結果
問題 | No.2083 OR Subset |
ユーザー | 👑 p-adic |
提出日時 | 2024-03-11 13:16:11 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 865 ms / 3,000 ms |
コード長 | 42,934 bytes |
コンパイル時間 | 8,167 ms |
コンパイル使用メモリ | 428,728 KB |
実行使用メモリ | 198,912 KB |
最終ジャッジ日時 | 2024-09-29 21:50:26 |
合計ジャッジ時間 | 17,576 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge4 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 184 ms
101,248 KB |
testcase_01 | AC | 185 ms
101,176 KB |
testcase_02 | AC | 187 ms
101,176 KB |
testcase_03 | AC | 532 ms
152,972 KB |
testcase_04 | AC | 361 ms
129,536 KB |
testcase_05 | AC | 783 ms
189,440 KB |
testcase_06 | AC | 347 ms
126,208 KB |
testcase_07 | AC | 199 ms
103,168 KB |
testcase_08 | AC | 207 ms
104,832 KB |
testcase_09 | AC | 524 ms
152,704 KB |
testcase_10 | AC | 400 ms
134,144 KB |
testcase_11 | AC | 303 ms
120,320 KB |
testcase_12 | AC | 259 ms
112,896 KB |
testcase_13 | AC | 844 ms
197,760 KB |
testcase_14 | AC | 820 ms
194,944 KB |
testcase_15 | AC | 836 ms
195,840 KB |
testcase_16 | AC | 865 ms
198,016 KB |
testcase_17 | AC | 841 ms
197,760 KB |
testcase_18 | AC | 188 ms
101,248 KB |
testcase_19 | AC | 846 ms
198,912 KB |
ソースコード
#ifndef INCLUDE_MODE #define INCLUDE_MODE // #define REACTIVE // #define USE_GETLINE #endif #ifdef INCLUDE_MAIN IN VO Solve() { CEXPR( uint , P , 998244353 ); using MP = Mod<P>; CEXPR( int , bound_N , 5000 ); CIN_ASSERT( N , 1 , bound_N); SecondStirlingNumberCalculator<MP,bound_N+1> ssn{}; MP overlapping[N+1][N+1] = {}; overlapping[0][1] = MP::one(); overlapping[1][1] = MP::Derepresent( 2 ); FOREQ( j , 2 , N ){ overlapping[j][1] = overlapping[j-1][1] * overlapping[1][1]; } FOREQ( j , 0 , N ){ auto& overlapping_j = overlapping[j]; overlapping_j[0] = MP::one(); overlapping_j[1] -= MP::Derepresent( j ); FOREQ( i , 2 , N ){ overlapping_j[i] = overlapping_j[i-1] * overlapping_j[1]; } } MP answer{}; FOREQ( i , 0 , N ){ FOREQ( j , 0 , i ){ answer += ssn.CountDisjointCover( N , i , j ) * overlapping[j][N-i]; } } RETURN( answer ); } REPEAT_MAIN(1); #else // INCLUDE_MAIN #ifdef INCLUDE_SUB // COMPAREに使用。圧縮時は削除する。 ll Naive( int N , int M , int K ) { ll answer = N + M + K; return answer; } // COMPAREに使用。圧縮時は削除する。 ll Answer( ll N , ll M , ll K ) { // START_WATCH; ll answer = N + M + K; // // TLに準じる乱択や全探索。デフォルトの猶予は100.0[ms]。 // CEXPR( double , TL , 2000.0 ); // while( CHECK_WATCH( TL ) ){ // } return answer; } // 圧縮時は中身だけ削除する。 IN VO Experiment() { // CEXPR( int , bound , 10 ); // FOREQ( N , 0 , bound ){ // FOREQ( M , 0 , bound ){ // FOREQ( K , 0 , bound ){ // COUT( N , M , K , ":" , Naive( N , M , K ) ); // } // } // // cout << Naive( N ) << ",\n"[N==bound]; // } } // 圧縮時は中身だけ削除する。 IN VO SmallTest() { // CEXPR( int , bound , 10 ); // FOREQ( N , 0 , bound ){ // FOREQ( M , 0 , bound ){ // FOREQ( K , 0 , bound ){ // COMPARE( N , M , K ); // } // } // // COMPARE( N ); // } } #define INCLUDE_MAIN #include __FILE__ #else // INCLUDE_SUB #ifdef INCLUDE_LIBRARY /* C-x 3 C-x o C-x C-fによるファイル操作用 BFS (5KB) c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt CoordinateCompress (3KB) c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/CoordinateCompress/compress.txt DFSOnTree (11KB) c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepthFirstSearch/Tree/a.hpp Divisor (4KB) c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt IntervalAddBIT (9KB) c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/IntervalAdd/compress.txt Polynomial (21KB) c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt UnionFind (3KB) c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/UnionFindForest/compress.txt */ // VVV 常設でないライブラリは以下に挿入する。 template <uint M , typename INT> inline constexpr INT Residue( INT n ) noexcept { return move( n < 0 ? ( ( ( ( ++n ) *= -1 ) %= M ) *= -1 ) += M - 1 : n %= M ); } template <typename INT1 , typename INT2> inline constexpr INT1 Residue( INT1 n , const INT2& M ) noexcept { return move( n < 0 ? ( ( ( ( ++n ) *= -1 ) %= M ) *= -1 ) += M - 1 : n %= M ); } template <typename INT> inline constexpr INT& Residue998244353( INT& n ) noexcept { constexpr const uint trunc = ( 1 << 23 ) - 1; INT n_u = n >> 23; n &= trunc; INT n_uq = ( n_u / 7 ) / 17; n_u -= n_uq * 119; n += n_u << 23; return n < n_uq ? n += 998244353 - n_uq : n -= n_uq; } using INT_TYPE_FOR_MOD = uint; template <INT_TYPE_FOR_MOD M> class Mod; template <INT_TYPE_FOR_MOD M> class ConstantsForMod { friend class Mod<M>; private: ConstantsForMod() = delete; static constexpr const INT_TYPE_FOR_MOD g_memory_bound = 1000000; static constexpr const INT_TYPE_FOR_MOD g_memory_length = M < g_memory_bound ? M : g_memory_bound; static constexpr INT_TYPE_FOR_MOD g_M_minus = M - 1; static constexpr INT_TYPE_FOR_MOD g_M_minus_2 = M - 2; static constexpr INT_TYPE_FOR_MOD g_M_minus_2_neg = 2 - M; }; #define DECLARATION_OF_COMPARISON_FOR_MOD( FUNC ) \ inline constexpr bool operator FUNC( const Mod<M>& n ) const noexcept \ #define DECLARATION_OF_ARITHMETIC_FOR_MOD( FUNC ) \ inline constexpr Mod<M> operator FUNC( const Mod<M>& n ) const noexcept; \ #define DEFINITION_OF_COMPARISON_FOR_MOD( FUNC ) \ template <INT_TYPE_FOR_MOD M> inline constexpr bool Mod<M>::operator FUNC( const Mod<M>& n ) const noexcept { return m_n FUNC n.m_n; } \ #define DEFINITION_OF_ARITHMETIC_FOR_MOD( FUNC ) \ template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M> Mod<M>::operator FUNC( const Mod<M>& n ) const noexcept { return move( Mod<M>( *this ) FUNC ## = n ); } \ template <INT_TYPE_FOR_MOD M , typename T> inline constexpr Mod<M> operator FUNC( T n0 , const Mod<M>& n1 ) noexcept { return move( Mod<M>( move( n0 ) ) FUNC ## = n1 ); } \ template <INT_TYPE_FOR_MOD M> class Mod { protected: INT_TYPE_FOR_MOD m_n; public: inline constexpr Mod() noexcept; inline constexpr Mod( const Mod<M>& n ) noexcept; inline constexpr Mod( Mod<M>&& n ) noexcept; template <typename T> inline constexpr Mod( T n ) noexcept; inline constexpr Mod<M>& operator=( Mod<M> n ) noexcept; inline constexpr Mod<M>& operator+=( const Mod<M>& n ) noexcept; inline constexpr Mod<M>& operator-=( const Mod<M>& n ) noexcept; inline constexpr Mod<M>& operator*=( const Mod<M>& n ) noexcept; inline Mod<M>& operator/=( const Mod<M>& n ); // n>=0である場合のみサポート。計算量O(log n)で2^n倍する。 inline constexpr Mod<M>& operator<<=( int n ) noexcept; // n>=0かつMが奇数である場合のみサポート。計算量O(n)で2^{-n}倍する。 inline constexpr Mod<M>& operator>>=( int n ) noexcept; inline constexpr Mod<M>& operator++() noexcept; inline constexpr Mod<M> operator++( int ) noexcept; inline constexpr Mod<M>& operator--() noexcept; inline constexpr Mod<M> operator--( int ) noexcept; DECLARATION_OF_COMPARISON_FOR_MOD( == ); DECLARATION_OF_COMPARISON_FOR_MOD( != ); DECLARATION_OF_COMPARISON_FOR_MOD( < ); DECLARATION_OF_COMPARISON_FOR_MOD( <= ); DECLARATION_OF_COMPARISON_FOR_MOD( > ); DECLARATION_OF_COMPARISON_FOR_MOD( >= ); DECLARATION_OF_ARITHMETIC_FOR_MOD( + ); DECLARATION_OF_ARITHMETIC_FOR_MOD( - ); DECLARATION_OF_ARITHMETIC_FOR_MOD( * ); DECLARATION_OF_ARITHMETIC_FOR_MOD( / ); // n>=0である場合のみサポート。計算量O(log n)で2^n倍を返す。 inline constexpr Mod<M> operator<<( int n ) const noexcept; // n>=0かつMが奇数である場合のみサポート。計算量O(n)で2^{-n}倍を返す。 inline constexpr Mod<M> operator>>( int n ) const noexcept; inline constexpr Mod<M> operator-() const noexcept; // -1倍する。 inline constexpr Mod<M>& SignInvert() noexcept; // Mが素数である場合のみサポート。-1乗する。 inline Mod<M>& Invert(); // Mが素数であるかexponent>=0である場合にのみサポート。exponent乗する。 template <typename INT> inline constexpr Mod<M>& Power( INT exponent ); // グローバルスコープでswapを定義するためのもの。 inline constexpr void swap( Mod<M>& n ) noexcept; inline constexpr const INT_TYPE_FOR_MOD& Represent() const noexcept; // 0 <= n < Mの場合のみサポート。 static inline constexpr Mod<M> Derepresent( const INT_TYPE_FOR_MOD& n ) noexcept; // Mが素数かつn < g_memory_lengthである場合のみサポート。 static inline const Mod<M>& Inverse( const INT_TYPE_FOR_MOD& n ) noexcept; // n < g_memory_lengthである場合のみサポート。 static inline const Mod<M>& Factorial( const INT_TYPE_FOR_MOD& n ) noexcept; // Mが素数かつn < g_memory_lengthである場合のみサポート。 static inline const Mod<M>& FactorialInverse( const INT_TYPE_FOR_MOD& n ) noexcept; // Mが素数かつn < g_memory_lengthである場合のみサポート。 static inline Mod<M> Combination( const INT_TYPE_FOR_MOD& n , const INT_TYPE_FOR_MOD& i ) noexcept; static inline const Mod<M>& zero() noexcept; static inline const Mod<M>& one() noexcept; private: template <typename INT> inline constexpr Mod<M>& PositivePower( INT exponent ) noexcept; template <typename INT> inline constexpr Mod<M>& NonNegativePower( INT exponent ) noexcept; template <typename T> inline constexpr Mod<M>& Ref( T&& n ) noexcept; // 0 <= n < Mの場合のみサポート。 static inline constexpr INT_TYPE_FOR_MOD& Normalise( INT_TYPE_FOR_MOD& n ) noexcept; }; // Mが素数でありnが0でない場合にのみサポート。 template <INT_TYPE_FOR_MOD M> inline Mod<M> Inverse( const Mod<M>& n ); template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M> Inverse_constexpr( Mod<M> n ); // Mが素数であるかexponent>=0である場合にのみサポート。 