結果
問題 |
No.3213 depth max K
|
ユーザー |
|
提出日時 | 2025-07-25 22:19:44 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 125 ms / 2,000 ms |
コード長 | 3,561 bytes |
コンパイル時間 | 1,750 ms |
コンパイル使用メモリ | 199,564 KB |
実行使用メモリ | 7,716 KB |
最終ジャッジ日時 | 2025-07-25 22:19:50 |
合計ジャッジ時間 | 4,730 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 41 |
ソースコード
#include <bits/stdc++.h> using namespace std; //入力が必ず-mod<a<modの時. template<const int mod> struct modint{ //mod変更が不可能. public: long long v = 0; static void setmod(int m){} //飾り. static constexpr long long getmod(){return mod;} modint(){v = 0;} modint(int a){v = a<0?a+mod:a;} modint(long long a){v = a<0?a+mod:a;} modint(unsigned int a){v = a;} modint(unsigned long long a){v = a;} long long val()const{return v;} modint &operator=(const modint &b) = default; modint operator+()const{return (*this);} modint operator-()const{return modint(0)-(*this);} modint operator+(const modint b)const{return modint(v)+=b;} modint operator-(const modint b)const{return modint(v)-=b;} modint operator*(const modint b)const{return modint(v)*=b;} modint operator/(const modint b)const{return modint(v)/=b;} modint operator+=(const modint b){ v += b.v; if(v >= mod) v -= mod; return *this; } modint operator-=(const modint b){ v -= b.v; if(v < 0) v += mod; return *this; } modint operator*=(const modint b){v = v*b.v%mod; return *this;} modint operator/=(modint b){ //b!=0 mod素数が必須. if(b == 0) assert(false); int left = mod-2; while(left){if(left&1) *this *= b; b *= b; left >>= 1;} return *this; } modint operator++(){*this += 1; return *this;} modint operator--(){*this -= 1; return *this;} modint operator++(int){*this += 1; return *this;} modint operator--(int){*this -= 1; return *this;} bool operator==(const modint b)const{return v == b.v;} bool operator!=(const modint b)const{return v != b.v;} bool operator>(const modint b)const{return v > b.v;} bool operator>=(const modint b)const{return v >= b.v;} bool operator<(const modint b)const{return v < b.v;} bool operator<=(const modint b)const{return v <= b.v;} modint pow(long long n)const{ modint ret = 1,p = v; if(n < 0) p = p.inv(),n = -n; while(n){ if(n&1) ret *= p; p *= p; n >>= 1; } return ret; } modint inv()const{return modint(1)/v;} //素数mod必須. }; using mint = modint<998244353>; const long long mod = 998244353; int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); int N,K; cin >> N >> K; int Limit = 100000; //Limit->必要なサイズ fac->x! facinv->1/x! inv->1/x. vector<mint> fac(Limit+1,1),facinv(Limit+1); { int mod = mint::getmod(),invstart = min(mod-1,Limit); for(int i=1; i<=Limit; i++) fac.at(i) = fac.at(i-1)*i; facinv.at(invstart) = fac.at(invstart).inv(); for(int i=invstart-1; i>=0; i--) facinv.at(i) = facinv.at(i+1)*(i+1); } vector<mint> inv(Limit+1); for(int i=1; i<=Limit; i++) inv.at(i) = fac.at(i-1)*facinv.at(i); //必要なら解放. auto nCr = [&](int n,int r) -> mint { if(n < r || r < 0 || n < 0) return 0; return fac.at(n)*facinv.at(r)*facinv.at(n-r); }; //https://oeis.org/A080936 vector<mint> C(N+1); for(int i=1; i<=N; i++) for(int k=0; k<=i; k++){ if((i+k)%2) C.at(i) -= nCr(k+2*K-2*i+1,k); else C.at(i) += nCr(k+2*K-2*i+1,k); } vector<mint> dp(N+2); dp.at(1) = 1; for(int i=1; i<=N; i++) for(int k=1; k<N-(K-1); k++){ int p = i-(k-1); if(p < 0) p = 0; if(k%2 == 0) dp.at(i+1) -= dp.at(p)*C.at(k); else dp.at(i+1) += dp.at(p)*C.at(k); } cout << dp.at(N-(K-1)).v << endl; }