#851334 (C++17(gcc12)) No.2974 関数の芽

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結果

問題	No.2974 関数の芽
コンテスト
ユーザー	👑 p-adic
提出日時	2023-03-20 20:01:33
言語	C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
結果	AC
実行時間	261 ms / 2,000 ms
コード長	9,569 bytes
コンパイル時間	11,502 ms
コンパイル使用メモリ	292,256 KB
最終ジャッジ日時	2025-02-11 15:41:14
ジャッジサーバーID （参考情報）	judge2 / judge4
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ファイルパターン	結果
other	AC * 24
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ソースコード

raw source code
#pragma GCC optimize ( "O3" )
#pragma GCC optimize( "unroll-loops" )
#pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
#include<bits/stdc++.h>
using namespace std;

using ll = long long;

#define MAIN main
#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 FOR_ITR( ARRAY , ITR , END ) for( auto ITR = ARRAY .begin() , END = ARRAY .end() ; ITR != END ; ITR ++ )
#define QUIT return 0
#define COUT( ANSWER ) cout << ( ANSWER ) << "\n"

// 通常の二分探索その１
// EXPRESSIONがANSWERの狭義単調増加関数の時、EXPRESSION >= TARGETを満たす最小の整数を返す。
// 広義単調増加関数を扱いたい時は等号成立の処理を消す。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  ll ANSWER;								\
  {									\
    ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM;				\
    ll VARIABLE_FOR_BINARY_SEARCH_U = MAXIMUM;				\
    ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
    ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH; \
    while( VARIABLE_FOR_BINARY_SEARCH_L != VARIABLE_FOR_BINARY_SEARCH_U ){ \
      VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \
      if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH == 0 ){		\
	found = true;							\
	break;								\
      } else {								\
	if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH > 0 ){		\
	  VARIABLE_FOR_BINARY_SEARCH_U = ANSWER;			\
	} else {							\
	  VARIABLE_FOR_BINARY_SEARCH_L = ANSWER + 1;			\
	}								\
	ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
      }									\
    }									\
  }									\

// 通常の二分探索その３
// EXPRESSIONがANSWERの狭義単調減少関数の時、EXPRESSION >= TARGETを満たす最大の整数を返す。
// 広義単調減少関数を扱いたい時は等号成立の処理を消す。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  ll ANSWER;								\
  {									\
    ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM;				\
    ll VARIABLE_FOR_BINARY_SEARCH_U = MAXIMUM;				\
    ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
    ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH; \
    while( VARIABLE_FOR_BINARY_SEARCH_L != VARIABLE_FOR_BINARY_SEARCH_U ){ \
      VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \
      if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH == 0 ){		\
	found = true;							\
	break;								\
      } else {								\
	if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH > 0 ){		\
	  VARIABLE_FOR_BINARY_SEARCH_L = ANSWER;			\
	} else {							\
	  VARIABLE_FOR_BINARY_SEARCH_U = ANSWER - 1;			\
	}								\
	ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
      }									\
    }									\
  }									\
  
template <typename T , int N>
class BIT
{
private:
  T m_fenwick[N + 1];

public:
  inline BIT();
  BIT( const T ( & a )[N] );

  inline void Set( const int& i , const T& n );

  inline BIT<T,N>& operator+=( const T ( & a )[N] );
  void Add( const int& i , const T& n );

  T InitialSegmentSum( const int& i_final );
  inline T IntervalSum( const int& i_start , const int& i_final );
  
};

template <typename T , int N> inline BIT<T,N>::BIT() : m_fenwick() {}
template <typename T , int N>
BIT<T,N>::BIT( const T ( & a )[N] ) : m_fenwick()
{

  for( int j = 1 ; j <= N ; j++ ){

    T& fenwick_j = m_fenwick[j];
    int i = j - 1;
    fenwick_j = a[i];
    int i_lim = j - ( j & -j );

    while( i != i_lim ){

      fenwick_j += m_fenwick[i];
      i -= ( i & -i );