template <INT_TYPE_FOR_MOD M , typename T> inline constexpr Mod<M> Power( Mod<M> n , T exponent ); template <INT_TYPE_FOR_MOD M> inline constexpr void swap( Mod<M>& n0 , Mod<M>& n1 ) noexcept; template <INT_TYPE_FOR_MOD M> inline string to_string( const Mod<M>& n ) noexcept; template <INT_TYPE_FOR_MOD M , class Traits> inline basic_istream<char,Traits>& operator>>( basic_istream<char,Traits>& is , Mod<M>& n ); template <INT_TYPE_FOR_MOD M , class Traits> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const Mod<M>& n ); template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>::Mod() noexcept : m_n() {} template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>::Mod( const Mod<M>& n ) noexcept : m_n( n.m_n ) {} template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>::Mod( Mod<M>&& n ) noexcept : m_n( move( n.m_n ) ) {} template <INT_TYPE_FOR_MOD M> template <typename T> inline constexpr Mod<M>::Mod( T n ) noexcept : m_n( Residue<M>( move( n ) ) ) { static_assert( is_constructible_v<INT_TYPE_FOR_MOD,decay_t<T> > ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>& Mod<M>::operator=( Mod<M> n ) noexcept { return Ref( m_n = move( n.m_n ) ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>& Mod<M>::operator+=( const Mod<M>& n ) noexcept { return Ref( Normalise( m_n += n.m_n ) ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>& Mod<M>::operator-=( const Mod<M>& n ) noexcept { return Ref( m_n < n.m_n ? ( m_n += M ) -= n.m_n : m_n -= n.m_n ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>& Mod<M>::operator*=( const Mod<M>& n ) noexcept { return Ref( m_n = Residue<M>( ull( m_n ) * n.m_n ) ); } template <> inline constexpr Mod<998244353>& Mod<998244353>::operator*=( const Mod<998244353>& n ) noexcept { ull m_n_copy = m_n; return Ref( m_n = move( ( m_n_copy *= n.m_n ) < 998244353 ? m_n_copy : Residue998244353( m_n_copy ) ) ); } template <INT_TYPE_FOR_MOD M> inline Mod<M>& Mod<M>::operator/=( const Mod<M>& n ) { return operator*=( Mod<M>( n ).Invert() ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>& Mod<M>::operator<<=( int n ) noexcept { assert( n >= 0 ); return *this *= Derepresent( 2 ).NonNegativePower( move( n ) ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>& Mod<M>::operator>>=( int n ) noexcept { assert( n >=0 ); while( n-- > 0 ){ ( ( m_n & 1 ) == 0 ? m_n : m_n += M ) >>= 1; } return *this; } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>& Mod<M>::operator++() noexcept { return Ref( m_n < ConstantsForMod<M>::g_M_minus ? ++m_n : m_n = 0 ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M> Mod<M>::operator++( int ) noexcept { Mod<M> n{ *this }; operator++(); return n; } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>& Mod<M>::operator--() noexcept { return Ref( m_n == 0 ? m_n = ConstantsForMod<M>::g_M_minus : --m_n ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M> Mod<M>::operator--( int ) noexcept { Mod<M> n{ *this }; operator--(); return n; } DEFINITION_OF_COMPARISON_FOR_MOD( == ); DEFINITION_OF_COMPARISON_FOR_MOD( != ); DEFINITION_OF_COMPARISON_FOR_MOD( > ); DEFINITION_OF_COMPARISON_FOR_MOD( >= ); DEFINITION_OF_COMPARISON_FOR_MOD( < ); DEFINITION_OF_COMPARISON_FOR_MOD( <= ); DEFINITION_OF_ARITHMETIC_FOR_MOD( + ); DEFINITION_OF_ARITHMETIC_FOR_MOD( - ); DEFINITION_OF_ARITHMETIC_FOR_MOD( * ); DEFINITION_OF_ARITHMETIC_FOR_MOD( / ); template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M> Mod<M>::operator<<( int n ) const noexcept { return move( Mod<M>( *this ) <<= n ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M> Mod<M>::operator>>( int n ) const noexcept { return move( Mod<M>( *this ) >>= n ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M> Mod<M>::operator-() const noexcept { return move( Mod<M>( *this ).SignInvert() ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M>& Mod<M>::SignInvert() noexcept { return Ref( m_n > 0 ? m_n = M - m_n : m_n ); } template <INT_TYPE_FOR_MOD M> inline Mod<M>& Mod<M>::Invert() { assert( m_n != 0 ); INT_TYPE_FOR_MOD m_n_neg; return m_n < ConstantsForMod<M>::g_memory_length ? Ref( m_n = Inverse( m_n ).m_n ) : ( ( m_n_neg = M - m_n ) < ConstantsForMod<M>::g_memory_length ) ? Ref( m_n = M - Inverse( m_n_neg ).m_n ) : PositivePower( INT_TYPE_FOR_MOD( ConstantsForMod<M>::g_M_minus_2 ) ); } template <INT_TYPE_FOR_MOD M> template <typename INT> inline constexpr Mod<M>& Mod<M>::PositivePower( INT exponent ) noexcept { Mod<M> power{ *this }; exponent--; while( exponent != 0 ){ ( exponent & 1 ) == 1 ? operator*=( power ) : *this; exponent >>= 1; power *= power; } return *this; } template <INT_TYPE_FOR_MOD M> template <typename INT> inline constexpr Mod<M>& Mod<M>::NonNegativePower( INT exponent ) noexcept { return exponent == 0 ? Ref( m_n = 1 ) : Ref( PositivePower( move( exponent ) ) ); } template <INT_TYPE_FOR_MOD M> template <typename INT> inline constexpr Mod<M>& Mod<M>::Power( INT exponent ) { bool neg = exponent < 0; assert( !