Submission #497688

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
497688	2021-12-23T15:04:24 Z	amoo_safar	Ruins 3 (JOI20_ruins3)	C++17	100 / 100	586 ms	336 KB

ruins3

#include <bits/stdc++.h>

#define pb push_back
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define debug(x) cerr << #x << " : " << x << '\n'

using namespace std;

const int N = 6e2 + 10;


namespace ModularInt {
	template<typename T>
	T inverse(T a, T pr){
		T u = 1, v = 0;
		while(a != 0){
			T dv = pr / a;
			pr -= dv * a; v -= dv * u;
			swap(a, pr); swap(u, v);
		}
		assert(pr == 1); // gcd(a, pr) != 1;
		return v;
	}

	template<typename ModT>
	class Mint {
	public:
		using T = typename decay<decltype(ModT::value)>::type;
		T val;
	

		Mint() : val() {}
		template<typename Q>
		Mint(const Q& x){ val = normalize(x); }
		Mint(const Mint& x) { val = x.val; }

		template <typename U>
		explicit operator U() const { return static_cast<U>(val); }

		constexpr static T _Mod() { return ModT::value; }

		friend Mint inverse(Mint x){ return inverse(x.val, _Mod()); }

		template<typename Q>
		static T normalize(const Q& x){
			T val;
			if(-_Mod() <= x && x < _Mod()) val = x;
			else val = x % _Mod();
			if(val < 0) val += _Mod();
			return val;
		}
		
		template<typename Q>
		Mint& operator=(const Q& x){ val = normalize(x); return *this; }

		Mint& operator +=(const Mint& other){ if(_Mod() <= (val += other.val)) val -= _Mod(); return *this; }
		Mint& operator -=(const Mint& other){ if((val -= other.val) < 0) val += _Mod(); return *this; }
		template<typename Q> Mint& operator +=(const Q& other){ return (*this) += Mint(other); };
		template<typename Q> Mint& operator -=(const Q& other){ return (*this) -= Mint(other); };
		Mint& operator ++(){ return (*this) += 1; }
		Mint& operator --(){ return (*this) -= 1; }
		Mint operator ++(int){ Mint res(*this); (*this) += 1; return res; }
		Mint operator --(int){ Mint res(*this); (*this) -= 1; return res; }
		Mint operator +(){ Mint res(val); return res; }
		Mint operator -(){ Mint res(-val); return res; }

		Mint& operator *=(const Mint& other){ val = (1ll * val * other.val) % _Mod(); return *this; }
		Mint& operator /=(const Mint& other){ return (*this) *= inverse(other); }
		template<typename Q> Mint& operator *=(const Q& other){ return (*this) *= Mint(other); }
		template<typename Q> Mint& operator /=(const Q& other){ return (*this) /= Mint(other); }
	};


	template<typename T> Mint<T> operator +(const Mint<T>& lhs, const Mint<T>& rhs){ return Mint<T>(lhs) += rhs; }
	template<typename T, typename Q>  Mint<T> operator +(const Q& lhs, const Mint<T>& rhs){ return Mint<T>(lhs) += rhs; }
	template<typename T, typename Q>  Mint<T> operator +(const Mint<T>& lhs, const Q& rhs){ return Mint<T>(lhs) += rhs; }

	template<typename T> Mint<T> operator -(const Mint<T>& lhs, const Mint<T>& rhs){ return Mint<T>(lhs) -= rhs; }
	template<typename T, typename Q>  Mint<T> operator -(const Q& lhs, const Mint<T>& rhs){ return Mint<T>(lhs) -= rhs; }
	template<typename T, typename Q>  Mint<T> operator -(const Mint<T>& lhs, const Q& rhs){ return Mint<T>(lhs) -= rhs; }

