結果

問題 No.1529 Constant Lcm
コンテスト
ユーザー ゆにぽけ
提出日時 2023-10-15 17:10:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 595 ms / 3,000 ms
コード長 4,354 bytes
コンパイル時間 1,094 ms
コンパイル使用メモリ 134,784 KB
最終ジャッジ日時 2025-02-17 07:56:58
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
sample AC * 2
other AC * 24
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 # 

#include<iostream>
#include<vector>
#include<algorithm>
#include<cstring>
#include<cassert>
#include<cmath>
#include<ctime>
#include<iomanip>
#include<numeric>
#include<stack>
#include<queue>
#include<map>
#include<unordered_map>
#include<set>
#include<unordered_set>
#include<bitset>
#include<random>
using namespace std;
template<int m> struct modint
{
	private:
	unsigned int value;
	static constexpr int mod() {return m;}

	public:
	constexpr modint(const long long x = 0) noexcept
	{
		long long y = x;
		if(y < 0 || y >= mod())
		{
			y %= mod();
			if(y < 0) y += mod();
		}
		value = (unsigned int)y;
	}
	constexpr unsigned int val() noexcept {return value;}
	constexpr modint &operator+=(const modint &other) noexcept
	{
		value += other.value;
		if(value >= mod()) value -= mod();
		return *this;
	}
	constexpr modint &operator-=(const modint &other) noexcept
	{
		unsigned int x = value;
		if(x < other.value) x += mod();
		x -= other.value;
		value = x;
		return *this;
	}
	constexpr modint &operator*=(const modint &other) noexcept
	{
		unsigned long long x = value;
		x *= other.value;
		value = (unsigned int) (x % mod());
		return *this;
	}
	constexpr modint &operator/=(const modint &other) noexcept
	{
		return *this *= other.inverse();
	}
	constexpr modint inverse() const noexcept
	{
		assert(value);
		long long a = value,b = mod(),x = 1,y = 0;
		while(b)
		{
			long long q = a/b;
			a -= q*b; swap(a,b);
			x -= q*y; swap(x,y);
		}
		return modint(x);
	}
	constexpr modint power(long long N) const noexcept
	{
		assert(N >= 0);
		modint p = *this,ret = 1;
		while(N)
		{
			if(N & 1) ret *= p;
			p *= p;
			N >>= 1;
		}
		return ret;
	}
	constexpr modint operator+() {return *this;}
	constexpr modint operator-() {return modint() - *this;}
	constexpr modint &operator++(int) noexcept {return *this += 1;}
	constexpr modint &operator--(int) noexcept {return *this -= 1;}
	friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;}
	friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;}
	friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;}
	friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;}
	friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;}
};
using mint = modint<998244353>;
//using mint = modint<1000000007>;


struct Eratosthenes {
    vector<int> isp,minfactor,myprime,moebius;

    Eratosthenes (int n) : isp(n+1,1),minfactor(n+1,__INT_MAX__),moebius(n+1,1){

        isp[0] = isp[1] = 0;
        minfactor[0] = 0;minfactor[1] = 1;

        for(int p = 2;p <= n;p++){
            if(!isp[p]) continue;
            minfactor[p] = p;
            moebius[p] = -1;
            myprime.push_back(p);

            for(int q = 2*p;q <= n;q += p){
                isp[q] = false;

                if(!((q/p)%p)) moebius[q] = 0;
                else moebius[q] = -moebius[q];


                minfactor[q] = min(minfactor[q],p);
            }
        }
    }

    vector<pair<int,int>> prime_factorize(int n) {
        vector<pair<int,int>> res;
        while(n-1){

            int p = minfactor[n];
            int exp = 0;

            while(minfactor[n] == p){
                n /= p;
                exp ++;
            }

            res.push_back(make_pair(p,exp));
        }

        return res;
    }

    vector<int> divisors(int n){
        vector<int> res;
        res.push_back(1);

        auto pf = prime_factorize(n);

        for(auto [p,e]:pf){
            int s = (int)res.size();

            for(int i = 0;i < s;i++){
                int v = 1;
                for(int j = 0;j < e;j++){
                    v *= p;
                    res.push_back(res[i]*v);
                }
            }
        }

        return res;
    }
};
int N;
void solve()
{
	cin >> N;
	Eratosthenes er(N);
	map<int,int> L;
	for(int i = 1;i <= N;i++)
	{
		int j = N-i;
		if(i > j) break;
		map<int,int> mp;
		for(auto [p,e] : er.prime_factorize(i)) mp[p] += e;
		for(auto [p,e] : er.prime_factorize(j)) mp[p] += e;
		for(auto [p,e]:mp) L[p] = max(L[p],e);
	}
	mint ans = 1;
	for(auto [p,e]:L) ans *= mint(p).power(e);

	cout << ans << endl;
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int tt = 1;
	//cin >> tt;
	while(tt--) solve();
}
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