

def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   List[Any]     ,					SCREAMING_SNAKE_CASE_		:   Tuple     ,					SCREAMING_SNAKE_CASE_		:   Union[str, Any]     ,					SCREAMING_SNAKE_CASE_		:   int      ):



     '''simple docstring'''





     global f  # a global dp table for knapsack
     if f[i][j] < 0:
          if j < wt[i - 1]:
               lowercase__   :       Any				=	mf_knapsack(i - 1     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_      )
          else:
               lowercase__   :       Dict				=	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]     ,					)
          lowercase__   :       Union[str, Any]				=	val
     return f[i][j]

def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   str     ,					SCREAMING_SNAKE_CASE_		:   List[str]     ,					SCREAMING_SNAKE_CASE_		:   List[Any]     ,					SCREAMING_SNAKE_CASE_		:   Any      ):



     '''simple docstring'''





     lowercase__   :       Optional[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_:
                    lowercase__   :       List[str]				=	max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]     ,					dp[i - 1][w_]      )
               else:
                    lowercase__   :       str				=	dp[i - 1][w_]

     return dp[n][w_], dp

def      snake_case__      (   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'      )

     lowercase__   :       Tuple				=	len(SCREAMING_SNAKE_CASE_      )
     if num_items != len(SCREAMING_SNAKE_CASE_      ):
          lowercase__   :       Tuple				=	(
              '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_      ):
               lowercase__   :       Tuple				=	(
                   'All weights must be integers but got weight of '
                   f"""type {type(wt[i]      )} at index {i}"""
               )
               raise TypeError(SCREAMING_SNAKE_CASE_      )

     lowercase__				,			lowercase__   :       int				=	knapsack(SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_      )
     lowercase__   :       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      snake_case__      (   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__":
       snake_case_        =			[3, 2, 4, 4]
       snake_case_        =			[4, 3, 2, 3]
       snake_case_        =			4
       snake_case_        =			6
       snake_case_        =			[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
       snake_case_  ,		snake_case_        =			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
       snake_case_  ,		snake_case_        =			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 __future__ import annotations


class 				SCREAMING_SNAKE_CASE__ :





    def __init__(				self						,       a						,       a):
         lowercase__				,			lowercase__   :       Dict				=	text, pattern
         lowercase__				,			lowercase__   :       Any				=	len(a), len(a)





    def 				snake_case_    (				self						,       a):

         for i in range(self.patLen - 1						,       -1						,       -1):
              if char == self.pattern[i]:
                   return i
         return -1





    def 				snake_case_    (				self						,       a):

         for i in range(self.patLen - 1						,       -1						,       -1):
              if self.pattern[i] != self.text[current_pos + i]:
                   return current_pos + i
         return -1





    def 				snake_case_    (				self):
         # searches pattern in text and returns index positions
         lowercase__   :       Any				=	[]
         for i in range(self.textLen - self.patLen + 1):
              lowercase__   :       Optional[Any]				=	self.mismatch_in_text(a)
              if mismatch_index == -1:
                   positions.append(a)
              else:
                   lowercase__   :       Optional[int]				=	self.match_in_pattern(self.text[mismatch_index])
                   lowercase__   :       Optional[Any]				=	(
                       mismatch_index - match_index
                   )  # shifting index lgtm [py/multiple-definition]
         return positions



snake_case_        =			'''ABAABA'''
snake_case_        =			'''AB'''
snake_case_        =			BoyerMooreSearch(text, pattern)
snake_case_        =			bms.bad_character_heuristic()

if len(positions) == 0:
       print('''No match found''')
else:
       print('''Pattern found in following positions: ''')
       print(positions)

