KB
testcase_34	AC	2 ms 6,940 KB
testcase_35	AC	3 ms 6,944 KB
testcase_36	AC	2 ms 6,940 KB
testcase_37	AC	2 ms 6,944 KB
testcase_38	AC	2 ms 6,940 KB
testcase_39	AC	2 ms 6,940 KB
testcase_40	AC	2 ms 6,944 KB
testcase_41	AC	2 ms 6,940 KB
testcase_42	AC	2 ms 6,940 KB
testcase_43	AC	3 ms 6,944 KB
testcase_44	AC	2 ms 6,944 KB
testcase_45	AC	2 ms 6,940 KB
testcase_46	AC	2 ms 6,940 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

raw source code

#ifdef ONLINE_JUDGE
#pragma GCC target("avx2,avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rrep(i, n) for (int i = int(n) - 1; i >= 0; i--)
#define all(x) (x).begin(), (x).end()
constexpr char ln = '\n';
istream& operator>>(istream& is, __int128_t& x) {
    x = 0;
    string s;
    is >> s;
    int n = int(s.size()), it = 0;
    if (s[0] == '-') it++;
    for (; it < n; it++) x = (x * 10 + s[it] - '0');
    if (s[0] == '-') x = -x;
    return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    deque<int> deq;
    while (x) deq.emplace_front(x % 10), x /= 10;
    for (int e : deq) os << e;
    return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
    return os << "(" << p.first << ", " << p.second << ")";
}
template<class T> 
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    for (int i = 0; i < int(v.size()); i++) {
        if (i) os << ", ";
        os << v[i];
    }
    return os << "}";
}
template<class Container> inline int SZ(Container& v) { return int(v.size()); }
template<class T> inline void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template<class T1, class T2> inline bool chmax(T1& a, T2 b) { if (a < b) {a = b; return true ;} return false ;}
template<class T1, class T2> inline bool chmin(T1& a, T2 b) { if (a > b) {a = b; return true ;} return false ;}
inline int topbit(int x) { return x == 0 ? -1 : 31 - __builtin_clz(x); }
inline int topbit(long long x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
inline int botbit(int x) { return x == 0 ? 32 : __builtin_ctz(x); }
inline int botbit(long long x) { return x == 0 ? 64 : __builtin_ctzll(x); }
inline int popcount(int x) { return __builtin_popcount(x); }
inline int popcount(long long x) { return __builtin_popcountll(x); }
inline int kthbit(long long x, int k) { return (x>>k) & 1; }
inline constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x-1) * 10; }
inline void print() { cout << "\n"; }
template<class T>
inline void print(const vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        if (i) cout << " ";
        cout << v[i];
    }
    print();
}
template<class T, class... Args>
inline void print(const T& x, const Args& ... args) {
    cout << x << " ";
    print(args...);
}
#ifdef MINATO_LOCAL
inline void debug_out() { cerr << endl; }
template <class T, class... Args>
inline void debug_out(const T& x, const Args& ... args) {
    cerr << " " << x;
    debug_out(args...);
}
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

template<int m> 
struct ModInt {
  public:
    static constexpr int mod() { return m; }
    static ModInt raw(int v) {
        ModInt x;
        x._v = v;
        return x;
    }

    ModInt() : _v(0) {}
    ModInt(long long v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }

    unsigned int val() const { return _v; }

    ModInt& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    ModInt& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    ModInt operator++(int) {
        ModInt result = *this;
        ++*this;
        return result;
    }
    ModInt operator--(int) {
        ModInt result = *this;
        --*this;
        return result;
    }

    ModInt& operator+=(const ModInt& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    ModInt& operator-=(const ModInt& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    ModInt& operator*=(const ModInt& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    ModInt& operator^=(long long n) {
        ModInt x = *this;
        *this = 1;
        if (n < 0) x = x.inv(), n = -n;
        while (n) {
            if (n & 1) *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }
    ModInt& operator/=(const ModInt& rhs) { return *this = *this * rhs.inv(); }

    ModInt operator+() const { return *this; }
    ModInt operator-() const { return ModInt() - *this; }

