結果

問題 No.181 A↑↑N mod M
ユーザー 👑 p-adicp-adic
提出日時 2022-10-31 16:36:33
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 18 ms / 5,000 ms
コード長 2,887 bytes
コンパイル時間 1,976 ms
コンパイル使用メモリ 196,692 KB
最終ジャッジ日時 2025-02-08 16:21:03
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
sample AC * 6
other AC * 37
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;

using uint = unsigned int;
using ll = long long;

#define TYPE_OF( VAR ) remove_const<remove_reference<decltype( VAR )>::type >::type
#define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) 
#define CIN( LL , A ) LL A; cin >> A 
#define ASSERT( A , MIN , MAX ) assert( MIN <= A && A <= MAX ) 
#define CIN_ASSERT( A , MIN , MAX ) CIN( TYPE_OF( MAX ) , A ); ASSERT( A , MIN , MAX ) 
#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) 
#define QUIT return 0 
#define RETURN( ANSWER ) cout << ( ANSWER ) << "\n"; QUIT 
#define RESIDUE( A , P ) ( A >= 0 ? A % P : P - ( - A - 1 ) % P - 1 ) 

#define POWER( ANSWER , ARGUMENT , EXPONENT , MODULO )			\
  TYPE_OF( ARGUMENT ) ANSWER = 1;					\
  {									\
    TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT );	\
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER = ( ANSWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % MODULO;	\
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT_FOR_SQUARE_FOR_POWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % MODULO; \
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\



ll CheckBounded( const ll& A , const ll& N , const ll& bound )
{
  if( bound <= 1 ){
    return -1;
  }
  if( N == 0 ){
    return 1;
  }
  ll A_power = 1;
  ll exponent = 0;
  while( A_power < bound ){
    A_power *= A;
    exponent++;
  }
  ll answer = CheckBounded( A , N - 1 , exponent );
  if( answer != -1 ){
    POWER( A_power_new , A , answer , bound );
    answer = A_power_new;
  }
  return answer;
}

inline constexpr const ll bound_M = 2000;

ll Solve( const ll& A , const ll& N , const ll& M )
{
  if( M == 1 ){
    return 0;
  } else if( A == 1 || N == 0 ){
    return 1;
  }
  ll A_power = 1;
  vector<ll> memory{};
  memory.push_back( A_power );
  uint memory_size = 1;
  uint period;
  bool searching = true;
  while( searching ){
    A_power = ( A_power * A ) % M;
    FOR( i , 0 , memory_size ){
      if( A_power == memory[i] ){
	period = memory_size - i;
	searching = false;
	break;
      }
    }
    memory.push_back( A_power );
    memory_size++;
  }
  ll answer = CheckBounded( A , N - 1 , bound_M );
  if( answer == -1 ){
    ll exponent = Solve( A , N - 1 , period ) - bound_M;
    exponent = RESIDUE( exponent , period );
    POWER( tetration , A , bound_M + exponent , M );
    answer = tetration;
  } else {
    POWER( tetration , A , answer , M );
    answer = tetration;
  }
  return answer % M;
}

int main()
{
  UNTIE;
  constexpr const ll bound = 1000000000;
  CIN_ASSERT( A , 1 , bound );
  CIN_ASSERT( N , 0 , bound );
  CIN_ASSERT( M , 1 , bound_M );
  RETURN( Solve( A , N , M ) );
}
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