#936730 (C++23) No.2578 Jewelry Store

• 問題: No.2578 Jewelry Store
• ユーザー: hitonanode
• 提出日時: 2023-12-06 00:58:09
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 974 ms / 3,500 ms
• コード長: 5,401 bytes
• コンパイル時間: 1,726 ms
• コンパイル使用メモリ: 124,688 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-27 00:49:03
• 合計ジャッジ時間: 10,242 ms
• ジャッジサーバーID （参考情報）: judge2 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	8 ms; 5,376 KB
testcase_03	AC	6 ms; 5,376 KB
testcase_04	AC	23 ms; 5,376 KB
testcase_05	AC	6 ms; 5,376 KB
testcase_06	AC	9 ms; 5,376 KB
testcase_07	AC	23 ms; 5,376 KB
testcase_08	AC	6 ms; 5,376 KB
testcase_09	AC	23 ms; 5,376 KB
testcase_10	AC	43 ms; 5,376 KB
testcase_11	AC	6 ms; 5,376 KB
testcase_12	AC	6 ms; 5,376 KB
testcase_13	AC	5 ms; 5,376 KB
testcase_14	AC	6 ms; 5,376 KB
testcase_15	AC	5 ms; 5,376 KB
testcase_16	AC	43 ms; 5,376 KB
testcase_17	AC	22 ms; 5,376 KB
testcase_18	AC	5 ms; 5,376 KB
testcase_19	AC	14 ms; 5,376 KB
testcase_20	AC	23 ms; 5,376 KB
testcase_21	AC	23 ms; 5,376 KB
testcase_22	AC	8 ms; 5,376 KB
testcase_23	AC	14 ms; 5,376 KB
testcase_24	AC	7 ms; 5,376 KB
testcase_25	AC	9 ms; 5,376 KB
testcase_26	AC	8 ms; 5,376 KB
testcase_27	AC	158 ms; 5,376 KB
testcase_28	AC	232 ms; 5,376 KB
testcase_29	AC	221 ms; 5,376 KB
testcase_30	AC	271 ms; 5,376 KB
testcase_31	AC	171 ms; 5,376 KB
testcase_32	AC	110 ms; 5,376 KB
testcase_33	AC	140 ms; 5,376 KB
testcase_34	AC	175 ms; 5,376 KB
testcase_35	AC	44 ms; 5,376 KB
testcase_36	AC	150 ms; 5,376 KB
testcase_37	AC	79 ms; 5,376 KB
testcase_38	AC	98 ms; 5,376 KB
testcase_39	AC	90 ms; 5,376 KB
testcase_40	AC	95 ms; 5,376 KB
testcase_41	AC	85 ms; 5,376 KB
testcase_42	AC	78 ms; 5,376 KB
testcase_43	AC	125 ms; 5,376 KB
testcase_44	AC	72 ms; 5,376 KB
testcase_45	AC	107 ms; 5,376 KB
testcase_46	AC	84 ms; 5,376 KB
testcase_47	AC	496 ms; 5,376 KB
testcase_48	AC	215 ms; 5,376 KB
testcase_49	AC	974 ms; 5,376 KB
testcase_50	AC	906 ms; 5,376 KB
testcase_51	AC	87 ms; 5,376 KB
testcase_52	AC	303 ms; 5,376 KB
testcase_53	AC	37 ms; 5,376 KB

ソースコード

#include <iostream>
#include <vector>
using namespace std;


uint32_t rand_int() // XorShift random integer generator
{
    static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    uint32_t t = x ^ (x << 11);
    x = y;
    y = z;
    z = w;
    return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}
double rand_double() { return (double)rand_int() / UINT32_MAX; }


#include <algorithm>
#include <array>
#include <cassert>
#include <numeric>
#include <vector>

namespace SPRP {
// http://miller-rabin.appspot.com/
const std::vector<std::vector<__int128>> bases{
    {126401071349994536},                              // < 291831
    {336781006125, 9639812373923155},                  // < 1050535501 (1e9)
    {2, 2570940, 211991001, 3749873356},               // < 47636622961201 (4e13)
    {2, 325, 9375, 28178, 450775, 9780504, 1795265022} // <= 2^64
};
inline int get_id(long long n) {
    if (n < 291831) {
        return 0;
    } else if (n < 1050535501) {
        return 1;
    } else if (n < 47636622961201)
        return 2;
    else { return 3; }
}
} // namespace SPRP

