結果

問題 No.718 行列のできるフィボナッチ数列道場 (1)
コンテスト
ユーザー Red_Black_GPGPU
提出日時 2019-12-11 21:52:47
言語 C++11（廃止可能性あり）
(gcc 13.3.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 5,435 bytes
コンパイル時間 2,983 ms
コンパイル使用メモリ 164,612 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-06-24 08:03:09
合計ジャッジ時間 2,549 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 20
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 # 

#include "bits/stdc++.h"
using namespace std;
#define REP(i, n) for(ll i = 0;i < n;i++)
#define ll long long
#define MOD 1000000007

ll n,k,x,y;

class modint {
public:
  long long value;
  //+
	const modint operator + (modint mtmp) const{
    modint mdnt;
    mdnt.value=(this->value+mtmp.value);
    if (mdnt.value>=MOD)mdnt.value-=MOD;
    return mdnt;
	}
	const modint operator + (long long ltmp) const{
    modint mdnt;
    long long tmp=ltmp%MOD;
    if (tmp<0)tmp+=MOD;
    mdnt.value=(this->value+tmp);
    if (mdnt.value>=MOD)mdnt.value-=MOD;
    return mdnt;
	}
  //-
	const modint operator - (modint mtmp) const{
    modint mdnt;
    mdnt.value=(this->value-mtmp.value+MOD);
    if (mdnt.value>=MOD)mdnt.value-=MOD;
    return mdnt;
	}
	const modint operator - (long long ltmp) const{
    modint mdnt;
    long long tmp=ltmp%MOD;
    if (tmp<0)tmp+=MOD;
    mdnt.value=(this->value-tmp+MOD);
    if (mdnt.value>=MOD)mdnt.value-=MOD;
    return mdnt;
	}
  //*
	const modint operator * (modint mtmp) const{
    modint mdnt;
    mdnt.value=(this->value*mtmp.value)%MOD;
    return mdnt;
	}
	const modint operator * (long long ltmp) const{
    modint mdnt;
    long long ltmpm=ltmp%MOD;
    if (ltmpm<0)ltmpm+=MOD;
    mdnt.value=(this->value*ltmpm)%MOD;
    return mdnt;
	}
  ///
	const modint operator / (long long ltmp) const{
    modint mdnt;
    long long ltmpm=ltmp%MOD;
    if (ltmpm<0)ltmpm+=MOD;
    long long mdnv=this->value;

