結果

問題 No.2075 GCD Subsequence
ユーザー ForestedForested
提出日時 2022-09-16 21:39:48
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 2,796 ms / 4,000 ms
コード長 9,590 bytes
コンパイル時間 1,396 ms
コンパイル使用メモリ 136,852 KB
実行使用メモリ 176,216 KB
最終ジャッジ日時 2023-08-23 14:39:56
合計ジャッジ時間 59,609 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge15
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
4,376 KB
testcase_02 AC 2 ms
4,376 KB
testcase_03 AC 2 ms
4,380 KB
testcase_04 AC 2 ms
4,380 KB
testcase_05 AC 2 ms
4,376 KB
testcase_06 AC 2 ms
4,380 KB
testcase_07 AC 2 ms
4,376 KB
testcase_08 AC 2,690 ms
175,796 KB
testcase_09 AC 2,720 ms
176,184 KB
testcase_10 AC 2,705 ms
175,908 KB
testcase_11 AC 2,671 ms
176,216 KB
testcase_12 AC 2,649 ms
175,968 KB
testcase_13 AC 2,646 ms
175,484 KB
testcase_14 AC 2,670 ms
175,784 KB
testcase_15 AC 2,617 ms
175,700 KB
testcase_16 AC 2,631 ms
175,752 KB
testcase_17 AC 2,681 ms
176,036 KB
testcase_18 AC 2,721 ms
176,152 KB
testcase_19 AC 2,755 ms
176,104 KB
testcase_20 AC 2,738 ms
176,208 KB
testcase_21 AC 2,740 ms
176,076 KB
testcase_22 AC 2,796 ms
175,860 KB
testcase_23 AC 2,733 ms
176,152 KB
testcase_24 AC 2,749 ms
176,176 KB
testcase_25 AC 2,711 ms
176,052 KB
testcase_26 AC 2,711 ms
176,104 KB
testcase_27 AC 2,692 ms
176,152 KB
testcase_28 AC 1,832 ms
126,848 KB
testcase_29 AC 2 ms
4,376 KB
testcase_30 AC 1 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 # 

#ifndef LOCAL
#define FAST_IO
#endif

// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64) x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64) x;
    return os;
}

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
// ============

#ifdef DEBUGF
#else
#define DBG(x) (void) 0
#endif

// ============

#include <cassert>
#include <iostream>
#include <type_traits>

// ============

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned) ((unsigned long long) ret * self % mod);
        }
        self = (unsigned) ((unsigned long long) self * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
// ============

template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

public:
    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) (x % mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const {
        return val;
    }

    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if (val < rhs.val)
            val += mod;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

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

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

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;

// ============
// ============

#include <vector>
#include <numeric>

class LinearSieve {
    std::vector<int> mpf;
    std::vector<int> ps;
    
public:
    LinearSieve(int n) : mpf(n + 1) {
        std::iota(mpf.begin(), mpf.end(), 0);
        for (int i = 2; i <= n; ++i) {
            if (mpf[i] == i) {
                ps.push_back(i);
            }
            for (int p : ps) {
                if (p > mpf[i] || i * p > n) {
                    break;
                }
                mpf[p * i] = p;
            }
        }
    }
    
    int min_prime_factor(int n) const {
        assert(n >= 2 && n < (int) mpf.size());
        return mpf[n];
    }
    
    std::vector<int> primes() const {
        return ps;
    }
    
    bool is_prime(int n) const {
        assert(n < (int) mpf.size());
        return n >= 2 && mpf[n] == n;
    }
    
    std::vector<std::pair<int, int>> factorize(int n) const {
        assert(n > 0 && n < mpf.size());
        std::vector<std::pair<int, int>> ret;
        while (n > 1) {
            int p = mpf[n];
            int ex = 0;
            while (n % p == 0) {
                n /= p;
                ++ex;
            }
            ret.emplace_back(p, ex);
        }
        return ret;
    }
};

// ============

using Mint = ModInt<998244353>;

int main() {
    i32 n;
    cin >> n;
    Vec<i32> a(n);
    REP(i, n) {
        cin >> a[i];
    }
    
    i32 mx = *max_element(ALL(a));
    
    LinearSieve sieve(mx);
    
    Vec<Vec<i32>> divs(mx + 1);
    REP(i, 1, mx + 1) {
        for (i32 j = i; j <= mx; j += i) {
            divs[j].push_back(i);
        }
    }
    DBG(divs);
    
    Vec<Vec<i32>> prs(mx + 1);
    for (i32 p : sieve.primes()) {
        for (i32 j = p; j <= mx; j += p) {
            prs[j].push_back(p);
        }
    }
    
    Vec<Mint> dp(mx + 1);
    REP(i, n) {
        Mint s(1);
        REP(bit, 1, 1 << prs[a[i]].size()) {
            i32 pr = 1;
            REP(j, prs[a[i]].size()) {
                if (bit & (1 << j)) {
                    pr *= prs[a[i]][j];
                }
            }
            Mint d = dp[pr];
            if (__builtin_parity(bit)) {
                s += d;
            } else {
                s -= d;
            }
        }
        DBG(dp);
        DBG(s);
        for (i32 d : divs[a[i]]) {
            dp[d] += s;
        }
        DBG(dp);
    }
    cout << dp[1] << '\n';
}
0