結果

問題 No.184 たのしい排他的論理和(HARD)
ユーザー KowerKoint2010KowerKoint2010
提出日時 2022-03-03 09:57:33
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 435 ms / 5,000 ms
コード長 14,418 bytes
コンパイル時間 2,709 ms
コンパイル使用メモリ 211,740 KB
実行使用メモリ 75,588 KB
最終ジャッジ日時 2024-07-17 06:56:15
合計ジャッジ時間 12,257 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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 1 ms
6,944 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
6,944 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 302 ms
54,572 KB
testcase_09 AC 62 ms
13,952 KB
testcase_10 AC 229 ms
42,360 KB
testcase_11 AC 161 ms
31,232 KB
testcase_12 AC 353 ms
62,856 KB
testcase_13 AC 391 ms
67,944 KB
testcase_14 AC 222 ms
40,064 KB
testcase_15 AC 426 ms
73,272 KB
testcase_16 AC 350 ms
61,588 KB
testcase_17 AC 374 ms
66,036 KB
testcase_18 AC 2 ms
6,940 KB
testcase_19 AC 2 ms
6,940 KB
testcase_20 AC 104 ms
75,588 KB
testcase_21 AC 433 ms
75,584 KB
testcase_22 AC 433 ms
75,584 KB
testcase_23 AC 2 ms
6,940 KB
testcase_24 AC 2 ms
6,940 KB
testcase_25 AC 2 ms
6,944 KB
testcase_26 AC 2 ms
6,944 KB
testcase_27 AC 2 ms
6,940 KB
testcase_28 AC 251 ms
46,820 KB
testcase_29 AC 363 ms
65,020 KB
testcase_30 AC 316 ms
57,888 KB
testcase_31 AC 268 ms
50,508 KB
testcase_32 AC 338 ms
62,132 KB
testcase_33 AC 435 ms
73,424 KB
testcase_34 AC 421 ms
72,660 KB
testcase_35 AC 431 ms
74,952 KB
testcase_36 AC 430 ms
74,688 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 # 

#line 2 "library/KowerKoint/template.cpp"

#ifndef ONLINE_JUDGE
#define _GLIBCXX_DEBUG
#endif

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

#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, a, b) for(ll i = a; i < (ll)(b); i++)
#define ALL(a) (a).begin(),(a).end()
#define END(...) { print(__VA_ARGS__); return; }

#ifdef ONLINE_JUDGE
#define DBG(...) {}
#else
#define DBG(a) { cerr << #a << ": "; dbg(a); }
#endif

using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using ll = long long;
using VL = vector<ll>;
using VVL = vector<VL>;
using VVVL = vector<VVL>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
using VS = vector<string>;
using VVS = vector<VS>;
using VVVS = vector<VVS>;
using VC = vector<char>;
using VVC = vector<VC>;
using VVVC = vector<VVC>;
using P = pair<int, int>;
using VP = vector<P>;
using VVP = vector<VP>;
using VVVP = vector<VVP>;
using LP = pair<ll, ll>;
using VLP = vector<LP>;
using VVLP = vector<VLP>;
using VVVLP = vector<VVLP>;

template <typename T>
using PQ = priority_queue<T>;
template <typename T>
using GPQ = priority_queue<T, vector<T>, greater<T>>;

constexpr int INF = 1001001001;
constexpr ll LINF = 1001001001001001001ll;
constexpr int DX[] = {1, 0, -1, 0};
constexpr int DY[] = {0, 1, 0, -1};

#ifdef aclmodint

using MI7 = modint1000000007;
using V7 = vector<MI7>;
using VV7 = vector<V7>;
using VVV7 = vector<VV7>;
using MI3 = modint998244353;
using V3 = vector<MI3>;
using VV3 = vector<V3>;
using VVV3 = vector<VV3>;

ostream &operator<<(ostream &os, const modint &x) {
    os << x.val();
    return os;
}

ostream &operator<<(ostream &os, const MI3 &x) {
    os << x.val();
    return os;
}

ostream &operator<<(ostream &os, const MI7 &x) {
    os << x.val();
    return os;
}

istream &operator>>(istream &is, modint &x) {
    int y; is >> y;
    x = y;
    return is;
}

istream &operator>>(istream &is, MI3 &x) {
    int y; is >> y;
    x = y;
    return is;
}

istream &operator>>(istream &is, MI7 &x) {
    int y; is >> y;
    x = y;
    return is;
}