    ModInt pow(long long n) const {
        ModInt r = *this;
        r ^= n;
        return r;
    }
    ModInt inv() const {
        int a = _v, b = umod(), y = 1, z = 0, t;
        for (; ; ) {
            t = a / b; a -= t * b;
            if (a == 0) {
                assert(b == 1 || b == -1);
                return ModInt(b * z);
            }
            y -= t * z;
            t = b / a; b -= t * a;
            if (b == 0) {
                assert(a == 1 || a == -1);
                return ModInt(a * y);
            }
            z -= t * y;
        }
    }

    friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; }
    friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; }
    friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; }
    friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; }
    friend ModInt operator^(const ModInt& lhs, long long rhs) { return ModInt(lhs) ^= rhs; }
    friend bool operator==(const ModInt& lhs, const ModInt& rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) { return lhs._v != rhs._v; }
    friend ModInt operator+(long long lhs, const ModInt& rhs) { return (ModInt(lhs) += rhs); }
    friend ModInt operator-(long long lhs, const ModInt& rhs) { return (ModInt(lhs) -= rhs); }
    friend ModInt operator*(long long lhs, const ModInt& rhs) { return (ModInt(lhs) *= rhs); }
    friend ostream &operator<<(ostream& os, const ModInt& rhs) { return os << rhs._v; }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
};
 
constexpr int MOD = 1000000007;
//constexpr int MOD = 998244353;

using mint = ModInt<MOD>;

template<int MAX_COL>
struct BitMatrix {
    int N,M;
    vector<bitset<MAX_COL>> A;
    BitMatrix() {}
    BitMatrix(int N) : N(N), M(MAX_COL), A(N) {}
    BitMatrix(int N, int M) : N(N), M(M), A(N) {}

    const bitset<MAX_COL> &operator[](int k) const {return A[k];}
    bitset<MAX_COL> &operator[](int k) {return A[k];}

    void clear() {
        for (int i = 0; i < N; i++) A[i].clear();
    }

    // xor subset 最大化は掃き出し法で解ける
    // ex 集合{65,66} の部分和(和は xor ) は集合{65,65^66} の部分和と一致する
    // 各列について立っている bit を一つにしてどう集合から部分和を選ぶと和が最大になるか明らかにする
    int GaussJordan(int isextened = 0) {
        int rank = 0;
        //左の列から掃き出していく
        for (int col = 0; col < M - isextened; col++) {
            int pivot = -1;
            for (int row = rank; row < N; row++) {
                if (A[row][col]) {
                    pivot = row;
                    break;
                }
            }
            if (pivot == -1) continue;
            // 最も左の bit が対角に並んでいく
            swap(A[pivot], A[rank]);
            for (int row = 0; row < N; row++) {
                // pivot のある列の値がすべて 0 になるように掃き出す
                if (row != rank && A[row][col]) A[row] ^= A[rank];
            }
            rank++;
        }
        return rank;
    }
};

constexpr int COL = 301;

using BM = BitMatrix<COL>;

//連立一次方程式 Ax = b の解を求める
//解なしなら -1 ,そうでないなら rank を返す
//解の個数は M - rank
// O(N * M^2 / 64)
//N : タテ,式の個数, M : ヨコ,変数の個数
pair<int, vector<int>> linear_equation(const BM& A, const vector<int>& b) {
    int N = A.N;
    int M = A.M;
    assert(N == int(b.size()));
    BM mat(N,M+1);
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            mat[i][j] = A[i][j];
        }
        mat[i][M] = b[i];
    }
    
    int rank = mat.GaussJordan(1);
    for (int i = rank; i < N; i++) {
        if (mat[i][M]) return {-1, vector<int>{}};
    }
    vector<int> ret(M);
    for (int i = 0; i < rank; i++) ret[i] = mat[i][M];
    return {rank,ret};
};

int main() {
    int N,M,X; cin >> N >> M >> X;
    vector<int> A(N);
    rep(i,N) cin >> A[i];

    BM mat(30+M,N);
    vector<int> b(30+M);
    rep(k,30) {
        rep(i,N) if (kthbit(A[i],k)) mat[k][i] = 1;
        b[k] = kthbit(X,k); 
    }

    rep(i,M) {
        int t,l,r; cin >> t >> l >> r;
        l--;
        for (int j = l; j < r; j++) {
            mat[30+i][j] = 1;
        }
        b[30+i] = t;
    }
    auto[rank,ret] = linear_equation(mat,b);

    if (rank==-1) {
        cout << 0 << ln;
        return 0;
    }
    cout << mint(2).pow(N-rank) << ln;
}

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結果

テストケース

ソースコード