Submission #497688

#TimeUsernameProblemLanguageResultExecution timeMemory
497688amoo_safarRuins 3 (JOI20_ruins3)C++17
100 / 100
586 ms336 KiB
#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 */
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