#endif

void print() { cout << '\n'; }
template<typename T>
void print(const T &t) { cout << t << '\n'; }
template<typename Head, typename... Tail>
void print(const Head &head, const Tail &... tail) {
    cout << head << ' ';
    print(tail...);
}

#ifdef ONLINE_JUDGE
template<typename... Args>
void dbg(const Args &... args) {}
#else
void dbg() { cerr << '\n'; }
template<typename T>
void dbg(const T &t) { cerr << t << '\n'; }
template<typename Head, typename... Tail>
void dbg(const Head &head, const Tail &... tail) {
    cerr << head << ' ';
    dbg(tail...);
}
#endif

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 != (int) 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>
pair<VI, vector<T>> compress(const vector<T> &a) {
    int n = a.size();
    vector<T> x;
    REP(i, n) x.push_back(a[i]);
    sort(ALL(x)); x.erase(unique(ALL(x)), x.end());
    VI res(n);
    REP(i, n) res[i] = lower_bound(ALL(x), a[i]) - x.begin();
    return make_pair(res, x);
}

template <typename T>
pair<vector<T>, vector<T>> factorial(int n) {
    vector<T> res(n+1), rev(n+1);
    res[0] = 1;
    REP(i, n) res[i+1] = res[i] * (i+1);
    rev[n] = 1 / res[n];
    for(int i = n; i > 0; i--) {
        rev[i-1] = rev[i] * i;
    }
    return make_pair(res, rev);
}

#ifdef aclsegtree

template<typename S>
struct value_size { S value; int size; };

template<typename S>
S min_op(S l, S r) { return min(l, r); };
template<typename S>
S max_op(S l, S r) { return max(l, r); };
template<typename S>
S sum_op(S l, S r) { return l + r; };
template<typename S>
value_size<S> sum_op_size(value_size<S> l, value_size<S> r) {
    return {l.value + r.value, l.size + r.size};
};

template<typename S>
S min_e() { return  numeric_limits<S>::max(); };
template<typename S>
S max_e() { return numeric_limits<S>::min(); };
template<typename S>
S sum_e() { return 0; }
template<typename S>
value_size<S> sum_e_size() { return {0, 0}; }
template<typename S>
value_size<S> min_e_size() { return {numeric_limits<S>::max(), 0}; }
template<typename S>
value_size<S> max_e_size() { return {numeric_limits<S>::min(), 0}; }

template<typename S, typename F>
S chmin_mapping(F f, S x) { return min(x, f); }
template<typename S, typename F>
S chmax_mapping(F f, S x) { return max(x, f); }
template<typename S, typename F>
S add_mapping(F f, S x) { return x + f; }
template<typename S, typename F>
value_size<S> add_mapping_size(F f, value_size<S> x) {
    return {x.value + x.size * f, x.size};
}
template <typename S,typename F, F ID>
S change_mapping(F f, S x) { return (f == ID? x : f); }
template <typename S,typename F, F ID>
value_size<S> change_mapping_size(F f, value_size<S> x) { 
    value_size<S> ret = {f * x.size, x.size};
    return (f == ID? x : ret); 
}
template <typename S, typename F1, typename F2>
S linear_mapping(pair<F1, F2> f, S x) { return x * f.first + f.second; }
template <typename S, typename F1, typename F2>
value_size<S> linear_mapping_size(pair<F1, F2> f, value_size<S> x) { return {x.value * f.first + x.size * f.second, x.size}; }

template<typename F>
F chmin_composition(F f, F g) { return min(f, g); }
template<typename F>
F chmax_composition(F f, F g) { return max(f, g); }
template<typename F>
F add_composition(F f, F g) { return f + g; }
template <typename F, F ID>
F change_composition(F f, F g) { return (f == ID? g : f); }
template<typename F1, typename F2>
pair<F1, F2> linear_composition(pair<F1, F2> f, pair<F1, F2> g) { return {f.first * g.first, f.first * g.second + f.second}; }

template<typename F>
F chmin_id() { return numeric_limits<F>::max(); }
template<typename F>
F chmax_id() { return numeric_limits<F>::min(); }
template<typename F>
F add_id() { return 0; }
template<typename F, F ID>
F change_id() { return ID; }
template<typename F1, typename F2>
pair<F1, F2> linear_id() { return {1, 0}; }

