


def 	a_      (    SCREAMING_SNAKE_CASE__					:      str		,			SCREAMING_SNAKE_CASE__					:      List[Any]		,			SCREAMING_SNAKE_CASE__					:      List[Any]		,			SCREAMING_SNAKE_CASE__					:      str     ):
       '''simple docstring'''





       global f  # a global dp table for knapsack
       if f[i][j] < 0:
              if j < wt[i - 1]:
                     _lowerCamelCase       :		str		=mf_knapsack(i - 1		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__     )
              else:
                     _lowerCamelCase       :		Tuple		=max(
                         mf_knapsack(i - 1		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__     )		,			mf_knapsack(i - 1		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			j - wt[i - 1]     ) + val[i - 1]		,			)
              _lowerCamelCase       :		Union[str, Any]		=val
       return f[i][j]




def 	a_      (    SCREAMING_SNAKE_CASE__					:      List[str]		,			SCREAMING_SNAKE_CASE__					:      Optional[int]		,			SCREAMING_SNAKE_CASE__					:      Dict		,			SCREAMING_SNAKE_CASE__					:      Dict     ):
       '''simple docstring'''





       _lowerCamelCase       :		List[Any]		=[[0] * (w + 1) for _ in range(n + 1     )]

       for i in range(1		,			n + 1     ):
              for w_ in range(1		,			w + 1     ):
                     if wt[i - 1] <= w_:
                            _lowerCamelCase       :		Dict		=max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]		,			dp[i - 1][w_]     )
                     else:
                            _lowerCamelCase       :		str		=dp[i - 1][w_]

       return dp[n][w_], dp




def 	a_      (    SCREAMING_SNAKE_CASE__					:      int		,			SCREAMING_SNAKE_CASE__					:      list		,			SCREAMING_SNAKE_CASE__					:      list     ):
       '''simple docstring'''





       if not (isinstance(SCREAMING_SNAKE_CASE__		,			(list, tuple)     ) and isinstance(SCREAMING_SNAKE_CASE__		,			(list, tuple)     )):
              raise ValueError(
                  'Both the weights and values vectors must be either lists or tuples'     )

       _lowerCamelCase       :		Union[str, Any]		=len(SCREAMING_SNAKE_CASE__     )
       if num_items != len(SCREAMING_SNAKE_CASE__     ):
              _lowerCamelCase       :		List[Any]		=(
                  'The number of weights must be the same as the number of values.\n'
                  F'''But got {num_items} weights and {len(SCREAMING_SNAKE_CASE__     )} values'''
              )
              raise ValueError(SCREAMING_SNAKE_CASE__     )
       for i in range(SCREAMING_SNAKE_CASE__     ):
              if not isinstance(wt[i]		,			SCREAMING_SNAKE_CASE__     ):
                     _lowerCamelCase       :		str		=(
                         'All weights must be integers but got weight of '
                         F'''type {type(wt[i]     )} at index {i}'''
                     )
                     raise TypeError(SCREAMING_SNAKE_CASE__     )

       _lowerCamelCase	,     _lowerCamelCase       :		Dict		=knapsack(SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__     )
       _lowerCamelCase       :		set		=set()
       _construct_solution(SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__     )

       return optimal_val, example_optional_set




def 	a_      (    SCREAMING_SNAKE_CASE__					:      list		,			SCREAMING_SNAKE_CASE__					:      list		,			SCREAMING_SNAKE_CASE__					:      int		,			SCREAMING_SNAKE_CASE__					:      int		,			SCREAMING_SNAKE_CASE__					:      set     ):
       '''simple docstring'''





       if i > 0 and j > 0:
              if dp[i - 1][j] == dp[i][j]:
                     _construct_solution(SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			i - 1		,			SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__     )
              else:
                     optimal_set.add(SCREAMING_SNAKE_CASE__     )
                     _construct_solution(SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__		,			i - 1		,			j - wt[i - 1]		,			SCREAMING_SNAKE_CASE__     )


if __name__ == "__main__":
 lowerCamelCase											=       [3, 2, 4, 4]
 lowerCamelCase											=       [4, 3, 2, 3]
 lowerCamelCase											=       4
 lowerCamelCase											=       6
 lowerCamelCase											=       [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
 lowerCamelCase					,				lowerCamelCase											=       knapsack(w, wt, val, n)
 print(optimal_solution)
 print(mf_knapsack(n, wt, val, w))  # switched the n and w