    }

  }

}

template <typename T , int N> inline void BIT<T,N>::Set( const int& i , const T& n ) { Add( i , n - IntervalSum( i , i ) ); }

template <typename T , int N> inline BIT<T,N>& BIT<T,N>::operator+=( const T ( & a )[N] ) { for( int i = 0 ; i < N ; i++ ){ Add( i , a[i] ); } return *this; }

template <typename T , int N>
void BIT<T,N>::Add( const int& i , const T& n )
{
  
  int j = i + 1;

  while( j <= N ){

    m_fenwick[j] += n;
    j += ( j & -j );

  }

  return;
  
}

template <typename T , int N> 
T BIT<T,N>::InitialSegmentSum( const int& i_final )
{

  T sum = 0;
  int j = ( i_final < N ? i_final : N - 1 ) + 1;

  while( j > 0 ){

    sum += m_fenwick[j];
    j -= j & -j;
    
  }

  return sum;
  
}

template <typename T , int N> inline T BIT<T,N>::IntervalSum( const int& i_start , const int& i_final ) { return InitialSegmentSum( i_final ) - InitialSegmentSum( i_start - 1 ); }

template <typename T , int N>
class IntervalAddBIT
{
private:
  // 母関数の微分の負の階差数列（(i-1)a_{i-1} - ia_i）の管理
  BIT<T,N> m_bit_0;
  // 階差数列（a_i - a_{i-1}）の管理
  BIT<T,N> m_bit_1;

public:
  inline IntervalAddBIT();
  inline IntervalAddBIT( const T ( & a )[N] );

  inline void Set( const int& i , const T& n );

  inline IntervalAddBIT<T,N>& operator+=( const T ( & a )[N] );
  inline void Add( const int& i , const T& n );
  inline void IntervalAdd( const int& i_start , const int& i_final , const T& n );

  inline T InitialSegmentSum( const int& i_final );
  inline T IntervalSum( const int& i_start , const int& i_final );
  
};

template <typename T , int N> inline IntervalAddBIT<T,N>::IntervalAddBIT() : m_bit_0() , m_bit_1() {}
template <typename T , int N> inline IntervalAddBIT<T,N>::IntervalAddBIT( const T ( & a )[N] ) : m_bit_0() , m_bit_1() { operator+=( a ); }

template <typename T , int N> inline void IntervalAddBIT<T,N>::Set( const int& i , const T& n ) { Add( i , n - IntervalSum( i , i ) ); }

template <typename T , int N> inline IntervalAddBIT<T,N>& IntervalAddBIT<T,N>::operator+=( const T ( & a )[N] ) { for( int i = 0 ; i < N ; i++ ){ Add( i , a[i] ); } return *this; }

template <typename T , int N> inline void IntervalAddBIT<T,N>::Add( const int& i , const T& n ) { IntervalAdd( i , i , n ); }

template <typename T , int N> inline void IntervalAddBIT<T,N>::IntervalAdd( const int& i_start , const int& i_final , const T& n ) { m_bit_0.Add( i_start , - ( i_start - 1 ) * n ); m_bit_0.Add( i_final + 1 , i_final * n ); m_bit_1.Add( i_start , n ); m_bit_1.Add( i_final + 1 , - n ); }


template <typename T , int N> inline T IntervalAddBIT<T,N>::InitialSegmentSum( const int& i_final ) { return m_bit_0.InitialSegmentSum( i_final ) + i_final * m_bit_1.InitialSegmentSum( i_final ); }

template <typename T , int N> inline T IntervalAddBIT<T,N>::IntervalSum( const int& i_start , const int& i_final ) { return InitialSegmentSum( i_final ) - InitialSegmentSum( i_start - 1 ); }


