結果

問題 No.2798 Multiple Chain
ユーザー shinchan
提出日時 2024-06-28 21:59:53
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 6 ms / 2,000 ms
コード長 6,801 bytes
コンパイル時間 3,019 ms
コンパイル使用メモリ 214,256 KB
最終ジャッジ日時 2025-02-22 01:06:08
ジャッジサーバーID
（参考情報） 		judge4 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 51
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 #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#define all(v) (v).begin(),(v).end()
#define pb(a) push_back(a)
#define rep(i, n) for(int i=0;i<n;i++)
#define foa(e, v) for(auto& e : v)
using ll = long long;
const ll MOD7 = 1000000007, MOD998 = 998244353, INF = (1LL << 60);
#define dout(a) cout<<fixed<<setprecision(10)<<a<<endl;
// montgomery modint (MOD < 2^62, MOD is odd)
struct MontgomeryModInt64 {
    using mint = MontgomeryModInt64;
    using u64 = uint64_t;
    using u128 = __uint128_t;
    
    // static menber
    static u64 MOD;
    static u64 INV_MOD;  // INV_MOD * MOD ≡ 1 (mod 2^64)
    static u64 T128;  // 2^128 (mod MOD)
    
    // inner value
    u64 val;
    
    // constructor
    MontgomeryModInt64() : val(0) { }
    MontgomeryModInt64(long long v) : val(reduce((u128(v) + MOD) * T128)) { }
    u64 get() const {
        u64 res = reduce(val);
        return res >= MOD ? res - MOD : res;
    }
    
    // mod getter and setter
    static u64 get_mod() { return MOD; }
    static void set_mod(u64 mod) {
        assert(mod < (1LL << 62));
        assert((mod & 1));
        MOD = mod;
        T128 = -u128(mod) % mod;
        INV_MOD = get_inv_mod();
    }
    static u64 get_inv_mod() {
        u64 res = MOD;
        for (int i = 0; i < 5; ++i) res *= 2 - MOD * res;
        return res;
    }
    static u64 reduce(const u128 &v) {
        return (v + u128(u64(v) * u64(-INV_MOD)) * MOD) >> 64;
    }
    
    // arithmetic operators
    mint operator + () const { return mint(*this); }
    mint operator - () const { return mint() - mint(*this); }
    mint operator + (const mint &r) const { return mint(*this) += r; }
    mint operator - (const mint &r) const { return mint(*this) -= r; }
    mint operator * (const mint &r) const { return mint(*this) *= r; }
    mint operator / (const mint &r) const { return mint(*this) /= r; }
    mint& operator += (const mint &r) {
        if ((val += r.val) >= 2 * MOD) val -= 2 * MOD;
        return *this;
    }
    mint& operator -= (const mint &r) {
        if ((val += 2 * MOD - r.val) >= 2 * MOD) val -= 2 * MOD;
        return *this;
    }
    mint& operator *= (const mint &r) {
        val = reduce(u128(val) * r.val);
        return *this;
    }
    mint& operator /= (const mint &r) {
        *this *= r.inv();
        return *this;
    }
    mint inv() const { return pow(MOD - 2); }
    mint pow(u128 n) const {
        mint res(1), mul(*this);
        while (n > 0) {
            if (n & 1) res *= mul;
            mul *= mul;
            n >>= 1;
        }
        return res;
    }
    // other operators
    bool operator == (const mint &r) const {
        return (val >= MOD ? val - MOD : val) == (r.val >= MOD ? r.val - MOD : r.val);
    }
    bool operator != (const mint &r) const {
        return (val >= MOD ? val - MOD : val) != (r.val >= MOD ? r.val - MOD : r.val);
    }
    mint& operator ++ () {
        ++val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    mint& operator -- () {
        if (val == 0) val += MOD;
        --val;
        return *this;
    }
    mint operator ++ (int) {
        mint res = *this;
        ++*this;
        return res;
    }
    mint operator -- (int) {
        mint res = *this;
        --*this;
        return res;
    }
    friend istream& operator >> (istream &is, mint &x) {
        long long t;
        is >> t;
        x = mint(t);
        return is;
    }
    friend ostream& operator << (ostream &os, const mint &x) {
        return os << x.get();
    }
    friend mint pow(const mint &r, long long n) {
        return r.pow(n);
    }
    friend mint inv(const mint &r) {
        return r.inv();
    }
};
typename MontgomeryModInt64::u64
MontgomeryModInt64::MOD, MontgomeryModInt64::INV_MOD, MontgomeryModInt64::T128;
// Miller-Rabin
bool MillerRabin(long long N, vector<long long> A) {
    using mint = MontgomeryModInt64;
    mint::set_mod(N);
    
