結果

問題 No.2318 Phys Bone Maker
ユーザー CoCo_Japan_panCoCo_Japan_pan
提出日時 2023-05-27 14:40:16
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,153 ms / 3,000 ms
コード長 10,293 bytes
コンパイル時間 12,837 ms
コンパイル使用メモリ 298,724 KB
最終ジャッジ日時 2025-02-13 09:16:56
ジャッジサーバーID
（参考情報） 		judge1 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 45
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ソースコード

diff # 

#line 2 "/home/cocojapanpan/Procon_CPP/proconLibrary/lib/template/procon.hpp"

#ifndef DEBUG
// 提出時にassertはオフ
#ifndef NDEBUG
#define NDEBUG
#endif
// 定数倍高速化
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif

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

#define ALL(x) (x).begin(), (x).end()
template <class T>
using vec = vector<T>;
template <class T, class S>
inline bool chmax(T &a, const S &b) {
    return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
    return (a > b ? a = b, 1 : 0);
}
template <class T>
constexpr T INF = 1'000'000'000;
template <>
constexpr int INF<int> = 1'000'000'000;
template <>
constexpr ll INF<ll> = ll(INF<int>) * INF<int> * 2;
#line 2 "/home/cocojapanpan/Procon_CPP/proconLibrary/lib/modint/modint_static.hpp"

#line 2 "/home/cocojapanpan/Procon_CPP/proconLibrary/lib/modint/innermath_modint.hpp"

#line 4 "/home/cocojapanpan/Procon_CPP/proconLibrary/lib/modint/innermath_modint.hpp"

namespace innermath_modint{
    using ll = long long;
    using ull = unsigned long long;

    // xのmodを[0, mod)で返す
    constexpr ll safe_mod(ll x, ll mod) {
        x %= mod;
        if (x < 0) x += mod;
        return x;
    }

    constexpr ll pow_mod_constexpr(ll x, ll n, ll mod) {
        if (mod == 1) return 0;
        ll ret = 1;
        ll beki = safe_mod(x, mod);
        while (n) {
            // LSBから順に見る
            if (n & 1) {
                ret = (ret * beki) % mod;
            }
            beki = (beki * beki) % mod;
            n >>= 1;
        }
        return ret;
    }

    // int型(2^32以下)の高速な素数判定
    constexpr bool is_prime_constexpr(int n) {
        if (n <= 1) return false;
        if (n == 2 || n == 7 || n == 61) return true;
        if (n % 2 == 0) return false;
        // ミラーラビン判定 int型ならa={2,7,61}で十分
        constexpr ll bases[] = {2, 7, 61};
        // n-1 = 2^r * d
        ll d = n - 1;
        while (d % 2 == 0) d >>= 1;
        // 素数modは1の平方根として非自明な解を持たない
        // つまり非自明な解がある→合成数
        for (ll a : bases) {
            ll t = d;
            ll y = pow_mod_constexpr(a, t, n);
            // yが1またはn-1になれば抜ける
            while (t != n - 1 && y != 1 && y != n - 1) {
                y = (y * y) % n;
                t <<= 1;
            }
            // 1の平方根として1と-1以外の解(非自明な解)が存在
            if (y != n - 1 && t % 2 == 0) {
                return false;
            }
        }
        return true;
    }

    // 拡張ユークリッドの互除法 g = gcd(a,b)と、ax = g (mod b)なる0 <= x <
    // b/gのペアを返す
    constexpr std::pair<ll, ll> inv_gcd(ll a, ll b) {
        a = safe_mod(a, b);
        // aがbの倍数
        if (a == 0) return {b, 0};
        // 以下 0 <= a < b
        // [1] s - m0 * a = 0 (mod b)
        // [2] t - m1 * a = 0 (mod b)
        // [3] s * |m1| + t * |m0| <= b
        ll s = b, t = a;
        ll m0 = 0, m1 = 1;
        while (t) {
            // s → s mod t
            // m0 → m0 - m1 * (s / t)
            ll u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            {
                ll tmp = t;
                t = s;
                s = tmp;
            }
            {
                ll tmp = m1;
                m1 = m0;
                m0 = tmp;
            }
        }
        // s = gcd(a, b)
        // 終了の直前のステップにおいて
        // [1] k * s - m0 * a = 0 (mod b)
        // [2] s - m1 * a = 0 (mod b)
        // [3] (k * s) * |m1| + s * |m0| <= b
        // |m0| < b / s
        if (m0 < 0) m0 += b / s;
        return {s, m0};
    }
}
#line 5 "/home/cocojapanpan/Procon_CPP/proconLibrary/lib/modint/modint_static.hpp"

template <const int MOD>
struct modint_static {
    using ll = long long;

