#427815 (C++17) No.980 Fibonacci Convolution Hard

• 問題: No.980 Fibonacci Convolution Hard
• ユーザー: beet
• 提出日時: 2020-02-09 17:19:24
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 99 ms / 2,000 ms
• コード長: 3,901 bytes
• コンパイル時間: 2,300 ms
• コンパイル使用メモリ: 211,736 KB
• 実行使用メモリ: 11,072 KB
• 最終ジャッジ日時: 2024-10-01 06:03:43
• 合計ジャッジ時間: 7,543 ms
• ジャッジサーバーID （参考情報）: judge5 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	94 ms; 10,932 KB
testcase_01	AC	96 ms; 11,028 KB
testcase_02	AC	95 ms; 10,900 KB
testcase_03	AC	90 ms; 10,956 KB
testcase_04	AC	95 ms; 11,072 KB
testcase_05	AC	97 ms; 11,004 KB
testcase_06	AC	97 ms; 10,992 KB
testcase_07	AC	96 ms; 11,000 KB
testcase_08	AC	94 ms; 10,996 KB
testcase_09	AC	92 ms; 10,988 KB
testcase_10	AC	93 ms; 10,932 KB
testcase_11	AC	99 ms; 11,072 KB
testcase_12	AC	95 ms; 11,064 KB
testcase_13	AC	96 ms; 11,052 KB
testcase_14	AC	96 ms; 10,896 KB
testcase_15	AC	96 ms; 11,036 KB
testcase_16	AC	78 ms; 11,036 KB

ソースコード

#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;

#endif
//BEGIN CUT HERE
// construct a charasteristic equation from sequence
template<typename T>
vector<T> berlekamp_massey(vector<T> &as){
  using Poly = vector<T>;
  int n=as.size();
  Poly bs({-T(1)}),cs({-T(1)});
  T y(1);
  for(int ed=1;ed<=n;ed++){
    int l=cs.size(),m=bs.size();
    T x(0);
    for(int i=0;i<l;i++) x+=cs[i]*as[ed-l+i];
    bs.emplace_back(0);
    m++;
    if(x==T(0)) continue;
    T freq=x/y;
    if(m<=l){
      for(int i=0;i<m;i++)
        cs[l-1-i]-=freq*bs[m-1-i];
      continue;
    }
    auto ts=cs;
    cs.insert(cs.begin(),m-l,T(0));
    for(int i=0;i<m;i++) cs[m-1-i]-=freq*bs[m-1-i];
    bs=ts;
    y=x;
  }
  return cs;
}
//END CUT HERE
#ifndef call_from_test

#define call_from_test
#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
#endif
//BEGIN CUT HERE
template<typename T,T MOD = 1000000007>
struct Mint{
  static constexpr T mod = MOD;
  T v;
  Mint():v(0){}
  Mint(signed v):v(v){}
  Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}

  Mint pow(long long k){
    Mint res(1),tmp(v);
    while(k){
      if(k&1) res*=tmp;
      tmp*=tmp;
      k>>=1;
    }
    return res;
  }

  static Mint add_identity(){return Mint(0);}
  static Mint mul_identity(){return Mint(1);}

  Mint inv(){return pow(MOD-2);}

  Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
  Mint& operator/=(Mint a){return (*this)*=a.inv();}

  Mint operator+(Mint a) const{return Mint(v)+=a;}
  Mint operator-(Mint a) const{return Mint(v)-=a;}
  Mint operator*(Mint a) const{return Mint(v)*=a;}
  Mint operator/(Mint a) const{return Mint(v)/=a;}

  Mint operator-() const{return v?Mint(MOD-v):Mint(v);}

  bool operator==(const Mint a)const{return v==a.v;}
  bool operator!=(const Mint a)const{return v!=a.v;}
  bool operator <(const Mint a)const{return v <a.v;}

  static Mint comb(long long n,int k){
    Mint num(1),dom(1);
    for(int i=0;i<k;i++){
      num*=Mint(n-i);
      dom*=Mint(i+1);
    }
    return num/dom;
  }
};
template<typename T,T MOD> constexpr T Mint<T, MOD>::mod;
template<typename T,T MOD>
ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}
//END CUT HERE
#ifndef call_from_test

//INSERT ABOVE HERE
signed ABC127_E(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int h,w,k;
  cin>>h>>w>>k;
  using M = Mint<int>;

  M ans{0};
  for(int d=1;d<h;d++)
    ans+=M(d)*M(h-d)*M(w)*M(w);

  for(int d=1;d<w;d++)
    ans+=M(d)*M(w-d)*M(h)*M(h);

  ans*=M::comb(h*w-2,k-2);
  cout<<ans<<endl;
  return 0;
}
/*
  verified on 2019/06/12
  https://atcoder.jp/contests/abc127/tasks/abc127_e
*/

signed main(){
  //ABC127_E();
  return 0;
}
#endif

#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
#endif
//BEGIN CUT HERE
struct FastIO{
  FastIO(){
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
}fastio_beet;
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif

#undef call_from_test

signed YUKI_980(){
  using M = Mint<int>;
  int p;
  cin>>p;

  const int n = 100;
  vector<M> as(n);
  as[0]=M(0);
  as[1]=M(0);
  as[2]=M(1);
  for(int i=3;i<n;i++) as[i]=M(p)*as[i-1]+as[i-2];

  vector<M> bs(n,M(0));
  for(int s=0;s<n;s++)
    for(int t=0;s+t<n;t++)
      bs[s+t]+=as[s]*as[t];

  auto cs=berlekamp_massey(bs);
  for(auto &c:cs) c/=cs.back();
  reverse(cs.begin(),cs.end());

  const int MAX = 2e6 + 100;
  vector<M> dp(MAX,0);
  for(int i=0;i<n;i++) dp[i]=bs[i];
  for(int i=n;i<MAX;i++)
    for(int j=0;j<(int)cs.size();j++)
      dp[i]-=dp[i-j]*cs[j];

  int q;
  cin>>q;
  for(int i=0;i<q;i++){
    int k;
    cin>>k;
    cout<<dp[k]<<"\n";
  }
  return 0;
}
/*
  verified on 2020/02/09
  https://yukicoder.me/problems/no/980
*/

signed main(){
  YUKI_980();
  return 0;
}
#endif