#299259 (C++17) No.303 割れません

• 問題: No.303 割れません
• ユーザー: beet
• 提出日時: 2018-11-23 17:17:15
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: TLE
• 実行時間: -
• コード長: 10,985 bytes
• コンパイル時間: 2,855 ms
• コンパイル使用メモリ: 214,856 KB
• 最終ジャッジ日時: 2025-01-06 17:32:19
• ジャッジサーバーID （参考情報）: judge5 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 10 TLE * 4

ソースコード

#include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}


template<typename K>
struct Matrix{
  typedef vector<K> arr;
  typedef vector<arr> mat;
  mat dat;

  Matrix(size_t r,size_t c):dat(r,arr(c,K())){}
  Matrix(mat dat):dat(dat){}

  size_t size() const{return dat.size();};
  bool empty() const{return size()==0;};
  arr& operator[](size_t k){return dat[k];};
  const arr& operator[](size_t k) const {return dat[k];};
  
  static Matrix cross(const Matrix &A,const Matrix &B){
    Matrix res(A.size(),B[0].size());    
    for(int i=0;i<(int)A.size();i++)
      for(int j=0;j<(int)B[0].size();j++)
        for(int k=0;k<(int)B.size();k++)
          res[i][j]+=A[i][k]*B[k][j];
    return res;
  }

  static Matrix identity(size_t n){
    Matrix res(n,n);
    for(int i=0;i<(int)n;i++) res[i][i]=K(1);
    return res;
  }
  
  Matrix pow(long long n) const{
    Matrix a(dat),res=identity(size());
    while(n){
      if(n&1) res=cross(res,a);
      a=cross(a,a);      
      n>>=1;
    }
    return res;
  }

  template<typename T> using ET = enable_if<is_floating_point<T>::value>;
  template<typename T> using EF = enable_if<!is_floating_point<T>::value>;
  
  template<typename T, typename ET<T>::type* = nullptr>
  static bool is_zero(T x){return abs(x)<1e-8;}
  template<typename T, typename EF<T>::type* = nullptr>
  static bool is_zero(T x){return x==T(0);}

  static Matrix gauss_jordan(const Matrix &A,const Matrix &B){
    int n=A.size(),l=B[0].size();
    Matrix C(n,n+l);
    for(int i=0;i<n;i++){
      for(int j=0;j<n;j++)
        C[i][j]=A[i][j];      
      for(int j=0;j<l;j++)
        C[i][n+j]=B[i][j];
    }
    for(int i=0;i<n;i++){
      int p=i;
      for(int j=i;j<n;j++)
        if(abs(C[p][i])<abs(C[j][i])) p=j;
      swap(C[i],C[p]);
      if(is_zero(C[i][i])) return Matrix(0,0);
      for(int j=i+1;j<n+l;j++) C[i][j]/=C[i][i];
      for(int j=0;j<n;j++){
        if(i==j) continue;
        for(int k=i+1;k<n+l;k++)
          C[j][k]-=C[j][i]*C[i][k];
      }
    }
    Matrix res(n,l);
    for(int i=0;i<n;i++)
      for(int j=0;j<l;j++)
        res[i][j]=C[i][n+j];
    return res;
  }
  
  Matrix inv() const{
    Matrix B=identity(size());
    return gauss_jordan(*this,B);
  }
  
  K determinant() const{
    Matrix A(dat);
    K res(1);
    int n=size();
    for(int i=0;i<n;i++){
      int p=i;
      for(int j=i;j<n;j++)
        if(abs(A[p][i])<abs(A[j][i])) p=j;      
      if(i!=p) swap(A[i],A[p]),res=-res;      
      if(is_zero(A[i][i])) return K(0);      
      res*=A[i][i];
      for(int j=i+1;j<n;j++) A[i][j]/=A[i][i];
      for(int j=i+1;j<n;j++)
        for(int k=i+1;k<n;k++)
          A[j][k]-=A[j][i]*A[i][k];
    }
    return res;
  }

  static arr linear_equations(const Matrix &A,const arr &b){
    Matrix B(b.size(),1);
    for(int i=0;i<(int)b.size();i++) B[i][0]=b[i];
    Matrix tmp=gauss_jordan(A,B);
    arr res(tmp.size());
    for(int i=0;i<(int)tmp.size();i++) res[i]=tmp[i][0];
    return res;
  }
  
  static K sigma(K x,long long n){
    Matrix A(2,2);
    A[0][0]=x;A[0][1]=0;
    A[1][0]=1;A[1][1]=1;
    return A.pow(n)[1][0];
  }
};


struct bigint {  
  using ll = long long; 
  constexpr static ll base = 1000000000;
  constexpr static ll base_digits = 9;

  vector<ll> a;
  ll sign;

  bigint():sign(1){}

  bigint(ll v){
    *this=v;
  }

  bigint(const string &s){
    read(s);
  }

  void operator=(const bigint &v){
    sign=v.sign;
    a=v.a;
  }

  void operator=(ll v){
    sign=1;
    if(v<0) sign=-1,v=-v;
    for(;v>0;v=v/base) a.push_back(v%base);
  }