template<typename S>
using RSumQ = segtree<S, sum_op<S>, sum_e<S>>;
template<typename S>
using RMaxQ = segtree<S, max_op<S>, max_e<S>>;
template<typename S>
using RMinQ = segtree<S, min_op<S>, min_e<S>>;

template<typename S, typename F>
using RAddSumQ = lazy_segtree<value_size<S>, sum_op_size<S>, sum_e_size<S>,
    F, add_mapping_size<S, F>, add_composition<F>, add_id<F>>;
template<typename S, typename F>
using RAddMinQ = lazy_segtree<S, min_op<S>, min_e<S>,
    F, add_mapping<S, F>, add_composition<F>, add_id<F>>;
template<typename S, typename F>
using RAddMaxQ = lazy_segtree<S, max_op<S>, max_e<S>,
    F, add_mapping<S, F>, add_composition<F>, add_id<F>>;
template<typename S, typename F>
using RMinMinQ = lazy_segtree<S, min_op<S>, min_e<S>,
    F, chmin_mapping<S, F>, chmin_composition<F>, chmin_id<F>>;
template<typename S, typename F>
using RMaxMaxQ = lazy_segtree<S, max_op<S>, max_e<S>,
    F, chmax_mapping<S, F>, chmax_composition<F>, chmax_id<F>>;
template<typename S, typename F, F ID>
using RChangeMinQ = lazy_segtree<S, min_op<S>, min_e<S>,
    F, change_mapping<S, F, ID>,
    change_composition<F, ID>,
    change_id<F, ID>>;
template<typename S, typename F, F ID>
using RChangeMaxQ = lazy_segtree<S, max_op<S>, max_e<S>,
    F, change_mapping<S, F, ID>,
    change_composition<F, ID>,
    change_id<F, ID>>;
template<typename S, typename F, F ID>
using RChangeSumQ = lazy_segtree<value_size<S>, sum_op_size<S>, sum_e_size<S>,
    F, change_mapping_size<S, F, ID>,
    change_composition<F, ID>,
    change_id<F, ID>>;
template<typename S, typename F1, typename F2>
using RLinearMinQ = lazy_segtree<S, min_op<S>, min_e<S>,
    pair<F1, F2>, linear_mapping<S, F1, F2>,
    linear_composition<F1, F2>,
    linear_id<F1, F2>>;
template<typename S, typename F1, typename F2>
using RLinearMaxQ = lazy_segtree<S, max_op<S>, max_e<S>,
    pair<F1, F2>, linear_mapping<S, F1, F2>,
    linear_composition<F1, F2>,
    linear_id<F1, F2>>;
template<typename S, typename F1, typename F2>
using RLinearSumQ = lazy_segtree<value_size<S>, sum_op_size<S>, sum_e_size<S>,
    pair<F1, F2>, linear_mapping_size<S, F1, F2>,
    linear_composition<F1, F2>,
    linear_id<F1, F2>>;
#endif
#line 1 "library/KowerKoint/internal_operator.hpp"
namespace internal_operator {
    template <typename T>
    T default_add(T a, T b) { return a + b; }
    template <typename T>
    T default_sub(T a, T b) { return a - b; }
    template <typename T>
    T zero() { return T(0); }
    template <typename T>
    T default_div(T a, T b) { return a / b; }
    template <typename T>
    T default_mult(T a, T b) { return a * b; }
    template <typename T>
    T one() { return T(1); }
    template <typename T>
    T default_xor(T a, T b) { return a ^ b; }
    template <typename T>
    T default_and(T a, T b) { return a & b; }
    template <typename T>
    T default_or(T a, T b) { return a | b; }
}

#line 4 "library/KowerKoint/math/matrix.hpp"

template <
    typename T,
    T (*add)(T, T)=internal_operator::default_add,
    T (*zero)()=internal_operator::zero,
    T (*mult)(T, T)=internal_operator::default_mult,
    T (*one)()=internal_operator::one,
    T (*sub)(T, T)=internal_operator::default_sub,
    T (*div)(T, T)=internal_operator::default_div
>
struct Matrix {
    vector<vector<T>> A;

    Matrix(size_t n, size_t m) : A(n, vector<T>(m, zero())) {}

    size_t height() const { return A.size(); }
    size_t width() const { return A[0].size(); }

    vector<T> &operator[](int i) { return A.at(i); }

    static Matrix I(size_t n) {
        Matrix ret(n, n);
        REP(i, n) ret[i][i] = one();
        return ret;
    }

