結果

問題 No.2318 Phys Bone Maker
コンテスト
ユーザー hliuser1
提出日時 2023-06-09 05:57:52
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 756 ms / 3,000 ms
コード長 2,873 bytes
コンパイル時間 3,898 ms
コンパイル使用メモリ 266,608 KB
実行使用メモリ 12,220 KB
最終ジャッジ日時 2024-12-31 12:49:03
合計ジャッジ時間 11,780 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 45
権限があれば一括ダウンロードができます
コンパイルメッセージ
In member function 'bool sieve::operator()(int)',
    inlined from 'int main()' at main.cpp:80:19:
main.cpp:44:49: warning: iteration 999999 invokes undefined behavior [-Waggressive-loop-optimizations]
   44 |     inline bool operator()(int n) { return spf[n] == n; }
      |                                            ~~~~~^
main.cpp: In function 'int main()':
main.cpp:79:29: note: within this loop
   79 |     for (int z{-1}, i{2}; i <= sieve::N; ++i)
      |                           ~~^~~~~~~~~~~

ソースコード

diff # 

// https://yukicoder.me/problems/no/2318
// use the trick from Hossam & trainees.
// compute list of all primes up to sqrt(N)
// use repeated division to find any remaining "big" primes
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
using namespace std;
using ll = long long;

static constexpr ll Q = 998244353;

template <typename K, typename V>
using Map = map<K, V>;

template <typename Int>
vector<Int> factorize(Int n, Int i=1) {
    vector<Int> f;
    f.reserve( sqrt(n) );
    for (; i*i < n; ++i)
        if (n % i == 0)
            f.push_back(i);
    i -= (i - (n / i) == 1);
    for (; i >= 1; i--)
        if (n % i == 0)
            f.push_back(n/i);
    return f;
}

struct sieve {
    static constexpr size_t N = 1000001;
    int spf[N] = {};
    sieve() {
        spf[0] = spf[1] = -1;
        for (int i = 3; i <= N; i += 2) spf[i] = i;
        for (int i = 2; i <= N; i += 2) spf[i] = 2;  // avoid lots of % later
        for (int i = 3; i*i <= N; i += 2) {
            if (spf[i] != i) continue;
            for (int j = i*i; j <= N; j += i)
                if (spf[j] == j)
                    spf[j] = i;
        }
    }
    inline bool operator()(int n) { return spf[n] == n; }
    template <class Int>
    inline Map<Int, int> factors(Int n) {
        Map<Int, int> mp;
        while (n != 1) {
            int p = spf[n];
            while (n % p == 0) {
                ++mp[p];
                n /= p;
            }
        }
        return mp;
    }
} prime;

ll primes[78498];  // list of all primes < 1e6

Map<ll, int> prime_factorize(ll x) {
    if (x < sieve::N)
        return prime.factors(x);
    Map<ll, int> mp;
    ll y = x;
    for (int p : primes) {
        while (y % p == 0) {
            y /= p;
            ++mp[p];
        }
        if (y == 1) break;
    }
    if (y != 1)
        mp[y] = 1;
    return mp;
}

signed main() {
    for (int z{-1}, i{2}; i <= sieve::N; ++i)
        if ( prime(i) )
            primes[++z] = i;

    ll N;
    cin >> N;
    unordered_map<ll, ll> dp;
    // dp[x] = sum(dp[y]*Z forall y such that x%y==0) where Z is # of z s.t. lcm(y,z) = x

    dp[1] = 1;
    auto facts = factorize(N);
    int X = facts.size();

    vector<Map<ll,int>> prime_facs(X);
    for (int i = 0; i < X; ++i) {
        ll f = facts[i];
        prime_facs[i] = prime_factorize(f);
    }

    for (int i = 1; i < X; ++i) {
        ll x = facts[i];
        auto& pfx = prime_facs[i];
        for (int j = 0; j < i; ++j) {
            ll y = facts[j];
            if (x % y != 0) continue;

            ll ways = dp[y];  // # of z where lcm(y,z) = x
            auto& pfy = prime_facs[j];
            for (auto [p, cnt] : pfx)
                if (pfy[p] == cnt)
                    ways = ways * (cnt+1) % Q;

            dp[x] = (dp[x]+ways) % Q;
        }
    }
    cout << dp[N] << '\n';
}
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