  bigint operator+(const bigint &v) const{
    if(sign==v.sign){
      bigint res=v;

      for(ll i=0,carry=0;i<(ll)max(a.size(),v.a.size())||carry;++i){
        if(i==(ll)res.a.size()) res.a.push_back(0);
        res.a[i]+=carry+(i<(ll)a.size()?a[i]:0);
        carry=res.a[i]>=base;
        if(carry) res.a[i]-=base;
      }
      return res;
    }
    return *this -(-v);
  }

  bigint operator-(const bigint &v) const{
    if(sign==v.sign){
      if(abs()>=v.abs()){
        bigint res=*this;
        for(ll i=0,carry=0;i<(ll)v.a.size()||carry;++i){
          res.a[i]-=carry+(i<(ll)v.a.size()?v.a[i]:0);
          carry=res.a[i]<0;
          if(carry) res.a[i]+=base;
        }
        res.trim();
        return res;
      }
      return -(v-*this);
    }
    return *this+(-v);
  }

  void operator*=(ll v){
    if(v<0) sign=-sign,v=-v;
    for(ll i=0,carry=0;i<(ll)a.size()|| carry;++i){
      if(i ==(ll)a.size()) a.push_back(0);
      ll cur=a[i] *(ll)v+carry;
      carry=(ll)(cur/base);
      a[i]=(ll)(cur%base);
      // asm("divl %%ecx" : "=a"(carry),"=d"(a[i]) : "A"(cur),"c"(base));
    }
    trim();
  }

  bigint operator*(ll v) const{
    bigint res=*this;
    res *=v;
    return res;
  }

  friend pair<bigint,bigint> divmod(const bigint &a1,const bigint &b1){
    ll norm=base/(b1.a.back()+1);   
    bigint a=a1.abs()*norm;
    bigint b=b1.abs()*norm;
    bigint q,r;
    q.a.resize(a.a.size());

    for(ll i=a.a.size()-1;i>=0;i--){
      r *=base;
      r+=a.a[i];
      ll s1=r.a.size()<=b.a.size() ? 0 : r.a[b.a.size()];
      ll s2=r.a.size()<=b.a.size()-1 ? 0 : r.a[b.a.size()-1];
      ll d=((ll)base*s1+s2)/b.a.back();
      r-=b*d;
      while(r<0) r+=b,--d;
      q.a[i]=d;
    }

    q.sign=a1.sign*b1.sign;
    r.sign=a1.sign;
    q.trim();
    r.trim();
    return make_pair(q,r/norm);
  }

  bigint operator/(const bigint &v) const{
    return divmod(*this,v).first;
  }

  bigint operator%(const bigint &v) const{
    return divmod(*this,v).second;
  }

  void operator/=(ll v){
    if(v<0) sign=-sign,v=-v;
    for(ll i=(ll)a.size()-1,rem=0;i>=0;--i){
      ll cur=a[i]+rem *(ll)base;
      a[i]=(ll)(cur/v);
      rem=(ll)(cur%v);
    }
    trim();
  }

  bigint operator/(ll v) const{
    bigint res=*this;
    res/=v;
    return res;
  }

  ll operator%(ll v) const{
    if(v<0) v=-v;
    ll m=0;
    for(ll i=a.size()-1;i>=0;--i) m=(a[i]+m *(ll)base)%v;
    return m*sign;
  }

  void operator+=(const bigint &v){
    *this=*this+v;
  }

  void operator-=(const bigint &v){
    *this=*this-v;
  }

  void operator*=(const bigint &v){
    *this=*this*v;
  }

  void operator/=(const bigint &v){
    *this=*this/v;
  }

  bool operator<(const bigint &v) const{
    if(sign!=v.sign) return sign<v.sign;
    if(a.size()!=v.a.size()) return a.size()*sign<v.a.size()*v.sign;
    for(ll i=a.size()-1;i>=0;i--)
      if(a[i]!=v.a[i]) return a[i]*sign<v.a[i]*sign;
    return false;
  }

  bool operator>(const bigint &v) const{
    return v<*this;
  }

  bool operator<=(const bigint &v) const{
    return !(v<*this);
  }

  bool operator>=(const bigint &v) const{
    return !(*this<v);
  }

  bool operator==(const bigint &v) const{
    return !(*this<v)&&!(v<*this);
  }

  bool operator!=(const bigint &v) const{
    return *this<v|| v<*this;
  }

  void trim(){
    while(!a.empty()&&!a.back()) a.pop_back();
    if(a.empty()) sign=1;
  }

  bool isZero() const{
    return a.empty()||(a.size()==1&&!a[0]);
  }

  bigint operator-() const{
    bigint res=*this;
    res.sign=-sign;
    return res;
  }

  bigint abs() const{
    bigint res=*this;
    res.sign*=res.sign;
    return res;
  }

  ll longValue() const{
    ll res=0;
    for(ll i=a.size()-1;i>=0;i--) res=res*base+a[i];
    return res*sign;
  }