( neg && m_n == 0 ) ); return neg ? PositivePower( move( exponent *= ConstantsForMod<M>::g_M_minus_2_neg ) ) : NonNegativePower( move( exponent ) ); } template <INT_TYPE_FOR_MOD M> inline constexpr void Mod<M>::swap( Mod<M>& n ) noexcept { std::swap( m_n , n.m_n ); } template <INT_TYPE_FOR_MOD M> inline const Mod<M>& Mod<M>::Inverse( const INT_TYPE_FOR_MOD& n ) noexcept { static Mod<M> memory[ConstantsForMod<M>::g_memory_length] = { zero() , one() }; static INT_TYPE_FOR_MOD length_curr = 2; while( length_curr <= n ){ memory[length_curr].m_n = M - memory[M % length_curr].m_n * ull( M / length_curr ) % M; length_curr++; } return memory[n]; } template <INT_TYPE_FOR_MOD M> inline const Mod<M>& Mod<M>::Factorial( const INT_TYPE_FOR_MOD& n ) noexcept { static Mod<M> memory[ConstantsForMod<M>::g_memory_length] = { one() , one() }; static INT_TYPE_FOR_MOD length_curr = 2; while( length_curr <= n ){ ( memory[length_curr] = memory[length_curr - 1] ) *= length_curr; length_curr++; } return memory[n]; } template <INT_TYPE_FOR_MOD M> inline const Mod<M>& Mod<M>::FactorialInverse( const INT_TYPE_FOR_MOD& n ) noexcept { static Mod<M> memory[ConstantsForMod<M>::g_memory_length] = { one() , one() }; static INT_TYPE_FOR_MOD length_curr = 2; while( length_curr <= n ){ ( memory[length_curr] = memory[length_curr - 1] ) *= Inverse( length_curr ); length_curr++; } return memory[n]; } template <INT_TYPE_FOR_MOD M> inline Mod<M> Mod<M>::Combination( const INT_TYPE_FOR_MOD& n , const INT_TYPE_FOR_MOD& i ) noexcept { return Factorial( n ) * FactorialInverse( i ) * FactorialInverse( n - i ); } template <INT_TYPE_FOR_MOD M> inline constexpr const INT_TYPE_FOR_MOD& Mod<M>::Represent() const noexcept { return m_n; } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M> Mod<M>::Derepresent( const INT_TYPE_FOR_MOD& n ) noexcept { Mod<M> n_copy{}; n_copy.m_n = n; return n_copy; } template <INT_TYPE_FOR_MOD M> inline const Mod<M>& Mod<M>::zero() noexcept { static constexpr const Mod<M> z{}; return z; } template <INT_TYPE_FOR_MOD M> inline const Mod<M>& Mod<M>::one() noexcept { static constexpr const Mod<M> o{ Derepresent( 1 ) }; return o; } template <INT_TYPE_FOR_MOD M> template <typename T> inline constexpr Mod<M>& Mod<M>::Ref( T&& n ) noexcept { return *this; } template <INT_TYPE_FOR_MOD M> inline constexpr INT_TYPE_FOR_MOD& Mod<M>::Normalise( INT_TYPE_FOR_MOD& n ) noexcept { return n < M ? n : n -= M; } template <INT_TYPE_FOR_MOD M> inline Mod<M> Inverse( const Mod<M>& n ) { return move( Mod<M>( n ).Invert() ); } template <INT_TYPE_FOR_MOD M> inline constexpr Mod<M> Inverse_constrexpr( Mod<M> n ) noexcept { return move( n.NonNegativePower( M - 2 ) ); } template <INT_TYPE_FOR_MOD M , typename INT> inline constexpr Mod<M> Power( Mod<M> n , INT exponent ) { return move( n.Power( move( exponent ) ) ); } template <INT_TYPE_FOR_MOD M> inline constexpr void swap( Mod<M>& n0 , Mod<M>& n1 ) noexcept { n0.swap( n1 ); } template <INT_TYPE_FOR_MOD M> inline string to_string( const Mod<M>& n ) noexcept { return to_string( n.Represent() ) + " + " + to_string( M ) + "Z"; } template <INT_TYPE_FOR_MOD M , class Traits> inline basic_istream<char,Traits>& operator>>( basic_istream<char,Traits>& is , Mod<M>& n ) { ll m; is >> m; n = m; return is; } template <INT_TYPE_FOR_MOD M , class Traits> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const Mod<M>& n ) { return os << n.Represent(); } template <typename T , int length> class SecondStirlingNumberCalculator { private: // N元集合の非交叉非空部分集合i個による被覆の個数をm_val[N][i]に格納する。 T m_val[length][length]; public: // (コンパイル時に)計算量O(length^2)で構築する。 constexpr inline SecondStirlingNumberCalculator(); constexpr inline const T ( &operator[]( const int& i ) const )[length]; // 以下N<lengthの場合のみサポート。(i<lengthでなくてもよい) // N元集合の非交叉非空部分集合i個による被覆の個数を返す。(O(1)) constexpr inline T CountDisjointCover( const int& N , const int& i ) const; // N元集合の非交叉非空部分集合i個の個数を返す。(O(1)) constexpr inline T CountDisjointSubset( const int& N , const int& i ) const; // 以下Tが正整数Mに対するMod<M>と表せる場合のみサポート。 // N元集合の長さiの非交叉非空部分集合列による被覆の個数を返す。(O(log min{N,i})) // (i彩色の個数はこれらを足し合わせればよい) inline T CountDisjointCoverSequence( const int& N , const int& i ) const; // N元集合の長さiの非交叉非空部分集合列の個数を返す。(O(log min{N,i})) inline T CountDisjointSubsetSequence( const int& N , const int& i ) const; // 以下Mがlength以上の素数である場合のみサポート。 // N元集合の要素数nの部分集合の非交叉非空部分集合i個による被覆の個数を返す。(O(log N)) inline T CountDisjointCover( const int& N , const int& n , const int& i ) const; // N元集合の要素数nの部分集合の長さiの非交叉非空部分集合列による被覆の個数を返す。(O(log N)) inline T CountDisjointCoverSequence( const int& N , const int& n , const int& i ) const; }; template <typename T , int length> constexpr inline SecondStirlingNumberCalculator<T,length>::SecondStirlingNumberCalculator() : m_val() { m_val[0][0] = 1; for( int i = 1 ; i < length ; i++ ){ auto& m_val_i = m_val[i]; const auto& m_val_i_minus = m_val[i - 1]; for( int j = 1 ; j < i ; j++ ){ ( ( m_val_i[j] = m_val_i_minus[j] ) *= j ) += m_val_i_minus[j - 1]; } m_val_i[i] = 1; } } template <typename T , int length> constexpr inline const T ( &SecondStirlingNumberCalculator<T,length>::operator[]( const int& i ) const )[length] { assert( i < length ); return m_val[i]; } template <typename T , int length> constexpr inline T SecondStirlingNumberCalculator<T,length>::CountDisjointCover( const int& N , const int& i ) const { assert( N < length ); return i <= N ? m_val[N][i] : T(); } template <typename T , int length> constexpr inline T SecondStirlingNumberCalculator<T,length>::CountDisjointSubset( const int& N , const int& i ) const { assert( N < length ); return i < N ? m_val[N][i] + m_val[N][i+1] : i == N ? m_val[N][i] : T(); } template <typename T , int length> inline T SecondStirlingNumberCalculator<T,length>::CountDisjointCoverSequence( const int& N , const int& i ) const { return CountDisjointCover( N , i ) * T::Factorial( i ); } template <typename T , int length> inline T SecondStirlingNumberCalculator<T,length>::CountDisjointSubsetSequence( const int& N , const int& i ) const { return CountDisjointSubset( N , i ) * T::Factorial( i ); } template <typename T , int length> inline T SecondStirlingNumberCalculator<T,length>::CountDisjointCover( const int& N , const int& n , const int& i ) const { return CountDisjointCover( n , i ) * T::Combination( N , n ); } template <typename T , int length> inline T SecondStirlingNumberCalculator<T,length>::CountDisjointCoverSequence( const int& N , const int& n , const int& i ) const { return CountDisjointCoverSequence( n , i ) * T::Combination( N , n ); } // AAA 常設でないライブラリは以上に挿入する。 #define INCLUDE_SUB #include __FILE__ #else // INCLUDE_LIBRARY #ifdef DEBUG #define _GLIBCXX_DEBUG #define REPEAT_MAIN( BOUND ) START_MAIN; signal( SIGABRT , &AlertAbort ); AutoCheck( exec_mode , use_getline ); if( exec_mode == sample_debug_mode || exec_mode == submission_debug_mode || exec_mode == library_search_mode ){ RE 0; } else if( exec_mode == experiment_mode ){ Experiment(); RE 0; } else if( exec_mode == small_test_mode ){ SmallTest(); RE 0; }; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if( exec_mode == solve_mode ){ if CE( bound_test_case_num > 1 ){ CERR( "テストケースの個数を入力してください。" ); SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } } else if( exec_mode == random_test_mode ){ CERR( "ランダムテストを行う回数を指定してください。" ); SET_LL( test_case_num ); } FINISH_MAIN #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック: " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); AS( ( MIN ) <= A && A <= ( MAX ) ) #define SET_ASSERT( A , MIN , MAX ) if( exec_mode == solve_mode ){ SET_LL( A ); ASSERT( A , MIN , MAX ); } else if( exec_mode == random_test_mode ){ CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ); } else { AS( false ); } #define SOLVE_ONLY ST_AS( __FUNCTION__[0] == 'S' ) #define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl #define COUT( ... ) VariadicCout( cout << "出力: " , __VA_ARGS__ ) << endl #define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << endl #define COUT_A( A , N ) cout << "出力: "; OUTPUT_ARRAY( cout , A , N ) << endl #define CERR_ITR( A ) OUTPUT_ITR( cerr , A ) << endl #define COUT_ITR( A ) cout << "出力: "; OUTPUT_ITR( cout , A ) << endl #else #pragma GCC optimize ( "O3" ) #pragma GCC optimize ( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if CE( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN #define ASSERT( A , MIN , MAX ) AS( ( MIN ) <= A && A <= ( MAX ) ) #define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX ) #define SOLVE_ONLY #define CERR( ... ) #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL #define CERR_A( A , N ) #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL #define CERR_ITR( A ) #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << ENDL #endif #ifdef REACTIVE #define ENDL endl #else #define ENDL "\n" #endif #ifdef USE_GETLINE #define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); } #define GETLINE_SEPARATE( SEPARATOR , ... ) SOLVE_ONLY; string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ ) #define GETLINE( ... ) SOLVE_ONLY; GETLINE_SEPARATE( '\n' , __VA_ARGS__ ) #else #define SET_LL( A ) cin >> A #define CIN( LL , ... ) SOLVE_ONLY; LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ ) #define SET_A( A , N ) SOLVE_ONLY; FOR( VARIABLE_FOR_SET_A , 0 , N ){ cin >> A[VARIABLE_FOR_SET_A]; } #define CIN_A( LL , A , N ) VE<LL> A( N ); SET_A( A , N ); #endif #include <bits/stdc++.h> using namespace std; #define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) ) #define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define FINISH_MAIN REPEAT( test_case_num ){ if CE( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } } #define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now() #define CURRENT_TIME static_cast<double>( chrono::duration_cast<chrono::microseconds>( chrono::system_clock::now() - watch ).count() / 1000.0 ) #define CHECK_WATCH( TL_MS ) ( CURRENT_TIME < TL_MS - 100.0 ) #define CEXPR( LL , BOUND , VALUE ) CE LL BOUND = VALUE #define SET_A_ASSERT( A , N , MIN , MAX ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ SET_ASSERT( A[VARIABLE_FOR_SET_A] , MIN , MAX ); } #define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX ) #define CIN_A_ASSERT( A , N , MIN , MAX ) vector<decldecay_t( MAX )> A( N ); SET_A_ASSERT( A , N , MIN , MAX ) #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( decldecay_t( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define FOREQ( VAR , INITIAL , FINAL ) for( decldecay_t( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ ) #define FOREQINV( VAR , INITIAL , FINAL ) for( decldecay_t( INITIAL ) VAR = INITIAL ; VAR + 1 > FINAL ; VAR -- ) #define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .BE() , end_ ## ARRAY = ARRAY .EN() #define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES ) #define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS ) #define OUTPUT_ARRAY( OS , A , N ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , 0 , N ){ OS << A[VARIABLE_FOR_OUTPUT_ARRAY] << (VARIABLE_FOR_OUTPUT_ARRAY==N-1?"":" "); } OS #define OUTPUT_ITR( OS , A ) { auto ITERATOR_FOR_OUTPUT_ITR = A.BE() , EN_FOR_OUTPUT_ITR = A.EN(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; WH( VARIABLE_FOR_OUTPUT_ITR ){ OS << *ITERATOR_FOR_COUT_ITR; ( VARIABLE_FOR_OUTPUT_ITR = ++ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR ) ? OS : OS << " "; } } OS #define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); RE #define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ ); auto answer = Answer( __VA_ARGS__ ); bool match = naive == answer; COUT( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ RE; } // 圧縮用 #define TE template #define TY typename #define US using #define ST static #define AS assert #define IN inline #define CL class #define PU public #define OP operator #define CE constexpr #define CO const #define NE noexcept #define RE return #define WH while #define VO void #define VE vector #define LI list #define BE begin #define EN end #define SZ size #define LE length #define PW Power #define MO move #define TH this #define CRI CO int& #define CRUI CO uint& #define CRL CO ll& #define VI virtual #define ST_AS static_assert #define reMO_CO remove_const #define is_COructible_v is_constructible_v #define rBE rbegin #define reSZ resize // 型のエイリアス #define decldecay_t( VAR ) decay_t<decltype( VAR )> TE <TY F , TY...Args> US ret_t = decltype( declval<F>()( declval<Args>()... ) ); TE <TY T> US inner_t = TY T::type; US uint = unsigned int; US ll = long long; US ull = unsigned long long; US ld = long double; US lld = __float128; TE <TY INT> US T2 = pair<INT,INT>; TE <TY INT> US T3 = tuple<INT,INT,INT>; TE <TY INT> US T4 = tuple<INT,INT,INT,INT>; US path = pair<int,ll>; // 入出力用 TE <CL Traits> IN basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is ) { RE is; } TE <CL Traits , TY Arg , TY... ARGS> IN basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is , Arg& arg , ARGS&... args ) { RE VariadicCin( is >> arg , args... ); } TE <CL Traits> IN basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , CO char& separator ) { RE is; } TE <CL Traits , TY Arg , TY... ARGS> IN basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , CO char& separator , Arg& arg , ARGS&... args ) { RE VariadicGetline( getline( is , arg , separator ) , separator , args... ); } TE <CL Traits , TY Arg> IN basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , CO VE<Arg>& arg ) { auto BE = arg.BE() , EN = arg.EN(); auto itr = BE; WH( itr != EN ){ ( itr == BE ? os : os << " " ) << *itr; itr++; } RE os; } TE <CL Traits , TY Arg1 , TY Arg2> IN basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , CO pair<Arg1,Arg2>& arg ) { RE os << arg.first << " " << arg.second; } TE <CL Traits , TY Arg> IN basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , CO Arg& arg ) { RE os << arg; } TE <CL Traits , TY Arg1 , TY Arg2 , TY... ARGS> IN basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , CO Arg1& arg1 , CO Arg2& arg2 , CO ARGS&... args ) { RE VariadicCout( os << arg1 << " " , arg2 , args... ); } // 算術用 TE <TY T> CE T PositiveBaseResidue( CO T& a , CO T& p ){ RE a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); } TE <TY T> CE T Residue( CO T& a , CO T& p ){ RE PositiveBaseResidue( a , p < 0 ? -p : p ); } TE <TY T> CE T PositiveBaseQuotient( CO T& a , CO T& p ){ RE ( a - PositiveBaseResidue( a , p ) ) / p; } TE <TY T> CE T Quotient( CO T& a , CO T& p ){ RE p < 0 ? PositiveBaseQuotient( -a , -p ) : PositiveBaseQuotient( a , p ); } #define POWER( ANSWER , ARGUMENT , EXPONENT ) \ ST_AS( ! is_same<decldecay_t( ARGUMENT ),int>::value && ! is_same<decldecay_t( ARGUMENT ),uint>::value ); \ decldecay_t( ARGUMENT ) ANSWER{ 1 }; \ { \ decldecay_t( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT ); \ decldecay_t( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \ WH( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){ \ if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){ \ ANSWER *= ARGUMENT_FOR_SQUARE_FOR_POWER; \ } \ ARGUMENT_FOR_SQUARE_FOR_POWER *= ARGUMENT_FOR_SQUARE_FOR_POWER; \ EXPONENT_FOR_SQUARE_FOR_POWER /= 2; \ } \ } \ #define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO ) \ ll ANSWER{ 1 }; \ { \ ll ARGUMENT_FOR_SQUARE_FOR_POWER = ( ( ARGUMENT ) % ( MODULO ) ) % ( MODULO ); \ ARGUMENT_FOR_SQUARE_FOR_POWER < 0 ? ARGUMENT_FOR_SQUARE_FOR_POWER += ( MODULO ) : ARGUMENT_FOR_SQUARE_FOR_POWER; \ decldecay_t( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \ WH( 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; \ } \ } \ #define FACTORIAL_MOD( ANSWER , ANSWER_INV , INVERSE , MAX_INDEX , CE_LENGTH , MODULO ) \ ll ANSWER[CE_LENGTH]; \ ll ANSWER_INV[CE_LENGTH]; \ ll INVERSE[CE_LENGTH]; \ { \ ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \ ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL; \ FOREQ( i , 1 , MAX_INDEX ){ \ ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= ( MODULO ); \ } \ ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \ FOREQ( i , 2 , MAX_INDEX ){ \ ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \ } \ } \ // 二分探索用 // EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= CO_TARGETの整数解を格納。 #define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , CO_TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \ ST_AS( ! is_same<decldecay_t( CO_TARGET ),uint>::value && ! is_same<decldecay_t( CO_TARGET ),ull>::value ); \ ll ANSWER = MINIMUM; \ { \ ll L_BS = MINIMUM; \ ll U_BS = MAXIMUM; \ ANSWER = UPDATE_ANSWER; \ ll EXPRESSION_BS; \ CO ll CO_TARGET_BS = ( CO_TARGET ); \ ll DIFFERENCE_BS; \ WH( L_BS < U_BS ){ \ DIFFERENCE_BS = ( EXPRESSION_BS = ( EXPRESSION ) ) - CO_TARGET_BS; \ CERR( "二分探索中:" , "L_BS =" , L_BS , "<=" , #ANSWER , "=" , ANSWER , "<=" , U_BS , "= U_BS :" , #EXPRESSION , "=" , EXPRESSION_BS , DIFFERENCE_BS > 0 ? ">" : DIFFERENCE_BS < 0 ? "<" : "=" , CO_TARGET_BS , "=" , #CO_TARGET ); \ if( DIFFERENCE_BS INEQUALITY_FOR_CHECK 0 ){ \ U_BS = UPDATE_U; \ } else { \ L_BS = UPDATE_L; \ } \ ANSWER = UPDATE_ANSWER; \ } \ if( L_BS > U_BS ){ \ CERR( "二分探索失敗:" , "L_BS =" , L_BS , ">" , U_BS , "= U_BS :" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \ CERR( "二分探索マクロにミスがある可能性があります。変更前の版に戻してください。" ); \ ANSWER = MAXIMUM + 1; \ } else { \ CERR( "二分探索終了:" , "L_BS =" , L_BS , "<=" , #ANSWER , "=" , ANSWER , "<=" , U_BS , "= U_BS" ); \ CERR( "二分探索が成功したかを確認するために" , #EXPRESSION , "を計算します。" ); \ CERR( "成功判定が不要な場合はこの計算を削除しても構いません。" ); \ EXPRESSION_BS = ( EXPRESSION ); \ CERR( "二分探索結果:" , #EXPRESSION , "=" , EXPRESSION_BS , ( EXPRESSION_BS > CO_TARGET_BS ? ">" : EXPRESSION_BS < CO_TARGET_BS ? "<" : "=" ) , CO_TARGET_BS ); \ if( EXPRESSION_BS DESIRED_INEQUALITY CO_TARGET_BS ){ \ CERR( "二分探索成功:" , #ANSWER , ":=" , ANSWER ); \ } else { \ CERR( "二分探索失敗:" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \ CERR( "単調でないか、単調増加性と単調減少性を逆にしてしまったか、探索範囲内に解が存在しません。" ); \ ANSWER = MAXIMUM + 1; \ } \ } \ } \ // 単調増加の時にEXPRESSION >= CO_TARGETの最小解を格納。 #define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , >= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 ) // 単調増加の時にEXPRESSION <= CO_TARGETの最大解を格納。 #define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , > , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 ) // 単調減少の時にEXPRESSION >= CO_TARGETの最大解を格納。 #define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , < , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 ) // 単調減少の時にEXPRESSION <= CO_TARGETの最小解を格納。 #define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , <= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 ) // t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。 TE <TY T> IN TY set<T>::iterator MaximumLeq( set<T>& S , CO T& t ) { CO auto EN = S.EN(); if( S.empty() ){ RE EN; } auto itr = S.upper_bound( t ); RE itr == EN ? S.find( *( S.rBE() ) ) : itr == S.BE() ? EN : --itr; } // t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。 TE <TY T> IN TY set<T>::iterator MaximumLt( set<T>& S , CO T& t ) { CO auto EN = S.EN(); if( S.empty() ){ RE EN; } auto itr = S.lower_bound( t ); RE itr == EN ? S.find( *( S.rBE() ) ) : itr == S.BE() ? EN : --itr; } // t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。 TE <TY T> IN TY set<T>::iterator MinimumGeq( set<T>& S , CO T& t ) { RE S.lower_bound( t ); } // tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。 TE <TY T> IN TY set<T>::iterator MinimumGt( set<T>& S , CO T& t ) { RE S.upper_bound( t ); } // 尺取り法用 // VAR_TPAがINITからUPDATEを繰り返しCONTINUE_CONDITIONを満たす限り、ON_CONDITIONを判定して // trueならON、falseならOFFとなる。直近のONの区間を[VAR_TPA_L,VAR_TPA_R)で管理する。 #define TPA( VAR_TPA , INIT , UPDATE , CONTINUE_CONDITION , ON_CONDITION , ONON , ONOFF , OFFON , OFFOFF , FINISH ) \ { \ auto VAR_TPA = INIT; \ auto VAR_TPA ## _L = VAR_TPA; \ auto VAR_TPA ## _R = VAR_TPA; \ bool on_TPA = false; \ int state_TPA = 3; \ WH( CONTINUE_CONDITION ){ \ bool on_TPA_next = ON_CONDITION; \ state_TPA = ( ( on_TPA ? 