結果

問題 No.1873 Bracket Swapping
ユーザー ytqm3
提出日時 2021-12-16 21:42:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 266 ms / 2,000 ms
コード長 3,897 bytes
コンパイル時間 2,772 ms
コンパイル使用メモリ 214,388 KB
最終ジャッジ日時 2025-01-26 23:48:07
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 27
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
typedef uint64_t u64;
typedef int64_t i64;
using namespace std;
template<u64 mod> struct modint{
  u64 val;
  modint(i64 val_=0):val((val_%i64(mod)+i64(mod))%i64(mod)){}
  modint operator-(){
    return (val==0)?0:mod-val;
  }
  modint operator+(modint rhs){
    return modint(*this)+=rhs;
  }
  modint operator-(modint rhs){
    return modint(*this)-=rhs;
  }
  modint operator*(modint rhs){
    return modint(*this)*=rhs;
  }
  modint operator/(modint rhs){
    return modint(*this)/=rhs;
  }
  modint operator^(i64 rhs){
    return modint(*this)^=rhs;
  }
  modint &operator+=(modint rhs){
    val+=rhs.val,val-=((val>=mod)?mod:0);
    return (*this);
  }
  modint &operator-=(modint rhs){
    val+=((val<rhs.val)?mod:0),val-=rhs.val;
    return (*this);
  }
  modint &operator*=(modint rhs){
    val=val*rhs.val%mod;
    return (*this);
  }
  modint &operator/=(modint rhs){
    return (*this)*=rhs^(mod-2);
  }
  modint &operator^=(i64 rhs){
    modint res=1,now=(*this);
    while(rhs){
      res*=((rhs&1)?now:1),now*=now,rhs>>=1;
    }
    return (*this)=res;
  }
  bool operator==(modint rhs){
    return val==rhs.val;
  }
  bool operator!=(modint rhs){
    return val!=rhs.val;
  }
  friend std::ostream &operator<<(std::ostream& os,modint x){
    return os<<(x.val);
  }
  friend std::istream &operator>>(std::istream& is,modint& x){
    u64 t;
    is>>t,x=t;
    return is;
  }
};
template<typename T> struct matrix{
  vector<vector<T>> val;
  int height,width;
  matrix(int H,int W,T init=0):val(H,vector<T> (W,init)),height(H),width(W){}
  vector<T> &operator[](int i){
    return val[i];
  }
  matrix operator+(matrix rhs){
    return matrix(*this)+=rhs;
  }
  matrix operator*(matrix rhs){
    return matrix(*this)*=rhs;
  }
  matrix operator+=(matrix rhs){
    for(int i=0;i<rhs.height;++i){
      for(int j=0;j<rhs.width;++j){
        (*this)[i][j]+=rhs[i][j];
      }
    }
    return (*this);
  }
  matrix operator*=(matrix rhs){
    matrix<T> res(height,rhs.width,0);
    for(int i=0;i<this->height;++i){
      for(int j=0;j<rhs.width;++j){
        for(int k=0;k<this->width;++k){
          res[i][j]+=(*this)[i][k]*rhs[k][j];
        }
      }
    }
    return (*this)=res;
  }
  matrix identity(int n){
    matrix res(n,n);
    for(int i=0;i<n;++i){
      res[i][i]=1;
    }
    return res;
  }
  matrix pow(i64 k){
    int n=(*this).height;
    matrix res=identity(n),now=(*this);
    while(k>0){
      if(k%2==1){
        res*=now;
      }
      now*=now;
      k/=2;
    }
    return (*this)=res;
  }
};
template<typename T> struct comb{
  vector<T> dat,idat;
  comb(int mx=3000000):dat(mx+1,1),idat(mx+1,1){
    for(int i=1;i<=mx;++i){
      dat[i]=dat[i-1]*i;
    }
    idat[mx]/=dat[mx];
    for(int i=mx;i>0;--i){
      idat[i-1]=idat[i]*i;
    }
  }
  T operator()(int n,int k){
    if(n<0||k<0||n<k){
      return 0;
    }
    return dat[n]*idat[k]*idat[n-k];
  }
};
int main(){
  constexpr u64 mod=998244353;
  typedef modint<mod> mint;
  string S;
  int K;
  cin>>S>>K;
  int N=S.size()/2;
  vector<vector<vector<mint>>> dp(2*N+1,vector<vector<mint>> (2*N+5,vector<mint> (2*N+5)));
  dp[0][0][0]=1;
  for(int i=0;i<2*N;++i){
    for(int j=0;j<=2*N;++j){
      for(int k=0;k<=2*N;++k){
        if(S[i]=='('){
          dp[i+1][j+1][k]+=dp[i][j][k];
          if(0<j){
            dp[i+1][j-1][k+1]+=dp[i][j][k];
          }
        }
        else{
          dp[i+1][j+1][k+1]+=dp[i][j][k];
          if(0<j){
            dp[i+1][j-1][k]+=dp[i][j][k];
          }
        }
      }
    }
  }
  matrix<mint> A(N+1,N+1),B(N+1,1);
  B[0][0]=1;
  for(int i=0;i<=N;++i){
    A[i][i]=N*(2*N-1)-i*i-(N-i)*(N-i);
    if(0<i){
      A[i-1][i]=i*i;
    }
    if(i<N){
      A[i+1][i]=(N-i)*(N-i);
    }
  }
  B=A.pow(K)*B;
  mint ans=0;
  comb<mint> C;
  for(int i=0;i<=N;++i){
    ans+=dp[2*N][0][2*i]*B[i][0]/(C(N,i)^2);
  }
  cout<<ans<<endl;
}
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