    long long s = 0, d = N - 1;
    while (d % 2 == 0) {
        ++s;
        d >>= 1;
    }
    for (auto a : A) {
        if (N <= a) return true;
        mint x = mint(a).pow(d);
        if (x != 1) {
            long long t;
            for (t = 0; t < s; ++t) {
                if (x == N - 1) break;
                x *= x;
            }
            if (t == s) return false;
        }
    }
    return true;
}
bool is_prime(long long N) {
    if (N <= 1) return false;
    else if (N == 2) return true;
    else if (N % 2 == 0) return false;
    else if (N < 4759123141LL)
        return MillerRabin(N, {2, 7, 61});
    else
        return MillerRabin(N, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}
// Pollard's Rho
unsigned int xor_shift_rng() {
    static unsigned int tx = 123456789, ty=362436069, tz=521288629, tw=88675123;
    unsigned int tt = (tx^(tx<<11));
    tx = ty, ty = tz, tz = tw;
    return ( tw=(tw^(tw>>19))^(tt^(tt>>8)) );
}
long long pollard(long long N) {
    if (N % 2 == 0) return 2;
    if (is_prime(N)) return N;
    
    using mint = MontgomeryModInt64;
    mint::set_mod(N);
    
    long long step = 0;
    while (true) {
        mint r = xor_shift_rng();  // random r
        auto f = [&](mint x) -> mint { return x * x + r; };
        mint x = ++step, y = f(x);
        while (true) {
            long long p = gcd((y - x).get(), N);
            if (p == 0 || p == N) break;
            if (p != 1) return p;
            x = f(x);
            y = f(f(y));
        }
    }
}
vector<long long> prime_factorize(long long N) {
    if (N == 1) return {};
    long long p = pollard(N);
    if (p == N) return {p};
    vector<long long> left = prime_factorize(p);
    vector<long long> right = prime_factorize(N / p);
    left.insert(left.end(), right.begin(), right.end());
    sort(left.begin(), left.end());
    return left;
}
template<class T> struct Partition {
    vector<vector<T> > P;
    constexpr Partition(int MAX) noexcept : P(MAX, vector<T>(MAX, 0)) {
        for (int k = 0; k < MAX; ++k) P[0][k] = 1;
        for (int n = 1; n < MAX; ++n) {
            for (int k = 1; k < MAX; ++k) {
                P[n][k] = P[n][k-1] + (n-k >= 0 ? P[n-k][k] : 0);
            }
        }
    }
    constexpr T get(int n, int k) {
        if (n < 0 || k < 0) return 0;
        return P[n][k];
    }
};
int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll n;
    cin >> n;
    auto res = prime_factorize(n);
    map<ll, ll> mp;
    foa(e, res) mp[e] ++;
    vector<ll> v;
    foa(e, mp) v.pb(e.second);
    ll ans = 0;
    Partition<ll> pt(60);
    for(ll i = 1; i < 60; i ++) {
        ll num = 1;
        foa(e, v) {
            num *= pt.get(e, i);
        }
        ll d = 1;
        foa(e, v) {
            d *= pt.get(e, i - 1);
        }
        ans += num - d;
    }
    cout << ans << endl;
    return 0;
}
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