#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
*/
# |
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 |
# |
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 |
# |
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 |