	template<typename T> Mint<T> operator *(const Mint<T>& lhs, const Mint<T>& rhs){ return Mint<T>(lhs) *= rhs; }
	template<typename T, typename Q>  Mint<T> operator *(const Q& lhs, const Mint<T>& rhs){ return Mint<T>(lhs) *= rhs; }
	template<typename T, typename Q>  Mint<T> operator *(const Mint<T>& lhs, const Q& rhs){ return Mint<T>(lhs) *= rhs; }

	template<typename T> Mint<T> operator /(const Mint<T>& lhs, const Mint<T>& rhs){ return Mint<T>(lhs) /= rhs; }
	template<typename T, typename Q>  Mint<T> operator /(const Q& lhs, const Mint<T>& rhs){ return Mint<T>(lhs) /= rhs; }
	template<typename T, typename Q>  Mint<T> operator /(const Mint<T>& lhs, const Q& rhs){ return Mint<T>(lhs) /= rhs; }

	template<typename T> bool operator ==(const Mint<T>& lhs, const Mint<T>& rhs){ return lhs.val == rhs.val; }
	template<typename T, typename Q>  bool operator ==(const Q& lhs, const Mint<T>& rhs){ return Mint<T>(lhs) == rhs; }
	template<typename T, typename Q>  bool operator ==(const Mint<T>& lhs, const Q& rhs){ return lhs == Mint<T>(rhs); }

	template<typename T> bool operator !=(const Mint<T>& lhs, const Mint<T>& rhs){ return !(lhs == rhs); }
	template<typename T, typename Q>  bool operator !=(const Q& lhs, const Mint<T>& rhs){ return !(lhs == rhs); }
	template<typename T, typename Q>  bool operator !=(const Mint<T>& lhs, const Q& rhs){ return !(lhs == rhs); }

	template<typename T, typename IO>
	IO& operator <<(IO& ostream, const Mint<T>& _x){
		return ostream << _x.val;
	}
	template<typename T, typename IO>
	IO& operator >>(IO& istream, Mint<T>& _x){
		return istream >> _x.val;
	}

	template<typename T, typename Q>
	Mint<T> bin_pow(const Mint<T>& base, Q power){
		assert(0 <= power);
		Mint<T> res = 1, pw = base;
		for(Q j = 1; j <= power; j <<= 1, pw *= pw)
			if(j & power)
				res *= pw;
		return res;
	}

	// Dynamic
	
	/*
	using ModType = int;
	struct VarMod { static ModType value; };
	ModType VarMod::value;
	ModType& MintMod = VarMod::value;
	using mi = Mint<VarMod>;
	*/

	// Static
	constexpr int MintMod = 1'000'000'007;
	using mi = Mint<integral_constant<decay<decltype(MintMod)>::type, MintMod>>;
};

using namespace ModularInt;

mi dp[N];
mi per[N];
int mk[N + N];

mi f[N], iv[N];
mi nCr(int n, int r){
	if(n < 0 || r < 0 || n < r) return 0;
	return f[n] * iv[r] * iv[n - r];
}
int main(){
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	f[0] = 1;
	for(int i = 1; i < N; i++) f[i] = i * f[i - 1];
	for(int i = 0; i < N; i++)iv[i] = inverse(f[i]);
	
	per[0] = 1;
	for(int i = 1; i < N; i++)
		for(int j = 0; j < i; j++)
			per[i] += nCr(i - 1, j) * per[j] * per[i - j - 1] * (i - j + 1);

	int n;
	cin >> n;
	int p;
	for(int i = 0; i < n; i++){
		cin >> p;
		mk[p] = 1;
	}
	dp[0] = 1;
	int c1 = 0, fr = 0;
	for(int _ = n + n; _; fr ++, _--){
		if(!mk[_]){
			for(int i = 0; i <= c1; i++) dp[i] *= max(0, i - fr + c1);
		} else {
			c1 ++;
			for(int i = c1; i >= 0; i--){
				for(int j = 0; j < i; j++){
					dp[i] += nCr((c1 - 1) - j, i - j - 1) * dp[j] * per[i - j - 1] * (i - j + 1);
				}
			}
		}
	}
	cout << dp[n] / bin_pow(mi(2), n) << '\n';
	return 0;
}
/*
10
2 8 9 13 15 16 17 18 19 20