1 : 0 ) << 1 ) | ( on_TPA_next ? 1 : 0 ); \ CERR( "尺取り中: [L,R) = [" , VAR_TPA ## _L , "," , VAR_TPA ## _R , ") ," , #VAR_TPA , "=" , VAR_TPA , "," , ( ( state_TPA >> 1 ) & 1 ) == 1 ? "on" : "off" , " ->" , ( state_TPA & 1 ) == 1 ? "on" : "off" ); \ if( state_TPA == 0 ){ \ OFFOFF; VAR_TPA ## _L = VAR_TPA ## _R = VAR_TPA; UPDATE; \ } else if( state_TPA == 1 ){ \ OFFON; VAR_TPA ## _L = VAR_TPA; UPDATE; VAR_TPA ## _R = VAR_TPA; \ } else if( state_TPA == 2 ){ \ ONOFF; VAR_TPA ## _L = VAR_TPA ## _R = VAR_TPA; UPDATE; \ } else { \ ONON; UPDATE; VAR_TPA ## _R = VAR_TPA; \ } \ on_TPA = on_TPA_next; \ } \ CERR( "尺取り終了: [L,R) = [" , VAR_TPA ## _L , "," , VAR_TPA ## _R , ") ," , #VAR_TPA , "=" , VAR_TPA ); \ FINISH; \ } \ // データ構造用 TE <TY T , TE <TY...> TY V> IN V<T> OP+( CO V<T>& a0 , CO V<T>& a1 ) { if( a0.empty() ){ RE a1; } if( a1.empty() ){ RE a0; } AS( a0.SZ() == a1.SZ() ); V<T> answer{}; for( auto itr0 = a0.BE() , itr1 = a1.BE() , EN0 = a0.EN(); itr0 != EN0 ; itr0++ , itr1++ ){ answer.push_back( *itr0 + *itr1 ); } RE answer; } TE <TY T , TY U> IN pair<T,U> OP+( CO pair<T,U>& t0 , CO pair<T,U>& t1 ) { RE { t0.first + t1.first , t0.second + t1.second }; } TE <TY T , TY U , TY V> IN tuple<T,U,V> OP+( CO tuple<T,U,V>& t0 , CO tuple<T,U,V>& t1 ) { RE { get<0>( t0 ) + get<0>( t1 ) , get<1>( t0 ) + get<1>( t1 ) , get<2>( t0 ) + get<2>( t1 ) }; } TE <TY T , TY U , TY V , TY W> IN tuple<T,U,V,W> OP+( CO tuple<T,U,V,W>& t0 , CO tuple<T,U,V,W>& t1 ) { RE { get<0>( t0 ) + get<0>( t1 ) , get<1>( t0 ) + get<1>( t1 ) , get<2>( t0 ) + get<2>( t1 ) , get<3>( t0 ) + get<3>( t1 ) }; } TE <TY T> IN T Add( CO T& t0 , CO T& t1 ) { RE t0 + t1; } TE <TY T> IN T XorAdd( CO T& t0 , CO T& t1 ){ RE t0 ^ t1; } TE <TY T> IN T Multiply( CO T& t0 , CO T& t1 ) { RE t0 * t1; } TE <TY T> IN CO T& Zero() { ST CO T z{}; RE z; } TE <TY T> IN CO T& One() { ST CO T o = 1; RE o; }\ TE <TY T> IN T AddInv( CO T& t ) { RE -t; } TE <TY T> IN T Id( CO T& v ) { RE v; } TE <TY T> IN T Min( CO T& a , CO T& b ){ RE a < b ? a : b; } TE <TY T> IN T Max( CO T& a , CO T& b ){ RE a < b ? b : a; } TE <TY T , TE <TY...> TY V> IN auto Get( CO V<T>& a ) { return [&]( CRI i = 0 ){ RE a[i]; }; } // グリッド問題用 int H , W , H_minus , W_minus , HW; VE<VE<bool>> non_wall; IN T2<int> EnumHW( CRI v ) { RE { v / W , v % W }; } IN int EnumHW_inv( CO T2<int>& ij ) { auto& [i,j] = ij; RE i * W + j; } CO string direction[4] = {"U","R","D","L"}; // (i,j)->(k,h)の方向番号を取得 IN int DirectionNumberOnGrid( CRI i , CRI j , CRI k , CRI h ){RE i<k?2:i>k?0:j<h?1:j>h?3:(AS(false),-1);} // v->wの方向番号を取得 IN int DirectionNumberOnGrid( CRI v , CRI w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);RE DirectionNumberOnGrid(i,j,k,h);} // 方向番号の反転U<->D、R<->L IN int ReverseDirectionNumberOnGrid( CRI n ){AS(0<=n&&n<4);RE(n+2)%4;} IN VO SetEdgeOnGrid( CO string& Si , CRI i , VE<LI<int>>& e , CO char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW_inv({i,j});if(i>0){e[EnumHW_inv({i-1,j})].push_back(v);}if(i+1<H){e[EnumHW_inv({i+1,j})].push_back(v);}if(j>0){e[EnumHW_inv({i,j-1})].push_back(v);}if(j+1<W){e[EnumHW_inv({i,j+1})].push_back(v);}}}} IN VO SetEdgeOnGrid( CO string& Si , CRI i , VE<LI<path>>& e , CO char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){CO int v=EnumHW_inv({i,j});if(i>0){e[EnumHW_inv({i-1,j})].push_back({v,1});}if(i+1<H){e[EnumHW_inv({i+1,j})].push_back({v,1});}if(j>0){e[EnumHW_inv({i,j-1})].push_back({v,1});}if(j+1<W){e[EnumHW_inv({i,j+1})].push_back({v,1});}}}} IN VO SetWallOnGrid( CO string& Si , CRI i , VE<VE<bool>>& non_wall , CO char& walkable = '.' , CO char& unwalkable = '#' ){non_wall.push_back(VE<bool>(W));auto& non_wall_i=non_wall[i];FOR(j,0,W){non_wall_i[j]=Si[j]==walkable?true:(assert(Si[j]==unwalkable),false);}} // デバッグ用 #ifdef DEBUG IN VO AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); } VO AutoCheck( int& exec_mode , CO bool& use_getline ); IN VO Solve(); IN VO Experiment(); IN VO SmallTest(); IN VO RandomTest(); ll GetRand( CRL Rand_min , CRL Rand_max ); IN VO BreakPoint( CRI LINE ) {} int exec_mode; CEXPR( int , solve_mode , 0 ); CEXPR( int , sample_debug_mode , 1 ); CEXPR( int , submission_debug_mode , 2 ); CEXPR( int , library_search_mode , 3 ); CEXPR( int , experiment_mode , 4 ); CEXPR( int , small_test_mode , 5 ); CEXPR( int , random_test_mode , 6 ); #ifdef USE_GETLINE CEXPR( bool , use_getline , true ); #else CEXPR( bool , use_getline , false ); #endif #else ll GetRand( CRL Rand_min , CRL Rand_max ) { ll answer = time( NULL ); RE answer * rand() % ( Rand_max + 1 - Rand_min ) + Rand_min; } #endif // VVV 常設ライブラリは以下に挿入する。 // AAA 常設ライブラリは以上に挿入する。 #define INCLUDE_LIBRARY #include __FILE__ #endif // INCLUDE_LIBRARY #endif // INCLUDE_SUB #endif // INCLUDE_MAIN