// Miller-Rabin primality test
// https://ja.wikipedia.org/wiki/%E3%83%9F%E3%83%A9%E3%83%BC%E2%80%93%E3%83%A9%E3%83%93%E3%83%B3%E7%B4%A0%E6%95%B0%E5%88%A4%E5%AE%9A%E6%B3%95
// Complexity: O(lg n) per query
struct {
    long long modpow(__int128 x, __int128 n, long long mod) noexcept {
        __int128 ret = 1;
        for (x %= mod; n; x = x * x % mod, n >>= 1) ret = (n & 1) ? ret * x % mod : ret;
        return ret;
    }
    bool operator()(long long n) noexcept {
        if (n < 2) return false;
        if (n % 2 == 0) return n == 2;
        int s = __builtin_ctzll(n - 1);

        for (__int128 a : SPRP::bases[SPRP::get_id(n)]) {
            if (a % n == 0) continue;
            a = modpow(a, (n - 1) >> s, n);
            bool may_composite = true;
            if (a == 1) continue;
            for (int r = s; r--; a = a * a % n) {
                if (a == n - 1) may_composite = false;
            }
            if (may_composite) return false;
        }
        return true;
    }
} is_prime;

struct {
    // Pollard's rho algorithm: find factor greater than 1
    long long find_factor(long long n) {
        assert(n > 1);
        if (n % 2 == 0) return 2;
        if (is_prime(n)) return n;
        long long c = 1;
        auto f = [&](__int128 x) -> long long { return (x * x + c) % n; };

        for (int t = 1;; t++) {
            for (c = 0; c == 0 or c + 2 == n;) c = rand_int() % n;
            long long x0 = t, m = std::max(n >> 3, 1LL), x, ys, y = x0, r = 1, g, q = 1;
            do {
                x = y;
                for (int i = r; i--;) y = f(y);
                long long k = 0;
                do {
                    ys = y;
                    for (int i = std::min(m, r - k); i--;)
                        y = f(y), q = __int128(q) * std::abs(x - y) % n;
                    g = std::__gcd<long long>(q, n);
                    k += m;
                } while (k < r and g <= 1);
                r <<= 1;
            } while (g <= 1);
            if (g == n) {
                do {
                    ys = f(ys);
                    g = std::__gcd(std::abs(x - ys), n);
                } while (g <= 1);
            }
            if (g != n) return g;
        }
    }

    std::vector<long long> operator()(long long n) {
        std::vector<long long> ret;
        while (n > 1) {
            long long f = find_factor(n);
            if (f < n) {
                auto tmp = operator()(f);
                ret.insert(ret.end(), tmp.begin(), tmp.end());
            } else
                ret.push_back(n);
            n /= f;
        }
        std::sort(ret.begin(), ret.end());
        return ret;
    }
    long long euler_phi(long long n) {
        long long ret = 1, last = -1;
        for (auto p : this->operator()(n)) ret *= p - (last != p), last = p;
        return ret;
    }
} FactorizeLonglong;

#include <atcoder/modint>
using mint = atcoder::modint998244353;

long long m;
vector<pair<long long, int>> facs;

template <typename T, typename F> void abstract_fwht(std::vector<T> &seq, F f) {
    const int n = seq.size();
    assert(__builtin_popcount(n) == 1);
    for (int w = 1; w < n; w *= 2) {
        for (int i = 0; i < n; i += w * 2) {
            for (int j = 0; j < w; j++) { f(seq[i + j], seq[i + j + w]); }
        }
    }
}

mint solve() {
    int n, B, C, D;
    cin >> n >> B >> C >> D;

    vector<mint> dp(1 << facs.size(), 1);

    mint W = B;
    while (n--) {
        long long a;
        cin >> a;

        int S = 0;
        bool is_bad = false;
        for (auto [p, d] : facs) {
            S *= 2;
            while (d and a % p == 0) a /= p, --d;
            if (!d) ++S;
        }
        if (a > 1) is_bad = true;
        if (!is_bad) dp.at(S) *= W + 1;

        W = W * C + D;
    }

    abstract_fwht(dp, [](mint &lo, mint &hi) { hi *= lo; });
    abstract_fwht(dp, [](mint &lo, mint &hi) { hi -= lo; });

    return dp.back() - (m == 1);
}

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);

    int T;
    cin >> T >> m;

    auto factors = FactorizeLonglong(m);
    sort(factors.begin(), factors.end());

    for (auto p : factors) {
        if (facs.empty() or facs.back().first != p) facs.emplace_back(p, 0);
        facs.back().second++;
    }

    while (T--) cout << solve().val() << '\n';
}