old_Math/Catalan_Number.cpp

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• Last update: 2022-07-19 22:14:43+09:00

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//Input: n, MOD
//Output: C_n mod MOD
//Time: O(1)
long long modpow(long long a, long long b){
	long long res = 1;
	while (b > 0){
		if (b % 2 == 1) res = res * a % MOD;
		a = a * a % MOD;
		b = b / 2;
	}
	return res;
}
long long modinv(long long a){
	return modpow(a, MOD - 2);
}
vector<long long> mf;
long long modfact(long long n){
	if (n < mf.size()){
		return mf[n];
	} else {
		if (mf.empty()) mf.push_back(1);
		long long res = mf.back();
		for (int i = mf.size(); i <= n; i++){
			res = res * i % MOD;
			mf.push_back(res);
		}
		return res;
	}
}
long long catalan_number(long long n){
	long long res;
	res = modfact(n * 2);
	res = res * modinv(modfact(n + 1)) % MOD;
	res = res * modinv(modfact(n)) % MOD;
	return res;
}

#line 1 "old_Math/Catalan_Number.cpp"
//Input: n, MOD
//Output: C_n mod MOD
//Time: O(1)
long long modpow(long long a, long long b){
	long long res = 1;
	while (b > 0){
		if (b % 2 == 1) res = res * a % MOD;
		a = a * a % MOD;
		b = b / 2;
	}
	return res;
}
long long modinv(long long a){
	return modpow(a, MOD - 2);
}
vector<long long> mf;
long long modfact(long long n){
	if (n < mf.size()){
		return mf[n];
	} else {
		if (mf.empty()) mf.push_back(1);
		long long res = mf.back();
		for (int i = mf.size(); i <= n; i++){
			res = res * i % MOD;
			mf.push_back(res);
		}
		return res;
	}
}
long long catalan_number(long long n){
	long long res;
	res = modfact(n * 2);
	res = res * modinv(modfact(n + 1)) % MOD;
	res = res * modinv(modfact(n)) % MOD;
	return res;
}

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