   public:
    constexpr modint_static(ll x = 0) noexcept : value(x % MOD) {
        if (value < 0) value += MOD;
    }
    constexpr int get_mod() const noexcept { return MOD; }
    constexpr ll val() const noexcept { return value; }
    constexpr modint_static operator-() const noexcept {
        return modint_static(-value);
    }
    constexpr modint_static& operator++() noexcept {
        ++value;
        if(value == MOD) value = 0;
        return *this;
    }
    constexpr modint_static& operator--() noexcept {
        if(value == 0) value = MOD;
        --value;
        return *this;
    }
    constexpr modint_static operator++(int) noexcept {
        modint_static cpy(*this);
        ++(*this);
        return cpy;
    }
    constexpr modint_static operator--(int) noexcept {
        modint_static cpy(*this);
        --(*this);
        return cpy;
    }
    constexpr modint_static& operator+=(const modint_static& rhs) noexcept {
        value += rhs.value;
        if (value >= MOD) value -= MOD;
        return *this;
    }
    constexpr modint_static& operator-=(const modint_static& rhs) noexcept {
        value += (MOD - rhs.value);
        if (value >= MOD) value -= MOD;
        return *this;
    }
    constexpr modint_static& operator*=(const modint_static& rhs) noexcept {
        (value *= rhs.value) %= MOD; // 定数だとコンパイラ最適化がかかる
        return *this;
    }
    constexpr modint_static operator+(const modint_static& rhs) const noexcept {
        modint_static cpy(*this);
        return cpy += rhs;
    }
    constexpr modint_static operator-(const modint_static& rhs) const noexcept {
        modint_static cpy(*this);
        return cpy -= rhs;
    }
    constexpr modint_static operator*(const modint_static& rhs) const noexcept {
        modint_static cpy(*this);
        return cpy *= rhs;
    }
    constexpr modint_static pow(ll beki) const noexcept {
        modint_static curbekimod(*this);
        modint_static ret(1);
        while (beki > 0) {
            if (beki & 1) ret *= curbekimod;
            curbekimod *= curbekimod;
            beki >>= 1;
        }
        return ret;
    }

    // valueの逆元を求める
    constexpr modint_static inv() const noexcept {
        // 拡張ユークリッドの互除法
        auto [gcd_value_mod, inv_value] = innermath_modint::inv_gcd(value, MOD);
        assert(gcd_value_mod == 1);
        return modint_static(inv_value);
    }
    constexpr modint_static& operator/=(const modint_static& rhs) noexcept {
        return (*this) *= rhs.inv();
    }
    constexpr modint_static operator/(const modint_static& rhs) const noexcept {
        modint_static cpy(*this);
        return cpy /= rhs;
    }

   private:
    ll value;
};

using mint998244353 = modint_static<998244353>;
using mint1000000007 = modint_static<1000000007>;
#line 3 "main.cpp"
using mint = mint998244353;

ll N;
vec<int> primeList;
map<ll, int> primeFactorized;
vec<pair<ll, map<ll, int>>> divisorsWithFactor{{1, {}}};
map<ll, int> divisorsToIndex;
vec<mint> dp;

void primeEnumerate() {
    int size = sqrt(N);
    vec<bool> seen(size + 1, false);
    for(int i = 2; i <= size; i++) {
        if(seen[i]) continue;
        primeList.push_back(i);
        for(int j = i; j <= size; j += i) {
            seen[j] = true;
        }
    }
}

void primeFactorizeN() {
    ll curN = N;
    for(ll prime : primeList) {
        while(curN % prime == 0) {
            curN /= prime;
            ++primeFactorized[prime];
        }
    }
    if(curN != 1) {
        ++primeFactorized[curN];
    }
}

void divisorsFactorize(map<ll, int>::iterator curIt) {
    if(curIt == primeFactorized.end()) return;
    int size = divisorsWithFactor.size();
    ll prime = curIt -> first;
    int beki = curIt -> second;
    for(int i = 0; i < size; i++) {
        ll cur = 1;
        for(int j = 1; j <= beki; j++) {
            cur *= prime;
            ll newNum = divisorsWithFactor[i].first * cur;
            map<ll, int> newMap = divisorsWithFactor[i].second;
            newMap[prime] = j;
            divisorsWithFactor.emplace_back(newNum, newMap);
        }
    }
    divisorsFactorize(next(curIt));
}

// debug
void printDivisorsFactorized() {
    for(const pair<ll, map<ll, int>> &p : divisorsWithFactor) {
        cerr << p.first << "\n";
        for(pair<ll, int> mp : p.second) {
            cerr << "素因数:" << mp.first << " べき:" << mp.second << "\n";
        }
    }
    cerr << endl;
}

void enumerateDivisors(const map<ll, int> &mp, vec<ll> &ret) {
    ret.clear();
    ret.push_back(1);
    for(const pair<ll, int> &p : mp) {
        int size = ret.size();
        ll prime = p.first;
        for(int i = 0; i < size; i++) {
            ll cur = 1;
            for(int j = 1; j <= p.second; j++) {
                cur *= prime;
                ret.push_back(ret[i] * cur);
            }
        }
    }
}

// debug
void printDivisors() {
    vec<ll> divisors;
    enumerateDivisors(divisorsWithFactor.back().second, divisors);
    for(ll d: divisors) {
        cerr << d << " ";
    }
    cerr << endl;
}

void compDP() {
    int size = divisorsWithFactor.size();
    dp.assign(size, 0);
    dp[0] = 1;
    for(int i = 1; i < size; i++) {
        vec<ll> divisors;
        enumerateDivisors(divisorsWithFactor[i].second, divisors);
        for(ll d : divisors) {
            if(d == divisorsWithFactor[i].first) break;
            ll q = divisorsWithFactor[i].first / d;
            // dにあってqにない素因数については自由度あり
            mint ziyudo = 1;
            for(pair<ll, int> p : divisorsWithFactor[divisorsToIndex[d]].second) {
                if(divisorsWithFactor[divisorsToIndex[q]].second.count(p.first)) continue;
                ziyudo *= (p.second + 1);
            }
            dp[i] += dp[divisorsToIndex[d]] * ziyudo;
        }
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> N;
    primeEnumerate();
    primeFactorizeN();
    divisorsFactorize(primeFactorized.begin());
    // printDivisors();
    for(int i = 0; i < (int)divisorsWithFactor.size(); i++) {
        divisorsToIndex[divisorsWithFactor[i].first] = i;
    }
    compDP();
    cout << dp.back().val() << "\n";
}
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