 # testing the dynamic programming problem with example
 # the optimal subset for the above example are items 3 and 4
 lowerCamelCase					,				lowerCamelCase											=       knapsack_with_example_solution(w, wt, val)
 assert optimal_solution == 8
 assert optimal_subset == {3, 4}
 print('optimal_value = ', optimal_solution)
 print('An optimal subset corresponding to the optimal value', optimal_subset)






from collections.abc import Generator
from math import sin




def 	a_      (    SCREAMING_SNAKE_CASE__					:      bytes     ):
       '''simple docstring'''





       if len(SCREAMING_SNAKE_CASE__     ) != 32:
              raise ValueError('Input must be of length 32'     )

       _lowerCamelCase       :		Any		=b''
       for i in [3, 2, 1, 0]:
              little_endian += string_aa[8 * i : 8 * i + 8]
       return little_endian




def 	a_      (    SCREAMING_SNAKE_CASE__					:      int     ):
       '''simple docstring'''





       if i < 0:
              raise ValueError('Input must be non-negative'     )

       _lowerCamelCase       :		Optional[int]		=format(SCREAMING_SNAKE_CASE__		,			'08x'     )[-8:]
       _lowerCamelCase       :		List[Any]		=b''
       for i in [3, 2, 1, 0]:
              little_endian_hex += hex_rep[2 * i : 2 * i + 2].encode('utf-8'     )
       return little_endian_hex




def 	a_      (    SCREAMING_SNAKE_CASE__					:      bytes     ):
       '''simple docstring'''





       _lowerCamelCase       :		Dict		=b''
       for char in message:
              bit_string += format(SCREAMING_SNAKE_CASE__		,			'08b'     ).encode('utf-8'     )
       _lowerCamelCase       :		Dict		=format(len(SCREAMING_SNAKE_CASE__     )		,			'064b'     ).encode('utf-8'     )

       # Pad bit_string to a multiple of 512 chars
       bit_string += b"1"
       while len(SCREAMING_SNAKE_CASE__     ) % 512 != 448:
              bit_string += b"0"
       bit_string += to_little_endian(start_len[32:]     ) + to_little_endian(start_len[:32]     )

       return bit_string




def 	a_      (    SCREAMING_SNAKE_CASE__					:      bytes     ):
       '''simple docstring'''





       if len(SCREAMING_SNAKE_CASE__     ) % 512 != 0:
              raise ValueError('Input must have length that\'s a multiple of 512'     )

       for pos in range(0		,			len(SCREAMING_SNAKE_CASE__     )		,			512     ):
              _lowerCamelCase       :		str		=bit_string[pos : pos + 512]
              _lowerCamelCase       :		Tuple		=[]
              for i in range(0		,			512		,			32     ):
                     block_words.append(int(to_little_endian(block[i : i + 32]     )		,			2     )     )
              yield block_words




def 	a_      (    SCREAMING_SNAKE_CASE__					:      int     ):
       '''simple docstring'''





       if i < 0:
              raise ValueError('Input must be non-negative'     )

       _lowerCamelCase       :		List[str]		=format(SCREAMING_SNAKE_CASE__		,			'032b'     )
       _lowerCamelCase       :		List[str]		=''
       for c in i_str:
              new_str += "1" if c == "0" else "0"
       return int(SCREAMING_SNAKE_CASE__		,			2     )




def 	a_      (    SCREAMING_SNAKE_CASE__					:      int		,			SCREAMING_SNAKE_CASE__					:      int     ):
       '''simple docstring'''





       return (a + b) % 2**32




def 	a_      (    SCREAMING_SNAKE_CASE__					:      int		,			SCREAMING_SNAKE_CASE__					:      int     ):
       '''simple docstring'''





       if i < 0:
              raise ValueError('Input must be non-negative'     )
       if shift < 0:
              raise ValueError('Shift must be non-negative'     )
       return ((i << shift) ^ (i >> (32 - shift))) % 2**32




def 	a_      (    SCREAMING_SNAKE_CASE__					:      bytes     ):
       '''simple docstring'''