  friend bigint gcd(const bigint &a,const bigint &b){
    return b.isZero() ? a : gcd(b,a%b);
  }

  friend bigint lcm(const bigint &a,const bigint &b){
    return a/gcd(a,b)*b;
  }

  void read(const string &s){
    sign=1;
    a.clear();
    ll pos=0;
    while(pos<(ll)s.size()&&(s[pos]=='-'|| s[pos]=='+')){
      if(s[pos]=='-') sign=-sign;
      ++pos;
    }
    for(ll i=s.size()-1;i>=pos;i-=base_digits){
      ll x=0;
      for(ll j=max(pos,i-base_digits+1);j<=i;j++) x=x*10+s[j]-'0';
      a.push_back(x);
    }
    trim();
  }

  friend istream &operator>>(istream &stream,bigint &v){
    string s;
    stream>>s;
    v.read(s);
    return stream;
  }

  friend ostream &operator<<(ostream &stream,const bigint &v){
    if(v.sign==-1) stream<<'-';
    stream<<(v.a.empty() ? 0 : v.a.back());
    for(ll i=(ll)v.a.size()-2;i>=0;--i)
      stream<<setw(base_digits)<<setfill('0')<<v.a[i];
    return stream;
  }

  static vector<ll> convert_base(const vector<ll> &a,
                                 ll old_digits,ll new_digits){
    vector<ll> p(max(old_digits,new_digits)+1);
    p[0]=1;
    for(ll i=1;i<(ll)p.size();i++) p[i]=p[i-1]*10;
    vector<ll>res;
    ll cur=0;
    ll cur_digits=0;
    for(ll i=0;i<(ll)a.size();i++){
      cur+=a[i]*p[cur_digits];
      cur_digits+=old_digits;
      while(cur_digits>=new_digits){
        res.push_back(signed(cur%p[new_digits]));
        cur/=p[new_digits];
        cur_digits-=new_digits;
      }
    }
    res.push_back((signed)cur);
    while(!res.empty()&&!res.back()) res.pop_back();
    return res;
  }

  typedef vector<ll> vll;

  static vll karatsubaMultiply(const vll &a,const vll &b){
    ll n=a.size();
    vll res(n+n);
    if(n<=32){
      for(ll i=0;i<n;i++)
        for(ll j=0;j<n;j++)
          res[i+j]+=a[i]*b[j];
      return res;
    }

    ll k=n>>1;
    vll a1(a.begin(),a.begin()+k);
    vll a2(a.begin()+k,a.end());
    vll b1(b.begin(),b.begin()+k);
    vll b2(b.begin()+k,b.end());

    vll a1b1=karatsubaMultiply(a1,b1);
    vll a2b2=karatsubaMultiply(a2,b2);

    for(ll i=0;i<k;i++) a2[i]+=a1[i];
    for(ll i=0;i<k;i++) b2[i]+=b1[i];

    vll r=karatsubaMultiply(a2,b2);
    for(ll i=0;i<(ll)a1b1.size();i++) r[i]-=a1b1[i];
    for(ll i=0;i<(ll)a2b2.size();i++) r[i]-=a2b2[i];

    for(ll i=0;i<(ll)r.size();i++) res[i+k]+=r[i];
    for(ll i=0;i<(ll)a1b1.size();i++) res[i]+=a1b1[i];
    for(ll i=0;i<(ll)a2b2.size();i++) res[i+n]+=a2b2[i];
    return res;
  }

  bigint operator*(const bigint &v) const{
    vector<ll>a6=convert_base(this->a,base_digits,6);
    vector<ll>b6=convert_base(v.a,base_digits,6);
    vll a(a6.begin(),a6.end());
    vll b(b6.begin(),b6.end());
    while(a.size()<b.size()) a.push_back(0);
    while(b.size()<a.size()) b.push_back(0);
    while(a.size() &(a.size()-1)) a.push_back(0),b.push_back(0);
    vll c=karatsubaMultiply(a,b);
    bigint res;
    res.sign=sign*v.sign;
    for(ll i=0,carry=0;i<(ll)c.size();i++){
      ll cur=c[i]+carry;
      res.a.push_back((ll)(cur%1000000));
      carry=(ll)(cur/1000000);
    }
    res.a=convert_base(res.a,6,base_digits);
    res.trim();
    return res;
  }
};

//INSERT ABOVE HERE
signed main(){
  int l;
  cin>>l;

  if(l==2){
    cout<<3<<endl;
    cout<<"INF"<<endl;
    return 0;
  }
  cout<<l<<endl;
  
  using M = Matrix<bigint>;
  M A(2,2);
  A[0][0]=1;A[0][1]=1;
  A[1][0]=1;A[1][1]=0;
  if(l&1) cout<<A.pow(l)[1][0]<<endl;
  else{
    auto B=A.pow(l/2);
    auto X=M::cross(B,B)[1][0];
    auto Y=B[1][0];
    cout<<X-Y*Y<<endl;
  }
  return 0;
}