結果

問題 No.891 隣接3項間の漸化式
ユーザー eQe
提出日時 2025-01-22 19:56:48
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 6,326 bytes
コンパイル時間 7,257 ms
コンパイル使用メモリ 333,704 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2025-01-22 19:56:57
合計ジャッジ時間 6,968 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 39
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>
#include<atcoder/all>
using namespace std;
namespace my{
using ml=atcoder::modint1000000007;
auto&operator>>(istream&i,ml&x){int t;i>>t;x=t;return i;}
auto&operator<<(ostream&o,const ml&x){return o<<(int)x.val();}
#define done(...) return pp(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__)
#define FO(n) for(ll ij=n;ij-->0;)
#define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);i<i##stop;i+=i##step)
#define fo(i,...) FO##__VA_OPT__(R)(i __VA_OPT__(,__VA_ARGS__))
#define fe(a,i,...) for(auto&&__VA_OPT__([)i __VA_OPT__(,__VA_ARGS__]):a)
#define single_testcase void solve();}int main(){my::io();my::solve();}namespace my{
void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<<fixed<<setprecision(15);}
using ll=long long;
using ull=unsigned long long;
using ulll=__uint128_t;
using lll=__int128_t;
istream&operator>>(istream&i,ulll&x){ull t;i>>t;x=t;return i;}
ostream&operator<<(ostream&o,const ulll&x){return(x<10?o:o<<x/10)<<ll(x%10);}
istream&operator>>(istream&i,lll&x){ll t;i>>t;x=t;return i;}
ostream&operator<<(ostream&o,const lll&x){return o<<string(x<0,'-')<<ulll(x>0?x:-x);}
constexpr auto range(bool s,auto...a){array<ll,3>r{0,0,1};ll I=0;((r[I++]=a),...);if(!s&&I==1)swap(r[0],r[1]);r[0]-=s;if(s)r[2]*=-1;return r;}
constexpr char newline=10;
constexpr char space=32;
lll pow(lll x,ll n){assert(n>=0);lll r=1;while(n)n&1?r*=x:r,x*=x,n>>=1;return r;}

template<ll k>auto pack_kth(const auto&...a){return get<k>(make_tuple(a...));}
template<class T,size_t...I>auto pack_slice_impl(index_sequence<I...>, const auto&...a){return array<T,sizeof...(I)>{get<I>(forward_as_tuple(a...))...};}
template<class T,size_t n>auto pack_slice(const auto&...a){return pack_slice_impl<T>(make_index_sequence<n>{},a...);}

template<class V>concept vectorial=is_base_of_v<vector<typename V::value_type>,V>;
template<class V>istream&operator>>(istream&i,vector<V>&v){fe(v,e)i>>e;return i;}
template<class V>ostream&operator<<(ostream&o,const vector<V>&v){fe(v,e)o<<e<<string(&e!=&v.back(),vectorial<V>?newline:space);return o;}

template<class V>struct vec:vector<V>{
  using vector<V>::vector;
  vec(const vector<V>&v){vector<V>::operator=(v);}

  template<class...A>requires(sizeof...(A)>=3)vec(A...a){const ll n=sizeof...(a)-1;auto t=pack_slice<ll,n>(a...);ll s[n];fo(i,n)s[i]=t[i];*this=make_vec(s,pack_kth<n>(a...));}
  template<class T,ll n,ll i=0>static auto make_vec(const ll(&s)[n],T x){if constexpr(i==n-1)return vec<T>(s[i],x);else{auto X=make_vec<T,n,i+1>(s,x);return vec<decltype(X)>(s[i],X);}}

  vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;}
  vec operator^(const vec&u)const{return vec{*this}^=u;}
  vec&operator+=(const vec&u){vec&v=*this;fo(i,v.size())v[i]+=u[i];return v;}
  vec&operator-=(const vec&u){vec&v=*this;fo(i,v.size())v[i]-=u[i];return v;}
  vec operator+(const vec&u)const{return vec{*this}+=u;}
  vec operator-(const vec&u)const{return vec{*this}-=u;}
  vec&operator++(){fe(*this,e)++e;return*this;}
  vec&operator--(){fe(*this,e)--e;return*this;}
  vec operator-()const{vec v=*this;fe(v,e)e=-e;return v;}