    long long x0=MOD,x1=ltmpm,x2,n0=0LL,n1=1LL,n2,t=mdnv%ltmpm,m,ans;
    if (t==0){
      mdnt.value=mdnv/ltmpm;
      return mdnt;
    } 
      for(int i=0;i<900;i++){
        m=x0/x1;
        x2=x0-x1*m;
        n2=(n0-m*n1)%MOD;
        if (x2==1){
          ans=(n2+MOD)%MOD;
          break;
        }
        x0=x1;x1=x2;
        n0=n1;n1=n2;
      }
    mdnt.value=(mdnv+((t*ans)%MOD)*ltmpm-t)/ltmpm;
    return mdnt;
  }
	const modint operator / (modint mtmp) const{
    return (*this)/mtmp.value;
	}
  //%
	const modint operator % (long long ltmp) const{
    modint mdnt;
    mdnt.value=(this->value%ltmp);
    return mdnt;
	}
  //代入演算子のオーバーロード
  modint &operator = (const modint mtmp) 
  {
      this->value = mtmp.value;
      return *this;
  }
  modint &operator = (const long long ltmp) 
  {
      this->value = ltmp%MOD;
      if ((this->value)<0)this->value+=MOD;
      return *this;
  }
  //+=
  modint &operator += (const modint mtmp) 
  {
      this->value = (this->value+mtmp.value);
      if (this->value>=MOD)this->value-=MOD;
      return *this;
  }
  modint &operator += (long long ltmp) 
  {
      long long tmp=ltmp%MOD;
      if (tmp<0)tmp+=MOD;
      this->value=(this->value+tmp);
      if (this->value>=MOD)this->value-=MOD;
      return *this;
  }
  //-=
  modint &operator -= (const modint mtmp) 
  {
      this->value = (this->value-mtmp.value+MOD);
      if (this->value>=MOD)this->value-=MOD;
      return *this;
  }
  modint &operator -= (long long ltmp) 
  {
      long long tmp=ltmp%MOD;
      if (tmp<0)tmp+=MOD;
      this->value=(this->value-tmp+MOD);
      if (this->value>=MOD)this->value-=MOD;
      return *this;
  }
  //*=
  modint &operator *= (const modint mtmp) 
  {
      this->value = this->value*mtmp.value%MOD;
      return *this;
  }
  modint &operator *= (long long ltmp) 
  {
      this->value = this->value*(ltmp%MOD)%MOD;
      if (this->value<0)this->value+=MOD;
      return *this;
  }
  ///=
  modint &operator /= (const modint mtmp) 
  {
      modint tmp=(*this)/mtmp.value;
      this->value = tmp.value;
      return *this;
  }
  modint &operator /= (long long ltmp) 
  {
      modint tmp=(*this)/ltmp;
      this->value = tmp.value;
      return *this;
  }
  //%=
  modint &operator %= (long long ltmp) 
  {
      this->value%=ltmp;
      return *this;
  }
  //exp関数
  //aのn乗 mod c
  modint exp(long long n){
    long long ans=1LL,aa=this->value,beki=n;
    for(int i=0;i<64;i++){
      if (beki%2==1) ans=ans*aa%MOD;
      aa=aa*aa%MOD;
      beki/=2;
      if (beki==0)break;
    }
    modint mdnt;
    mdnt.value=ans;
    return mdnt;
  }
  //friend ostream& operator << (ostream& os, const modint& m);
};

ostream& operator << (ostream& os, const modint& m)
{
  os << m.value;
  return os;
}







using vi = vector<modint>; // intの1次元の型に vi という別名をつける
using vvi = vector<vi>; // intの2次元の型に vvi という別名をつける





//行列累乗
void matmul(vvi &C,vvi A,vvi B)
{
	REP(i,k){	
		REP(j,k){	
			C[i][j]=0;
			REP(l,k){
				C[i][j]=C[i][j]+A[l][j]*B[i][l];
				//C[i][j]%=M;
			}
		}
	}
}

void matpow(vvi &matans,vvi &imat,ll num){
  //vvi matans(k, vi(k,0));  // k * k の正方行列
  vvi updmat(k, vi(k));  // k * k の正方行列
  REP(i,k) matans[i][i]=1;//単位行列 I
  REP(i,k)REP(j,k)updmat[i][j]=imat[i][j];
	while(num)
	{
		if (num%2==1)
		{
			matmul(matans,matans,updmat);
		}
		num/=2;
		matmul(updmat,updmat,updmat);
	}
	return;
}




int main(){
  modint ans;
  ans=0;
  cin >> n;

		k=4;
  	vvi mat2d(k, vi(k));  // k * k の正方行列
		mat2d[0][0]=1;
		mat2d[1][0]=1;
		mat2d[2][0]=2;
		mat2d[0][1]=1;
    mat2d[1][1]=0;
    mat2d[2][1]=0;
		mat2d[0][2]=1;
		mat2d[1][2]=0;
		mat2d[2][2]=1;

    mat2d[0][3]=1;
    mat2d[3][3]=1;

  	vvi ansmat(k, vi(k));  // k * k の正方行列
		matpow(ansmat,mat2d,n);
    ans=ansmat[0][3]*1+ansmat[1][3]*0+ansmat[2][3]*0+ansmat[3][3]*0;

  cout<<ans<<endl;
  return 0;
}
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