int MAIN()
{
  UNTIE;
  CEXPR( int , bound_Q , 100000 );
  CIN_ASSERT( Q , 1 , bound_Q );
  CEXPR( ll , bound , 1000000000 );
  ll KM[bound_Q][2];
  ll LN[bound_Q][2];
  ll X[bound_Q];
  map<ll,int> X_inv{};
  X_inv[-bound-1];
  X_inv[bound+1];
  FOR( q , 0 , Q ){
    CIN_ASSERT( Kq , -bound , bound );
    CIN_ASSERT( Lq , -bound , bound );
    CIN_ASSERT( Mq , -bound , bound );
    CIN_ASSERT( Nq , -bound , bound );
    CIN_ASSERT( Xq , -bound , bound );
    ll ( &KMq )[2] = KM[q];
    ll ( &LNq )[2] = LN[q];
    KMq[0] = Kq;
    LNq[0] = Lq;
    KMq[1] = Mq;
    LNq[1] = Nq;
    X_inv[X[q] = Xq];
  }
  ll TheAtsuX[bound_Q+2];
  int i_max = -1;
  FOR_ITR( X_inv , itr , end ){
    TheAtsuX[itr->second = ++i_max] = itr->first;
  }
  IntervalAddBIT<ll,bound_Q+2> FGL[2][2] = {};
  IntervalAddBIT<ll,bound_Q+2> FGR[2][2] = {};
  FOR( q , 0 , Q ){
    ll ( &KMq )[2] = KM[q];
    ll ( &LNq )[2] = LN[q];
    FOR( j , 0 , 2 ){
      ll& KMqj = KMq[j];
      ll& LNqj = LNq[j];
      IntervalAddBIT<ll,bound_Q+2> ( &FGLj )[2] = FGL[j];
      IntervalAddBIT<ll,bound_Q+2> ( &FGRj )[2] = FGR[j];
      if( KMqj == 0 ){
	if( LNqj > 0 ){
	  FGLj[0].IntervalAdd( 0 , i_max , LNqj );
	  FGRj[0].IntervalAdd( 0 , i_max , LNqj );
	}
      } else if( KMqj > 0 ){
	bool found = false;
	BS1( i , 0 , i_max , KMqj * TheAtsuX[i] + LNqj , 0 );
	if( found ){
	  FGLj[0].IntervalAdd( i + 1 , i_max , LNqj );
	  FGLj[1].IntervalAdd( i + 1 , i_max , KMqj );
	} else {
	  FGLj[0].IntervalAdd( i , i_max , LNqj );
	  FGLj[1].IntervalAdd( i , i_max , KMqj );
	}
	FGRj[0].IntervalAdd( i , i_max , LNqj );
	FGRj[1].IntervalAdd( i , i_max , KMqj );
      } else {
	bool found = false;
	BS3( i , 0 , i_max , KMqj * TheAtsuX[i] + LNqj , 0 );
	if( found ){
	  FGRj[0].IntervalAdd( 0 , i - 1 , LNqj );
	  FGRj[1].IntervalAdd( 0 , i - 1 , KMqj );
	} else {
	  FGRj[0].IntervalAdd( 0 , i , LNqj );
	  FGRj[1].IntervalAdd( 0 , i , KMqj );
	}
	FGLj[0].IntervalAdd( 0 , i , LNqj );
	FGLj[1].IntervalAdd( 0 , i , KMqj );
      }
    }
    IntervalAddBIT<ll,bound_Q+2> ( &FL )[2] = FGL[0];
    IntervalAddBIT<ll,bound_Q+2> ( &FR )[2] = FGR[0];
    IntervalAddBIT<ll,bound_Q+2> ( &GL )[2] = FGL[1];
    IntervalAddBIT<ll,bound_Q+2> ( &GR )[2] = FGR[1];
    int& i = X_inv[X[q]];
    if(
       FL[0].IntervalSum( i , i ) == GL[0].IntervalSum( i , i ) &&
       FL[1].IntervalSum( i , i ) == GL[1].IntervalSum( i , i ) &&
       FR[1].IntervalSum( i , i ) == GR[1].IntervalSum( i , i )
       ){
      COUT( "Yes" );
    } else {
      COUT( "No" );
    }
  }
  QUIT;
}
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結果

ソースコード