    Matrix &operator+=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        REP(i, n) REP(j, m) A[i][j] = add(A[i][j], B[i][j]);
        return *this;
    }
    Matrix operator+(const Matrix &B) const {
        return (Matrix(*this) += B);
    }

    Matrix &operator-=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        REP(i, n) REP(j, m) A[i][j] = sub(A[i][j], B[i][j]);
        return *this;
    }
    Matrix operator-(const Matrix &B) const {
        return (Matrix(*this) -= B);
    }

    Matrix &operator*=(const Matrix &B) {
        size_t n = height(), m = width(), l = B.width();
        assert(m == B.height());
        vector<vector<T>> res(n, vector<T>(l, zero()));
        REP(i, n) REP(j, m) REP(k, l) res[i][k] = add(res[i][k], mult(A[i][j], B[j][k]));
        A.swap(res);
        return (*this);
    }
    Matrix operator*(const Matrix &B) const {
        return (Matrix(*this) *= B);
    }

    friend istream &operator>>(istream &is, Matrix &mat) {
        size_t n = mat.height(), m = mat.width();
        REP(i, n) REP(j, m) is >> mat[i][j];
        return is;
    }

    friend ostream &operator<<(ostream &os, Matrix &mat) {
        size_t n = mat.height(), m = mat.width();
        REP(i, n) {
            REP(j, m) os << mat[i][j] << (j==m-1? '\n' : ' ');
        }
        return os;
    }

    pair<Matrix, T> gaussian_elimination() const {
        int n = height(), m = width();
        Matrix mat(*this);
        T det = one();
        VI columns;
        int i = 0;
        int j = 0;
        while(i < n && j < m) {
            int idx = -1;
            FOR(k, i, n) if(mat[k][j] != zero()) idx = k;
            if(idx == -1) {
                det = zero();
                j++;
                continue;
            }
            if(i != idx) {
                det *= sub(zero(), one());
                swap(mat[i], mat[idx]);
            }
            det *= mat[i][j];
            T scale = mat[i][j];
            REP(l, m) mat[i][l] = div(mat[i][l], scale);
            FOR(k, i+1, n) {
                T scale = mat[k][j];
                REP(l, m) mat[k][l] = sub(mat[k][l], mult(mat[i][l], scale));
            }
            columns.push_back(j);
            i++;
            j++;
        }
        REP(i, columns.size()) {
            int j = columns[i];
            REP(k, i) {
                T scale = mat[k][j];
                FOR(l, j, m) {
                    mat[k][l] = sub(mat[k][l], mult(mat[i][l], scale));
                }
            }
        }
        return make_pair(mat, det);
    }

    Matrix inv() const {
        int n = height();
        Matrix and_i(n, n*2, zero());
        REP(i, n) REP(j, n) and_i[i][j] = A[i][j];
        REP(i, n) and_i[i][n+i] = one();
        auto& [i_and, det] = and_i.gaussian_elimination();
        assert(det != zero());
        Matrix res(n, n);
        REP(i, n) REP(j, n) res[i][j] = i_and[i][n+i];
        return res;
    }

    Matrix operator^=(ll n) {
        if(n < 0) {
            *this = this->inv();
            n = -n;
        }
        Matrix res = Matrix::I(height());
        while(n) {
            if(n & 1) res *= *this;
            *this *= *this;
            n >>= 1LL;
        }
        A.swap(res.A);
        return (*this);
    }
    Matrix operator^(const ll n) const {
        return (Matrix(*this) ^= n);
    }
};
#line 2 "library/KowerKoint/test/yukicoder-184/main.cpp"

int main(void) {
    int n; cin >> n;
    VL a(n); cin >> a;
    Matrix<
        int,
        internal_operator::default_xor<int>,
        internal_operator::zero<int>,
        internal_operator::default_and<int>,
        internal_operator::one<int>,
        internal_operator::default_xor<int>,
        internal_operator::default_and<int>
    > mat(61, n);
    REP(i, 61) REP(j, n) mat[i][j] = a[j] >> i & 1LL;
    auto basis = mat.gaussian_elimination().first;
    ll ans = 1;
    REP(i, 61) {
        REP(j, n) if(basis[i][j]) {
            ans <<= 1LL;
            break;
        }
    }
    print(ans);
}
0