#663134 (C++17) No.1529 Constant Lcm

• 問題: No.1529 Constant Lcm
• ユーザー: tokusakurai
• 提出日時: 2021-06-04 20:12:57
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 56 ms / 3,000 ms
• コード長: 5,195 bytes
• コンパイル時間: 2,171 ms
• コンパイル使用メモリ: 204,804 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-04-29 23:16:54
• 合計ジャッジ時間: 3,593 ms
• ジャッジサーバーID （参考情報）: judge4 / 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	1 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	49 ms; 5,376 KB
testcase_11	AC	20 ms; 5,376 KB
testcase_12	AC	3 ms; 5,376 KB
testcase_13	AC	43 ms; 5,376 KB
testcase_14	AC	30 ms; 5,376 KB
testcase_15	AC	29 ms; 5,376 KB
testcase_16	AC	21 ms; 5,376 KB
testcase_17	AC	13 ms; 5,376 KB
testcase_18	AC	14 ms; 5,376 KB
testcase_19	AC	30 ms; 5,376 KB
testcase_20	AC	49 ms; 5,376 KB
testcase_21	AC	49 ms; 5,376 KB
testcase_22	AC	51 ms; 5,376 KB
testcase_23	AC	48 ms; 5,376 KB
testcase_24	AC	51 ms; 5,376 KB
testcase_25	AC	56 ms; 5,376 KB

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define each(e, v) for(auto &e: v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
//const int MOD = 1000000007;
const int MOD = 998244353;
const int inf = (1<<30)-1;
const ll INF = (1LL<<60)-1;
template<typename T> bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;};
template<typename T> bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;};

struct io_setup{
    io_setup(){
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

template<int mod>
struct Mod_Int{
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    Mod_Int &operator += (const Mod_Int &p){
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator -= (const Mod_Int &p){
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator *= (const Mod_Int &p){
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator /= (const Mod_Int &p){
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator ++ () {return *this += Mod_Int(1);}

    Mod_Int operator ++ (int){
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator -- () {return *this -= Mod_Int(1);}

    Mod_Int operator -- (int){
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator - () const {return Mod_Int(-x);}

    Mod_Int operator + (const Mod_Int &p) const {return Mod_Int(*this) += p;}

    Mod_Int operator - (const Mod_Int &p) const {return Mod_Int(*this) -= p;}

    Mod_Int operator * (const Mod_Int &p) const {return Mod_Int(*this) *= p;}

    Mod_Int operator / (const Mod_Int &p) const {return Mod_Int(*this) /= p;}

    bool operator == (const Mod_Int &p) const {return x == p.x;}

    bool operator != (const Mod_Int &p) const {return x != p.x;}

    Mod_Int inverse() const{
        assert(*this != Mod_Int(0));
        return pow(mod-2);
    }

    Mod_Int pow(long long k) const{
        Mod_Int now = *this, ret = 1;
        for(; k > 0; k >>= 1, now *= now){
            if(k&1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator << (ostream &os, const Mod_Int &p){
        return os << p.x;
    }

    friend istream &operator >> (istream &is, Mod_Int &p){
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

using mint = Mod_Int<MOD>;

template<typename T>
vector<T> divisors(const T &n){
    vector<T> ret;
    for(T i = 1; i*i <= n; i++){
        if(n%i == 0){
            ret.push_back(i);
            if(i*i != n) ret.push_back(n/i);
        }
    }
    sort(begin(ret), end(ret));
    return ret;
}

template<typename T>
vector<pair<T, int>> prime_factor(T n){
    vector<pair<T, int>> ret;
    for(T i = 2; i*i <= n; i++){
        int cnt = 0;
        while(n%i == 0) cnt++, n /= i;
        if(cnt > 0) ret.emplace_back(i, cnt);
    }
    if(n > 1) ret.emplace_back(n, 1);
    return ret;
}

template<typename T>
bool is_prime(const T &n){
    if(n == 1) return false;
    for(T i = 2; i*i <= n; i++){
        if(n%i == 0) return false;
    }
    return true;
}

//1,2,...,nのうちkと互いに素である自然数の個数
template<typename T>
T coprime(T n, T k){
    vector<pair<T, int>> ps = prime_factor(k);
    int m = ps.size();
    T ret = 0;
    for(int i = 0; i < (1<<m); i++){
        T prd = 1;
        for(int j = 0; j < m; j++){
            if((i>>j)&1) prd *= ps[j].first;
        }
        ret += (__builtin_parity(i)? -1 : 1)*(n/prd);
    }
    return ret;
}

vector<bool> Eratosthenes(const int &n){
    vector<bool> ret(n+1, true);
    if(n >= 0) ret[0] = false;
    if(n >= 1) ret[1] = false;
    for(int i = 2; i*i <= n; i++){
        if(!ret[i]) continue;
        for(int j = i+i; j <= n; j += i) ret[j] = false;
    }
    return ret;
}

vector<int> Eratosthenes2(const int &n){
    vector<int> ret(n+1);
    iota(begin(ret), end(ret), 0);
    if(n >= 0) ret[0] = -1;
    if(n >= 1) ret[1] = -1;
    for(int i = 2; i*i <= n; i++){
        if(ret[i] < i) continue;
        for(int j = i+i; j <= n; j += i) ret[j] = min(ret[j], i);
    }
    return ret;
}

int main(){
    int N; cin >> N;

    vector<bool> p = Eratosthenes(N);

    mint ans = 1;

    rep2(i, 2, N){
        if(!p[i]) continue;
        
        int M = 0;

        for(int j = i; j < N; j += i){
            int a = j, b = N-j, c = 0;
            while(a%i == 0){
                a /= i, c++;
            }
            while(b%i == 0){
                b /= i, c++;
            }
            chmax(M, c);
        }

        ans *= mint(i).pow(M);
    }

    cout << ans << '\n';
}