*/

Subtask #1

6.0 / 6.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	5 ms	208 KB	Output is correct
2	Correct	3 ms	208 KB	Output is correct
3	Correct	4 ms	316 KB	Output is correct
4	Correct	3 ms	336 KB	Output is correct
5	Correct	3 ms	208 KB	Output is correct
6	Correct	3 ms	208 KB	Output is correct
7	Correct	4 ms	336 KB	Output is correct
8	Correct	3 ms	328 KB	Output is correct
9	Correct	3 ms	336 KB	Output is correct
10	Correct	3 ms	328 KB	Output is correct

Subtask #2

52.0 / 52.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	5 ms	208 KB	Output is correct
2	Correct	3 ms	208 KB	Output is correct
3	Correct	4 ms	316 KB	Output is correct
4	Correct	3 ms	336 KB	Output is correct
5	Correct	3 ms	208 KB	Output is correct
6	Correct	3 ms	208 KB	Output is correct
7	Correct	4 ms	336 KB	Output is correct
8	Correct	3 ms	328 KB	Output is correct
9	Correct	3 ms	336 KB	Output is correct
10	Correct	3 ms	328 KB	Output is correct
11	Correct	4 ms	208 KB	Output is correct
12	Correct	4 ms	208 KB	Output is correct
13	Correct	4 ms	336 KB	Output is correct
14	Correct	4 ms	336 KB	Output is correct
15	Correct	4 ms	208 KB	Output is correct
16	Correct	6 ms	208 KB	Output is correct
17	Correct	4 ms	332 KB	Output is correct
18	Correct	4 ms	332 KB	Output is correct
19	Correct	4 ms	208 KB	Output is correct
20	Correct	5 ms	208 KB	Output is correct

Subtask #3

42.0 / 42.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	5 ms	208 KB	Output is correct
2	Correct	3 ms	208 KB	Output is correct
3	Correct	4 ms	316 KB	Output is correct
4	Correct	3 ms	336 KB	Output is correct
5	Correct	3 ms	208 KB	Output is correct
6	Correct	3 ms	208 KB	Output is correct
7	Correct	4 ms	336 KB	Output is correct
8	Correct	3 ms	328 KB	Output is correct
9	Correct	3 ms	336 KB	Output is correct
10	Correct	3 ms	328 KB	Output is correct
11	Correct	4 ms	208 KB	Output is correct
12	Correct	4 ms	208 KB	Output is correct
13	Correct	4 ms	336 KB	Output is correct
14	Correct	4 ms	336 KB	Output is correct
15	Correct	4 ms	208 KB	Output is correct
16	Correct	6 ms	208 KB	Output is correct
17	Correct	4 ms	332 KB	Output is correct
18	Correct	4 ms	332 KB	Output is correct
19	Correct	4 ms	208 KB	Output is correct
20	Correct	5 ms	208 KB	Output is correct
21	Correct	569 ms	328 KB	Output is correct
22	Correct	577 ms	312 KB	Output is correct
23	Correct	572 ms	328 KB	Output is correct
24	Correct	568 ms	316 KB	Output is correct
25	Correct	565 ms	332 KB	Output is correct
26	Correct	575 ms	336 KB	Output is correct
27	Correct	555 ms	328 KB	Output is correct
28	Correct	556 ms	208 KB	Output is correct
29	Correct	568 ms	336 KB	Output is correct
30	Correct	567 ms	332 KB	Output is correct
31	Correct	558 ms	312 KB	Output is correct
32	Correct	586 ms	312 KB	Output is correct
33	Correct	580 ms	316 KB	Output is correct
34	Correct	580 ms	336 KB	Output is correct
35	Correct	577 ms	312 KB	Output is correct
36	Correct	561 ms	336 KB	Output is correct