#816981 (C++17) No.2177 Recurring ab

• 問題: No.2177 Recurring ab
• ユーザー: 👑 p-adic
• 提出日時: 2022-11-16 23:36:47
• 言語: C++17 (gcc 13.2.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 2,289 bytes
• コンパイル時間: 3,568 ms
• コンパイル使用メモリ: 201,456 KB
• 実行使用メモリ: 4,348 KB
• 最終ジャッジ日時: 2023-10-17 20:53:18
• 合計ジャッジ時間: 2,854 ms
• ジャッジサーバーID （参考情報）: judge15 / judge12

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 4,348 KB
testcase_01	AC	2 ms; 4,348 KB
testcase_02	AC	2 ms; 4,348 KB
testcase_03	AC	2 ms; 4,348 KB
testcase_04	AC	2 ms; 4,348 KB
testcase_05	AC	2 ms; 4,348 KB
testcase_06	AC	2 ms; 4,348 KB
testcase_07	AC	2 ms; 4,348 KB
testcase_08	AC	2 ms; 4,348 KB
testcase_09	AC	2 ms; 4,348 KB
testcase_10	AC	2 ms; 4,348 KB
testcase_11	AC	2 ms; 4,348 KB
testcase_12	AC	2 ms; 4,348 KB
testcase_13	AC	2 ms; 4,348 KB
testcase_14	AC	2 ms; 4,348 KB
testcase_15	AC	2 ms; 4,348 KB
testcase_16	AC	2 ms; 4,348 KB
testcase_17	AC	2 ms; 4,348 KB
testcase_18	AC	2 ms; 4,348 KB
testcase_19	AC	2 ms; 4,348 KB
testcase_20	AC	2 ms; 4,348 KB

ソースコード

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

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 CEXPR( LL , BOUND , VALUE ) constexpr const LL BOUND = VALUE 
#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 CHECK_REDUNDANT_INPUT string VARIABLE_FOR_CHECK_REDUNDANT_INPUT = ""; cin >> VARIABLE_FOR_CHECK_REDUNDANT_INPUT; assert( VARIABLE_FOR_CHECK_REDUNDANT_INPUT == "" ); assert( ! cin );
// #define CHECK_REDUNDANT_INPUT string VARIABLE_FOR_CHECK_REDUNDANT_INPUT = ""; getline( cin , VARIABLE_FOR_CHECK_REDUNDANT_INPUT ); assert( VARIABLE_FOR_CHECK_REDUNDANT_INPUT == "" ); assert( ! cin );

int main()
{
  CEXPR( ll , bound_N , 100000000 );
  CIN_ASSERT( N , 1 , bound_N );
  // CHECK_REDUNDANT_INPUT;
  // (pa+b)/(p^2-1) > 1/N
  // <=> N(pa+b) > p^2-1
  // <=> p^2 - Nap - (Nb+1) < 0
  // <=> Na/2 - (sqrt((Na)^2+4(Nb+1)))/2 < p < Na/2 + (sqrt((Na)^2+4(Nb+1)))/2
  ll answer = 0;
  ll Na = -N;
  CEXPR( ll , bound_ab , 10 );
  CEXPR( ll , bound_p , 1000000000 );
  FOR( a , 0 , bound_ab ){
    Na += N;
    ll Na2 = Na * Na;
    double Na_half = Na / 2.0;
    ll Nb_plus = -N + 1;
    FOR( b , 0 , bound_ab ){
      Nb_plus += N;
      if( a != b ){
	double r = sqrt( Na2 + 4 * Nb_plus ) / 2.0;
	ll low = Na_half - r;
	if( low * low - Na * low - Nb_plus >= 0 ){
	  low++;
	}
	low = max( max( max( a , b ) + 1 , (ll)2 ) , low );
	ll upp = Na_half + r;
	if( upp * upp - Na * upp - Nb_plus >= 0 ){
	  upp--;
	}
	upp = min( bound_p , upp );
	if( low <= upp ){
	  answer += upp - low + 1;
	  // デバッグ用
	  // for( ll p = low ; p <= upp ; p++ ){
	  //   cout << "(p,a,b) = (" << p << "," << a << "," << b << ")" << endl;
	  //   assert( ( p * a + b ) * N > p * p - 1 );
	  //   assert( 2 <= p && a <= p - 1 && b <= p - 1 && p <= bound_p );
	  // }
	}
      }
    }
  }
  RETURN( answer );
}