  ll size()const{return vector<V>::size();}
};
template<ll rank,class T>struct tensor_helper{using type=vec<typename tensor_helper<rank-1,T>::type>;};
template<class T>struct tensor_helper<0,T>{using type=T;};
template<ll rank,class T>using tensor=typename tensor_helper<rank,T>::type;
template<class...A>requires(sizeof...(A)>=2)vec(A...a)->vec<tensor<sizeof...(a)-2,remove_reference_t<decltype(get<sizeof...(a)-1>(declval<tuple<A...>>()))>>>;
vec(ll)->vec<ll>;

void lin(auto&...a){(cin>>...>>a);}
template<char c=space>void pp(const auto&...a){ll n=sizeof...(a);((cout<<a<<string(--n>0,c)),...);cout<<newline;}

template<class T>struct matrix:vec<vec<T>>{
  using vec<vec<T>>::vec;
  matrix()=default;
  matrix(ll h){this->resize(h,vec<T>(h));}
  matrix(ll h,ll w,T x={}){this->resize(h,vec<T>(w,x));}

  inline ll h()const{return this->size();}
  inline ll w()const{return this->size()?(*this)[0].size():0;}

  auto operator*(const matrix&a)const{return matrix{*this}*=a;}

  auto&operator*=(const matrix&a){
    assert(w()==a.h());
    matrix r(h(),a.w());
    fo(i,h())fo(k,w())fo(j,a.w())r[i][j]+=(*this)[i][k]*a[k][j];
    swap(*this,r);
    return*this;
  }

  friend vec<T>operator*(const vec<T>&v,const matrix&a){
    assert(v.size()==a.h());
    vec<T>r(a.w());
    fo(i,a.h())fo(j,a.w())r[i]+=v[i]*a[i][j];
    return r;
  }

  auto pow(ll n)const{
    matrix x{*this};
    matrix r(h());
    fo(i,h())r[i][i]=1;
    while(n)n&1?r*=x:r,x*=x,n>>=1;
    return r;
  }

  T det()const{
    assert(h()==w());
    matrix a{*this};
    bool is_neg=0;
    fo(I,h()){
      if(a[I][I]==0){
        fo(i,I+1,h()){
          if(a[i][I]!=0){
            swap(a[i],a[I]);
            is_neg^=1;
            break;
          }
        }
        if(a[I][I]==0)return 0;
      }
      fo(i,I+1,h()){
        while(a[i][I]!=0){
          ll q=a[I][I].val()/a[i][I].val();
          T minus_q{-q};
          fo(j,I,w())a[I][j]+=a[i][j]*minus_q;
          swap(a[I],a[i]);
          is_neg^=1;
        }
      }
    }

    T r=1;
    fo(I,h())r*=a[I][I];
    return r*(1-is_neg*2);
  }

  auto inner_gauss_jordan_elimination()const{
    matrix r{*this};
    ll I=0;
    T det_prime_mod=1;
    fo(J,w()){
      if(I==h())break;
      if(r[I][J]==0){
        fo(i,I+1,h()){
          if(r[i][J]!=0){
            swap(r[i],r[I]);
            det_prime_mod=-det_prime_mod;
            break;
          }
        }
        if(r[I][J]==0){
          det_prime_mod=0;
          continue;
        }
      }
      det_prime_mod*=r[I][J];
      T C=r[I][J].inv();
      fo(j,J,w())r[I][j]*=C;
      fo(i,h())if(T c=r[i][J];i!=I)fo(j,J,w())r[i][j]-=r[I][j]*c;
      ++I;
    }
    return tuple{r,I,det_prime_mod};
  }

  auto gauss_jordan_elimination()const{return get<0>(inner_gauss_jordan_elimination());}

  auto inv()const{
    assert(h()==w());
    assert(det()!=0);
    matrix a(h(),w()*2);
    fo(i,h())fo(j,w())a[i][j]=(*this)[i][j];
    fo(i,h())a[i][i+w()]=1;
    a=a.gauss_jordan_elimination();

    matrix r(h(),w());
    fo(i,h())fo(j,w())r[i][j]=a[i][j+w()];
    return r;
  }
};

single_testcase
void solve(){
  LL(a,b,N);
  if(N==0)done(0);

  matrix<ml>A{{a,b},{1,0}};
  A=A.pow(N-1);
  pp(A[0][0]);
}}
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