       _lowerCamelCase       :		int		=preprocess(SCREAMING_SNAKE_CASE__     )

       _lowerCamelCase       :		Dict		=[int(2**32 * abs(sin(i + 1     )     )     ) for i in range(64     )]

       # Starting states
       _lowerCamelCase       :		str		=0X67_45_23_01
       _lowerCamelCase       :		Union[str, Any]		=0Xef_cd_ab_89
       _lowerCamelCase       :		List[str]		=0X98_ba_dc_fe
       _lowerCamelCase       :		int		=0X10_32_54_76

       _lowerCamelCase       :		Optional[int]		=[
           7,
           12,
           17,
           22,
           7,
           12,
           17,
           22,
           7,
           12,
           17,
           22,
           7,
           12,
           17,
           22,
           5,
           9,
           14,
           20,
           5,
           9,
           14,
           20,
           5,
           9,
           14,
           20,
           5,
           9,
           14,
           20,
           4,
           11,
           16,
           23,
           4,
           11,
           16,
           23,
           4,
           11,
           16,
           23,
           4,
           11,
           16,
           23,
           6,
           10,
           15,
           21,
           6,
           10,
           15,
           21,
           6,
           10,
           15,
           21,
           6,
           10,
           15,
           21,
       ]

       # Process bit string in chunks, each with 16 32-char words
       for block_words in get_block_words(SCREAMING_SNAKE_CASE__     ):
              _lowerCamelCase       :		Union[str, Any]		=aa
              _lowerCamelCase       :		List[Any]		=ba
              _lowerCamelCase       :		Dict		=ca
              _lowerCamelCase       :		List[Any]		=da

              # Hash current chunk
              for i in range(64     ):
                     if i <= 15:
                            # f = (b & c) | (not_32(b) & d)     # Alternate definition for f
                            _lowerCamelCase       :		Optional[Any]		=d ^ (b & (c ^ d))
                            _lowerCamelCase       :		Dict		=i
                     elif i <= 31:
                            # f = (d & b) | (not_32(d) & c)     # Alternate definition for f
                            _lowerCamelCase       :		Optional[int]		=c ^ (d & (b ^ c))
                            _lowerCamelCase       :		List[str]		=(5 * i + 1) % 16
                     elif i <= 47:
                            _lowerCamelCase       :		str		=b ^ c ^ d
                            _lowerCamelCase       :		int		=(3 * i + 5) % 16
                     else:
                            _lowerCamelCase       :		Optional[Any]		=c ^ (b | not_aa(SCREAMING_SNAKE_CASE__     ))
                            _lowerCamelCase       :		Dict		=(7 * i) % 16
                     _lowerCamelCase       :		Any		=(f + a + added_consts[i] + block_words[g]) % 2**32
                     _lowerCamelCase       :		str		=d
                     _lowerCamelCase       :		Any		=c
                     _lowerCamelCase       :		Union[str, Any]		=b
                     _lowerCamelCase       :		Dict		=sum_aa(SCREAMING_SNAKE_CASE__		,			left_rotate_aa(SCREAMING_SNAKE_CASE__		,			shift_amounts[i]     )     )

              # Add hashed chunk to running total
              _lowerCamelCase       :		Optional[Any]		=sum_aa(SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__     )
              _lowerCamelCase       :		List[str]		=sum_aa(SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__     )
              _lowerCamelCase       :		Optional[int]		=sum_aa(SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__     )
              _lowerCamelCase       :		List[str]		=sum_aa(SCREAMING_SNAKE_CASE__		,			SCREAMING_SNAKE_CASE__     )

       _lowerCamelCase       :		List[Any]		=reformat_hex(SCREAMING_SNAKE_CASE__     ) + reformat_hex(SCREAMING_SNAKE_CASE__     ) + reformat_hex(SCREAMING_SNAKE_CASE__     ) + reformat_hex(SCREAMING_SNAKE_CASE__     )
       return digest


if __name__ == "__main__":
 import doctest

 doctest.testmod()


