"""simple docstring"""



from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst



def 					_lowerCamelCase(					):
       __a     				=  9, 1_4  # noqa: F841
       __a     				=  [
           [0, 1, 4],
           [0, 7, 8],
           [1, 2, 8],
           [7, 8, 7],
           [7, 6, 1],
           [2, 8, 2],
           [8, 6, 6],
           [2, 3, 7],
           [2, 5, 4],
           [6, 5, 2],
           [3, 5, 1_4],
           [3, 4, 9],
           [5, 4, 1_0],
           [1, 7, 1_1],
       ]

       __a     				=  defaultdict(snake_case_							)
       for nodea, nodea, cost in edges:
              adjancency[nodea].append([nodea, cost]							)
              adjancency[nodea].append([nodea, cost]							)

       __a     				=  mst(snake_case_							)

       __a     				=  [
           [7, 6, 1],
           [2, 8, 2],
           [6, 5, 2],
           [0, 1, 4],
           [2, 5, 4],
           [2, 3, 7],
           [0, 7, 8],
           [3, 4, 9],
       ]

       for answer in expected:
              __a     				=  tuple(answer[:2]							)
              __a     				=  tuple(edge[::-1]							)
              assert edge in result or reverse in result
"""simple docstring"""



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



def 					_lowerCamelCase(					a ,  a ,  a ,  a							):
       __a     				=  [[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_:
                            __a     				=  max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]] ,  dp[i - 1][w_]							)
                     else:
                            __a     				=  dp[i - 1][w_]

       return dp[n][w_], dp



def 					_lowerCamelCase(					a ,  a ,  a							):
       if not (isinstance(a ,  (list, tuple)							) and isinstance(a ,  (list, tuple)							)):
              raise ValueError(
                  "Both the weights and values vectors must be either lists or tuples"							)

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

       __a				, __a     				=  knapsack(a ,  a ,  a ,  a							)
       __a     				=  set()
       _construct_solution(a ,  a ,  a ,  a ,  a							)

       return optimal_val, example_optional_set



def 					_lowerCamelCase(					a ,  a ,  a ,  a ,  a							):
       # for the current item i at a maximum weight j to be part of an optimal subset,
       # the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
       # where i - 1 means considering only the previous items at the given maximum weight
       if i > 0 and j > 0:
              if dp[i - 1][j] == dp[i][j]:
                     _construct_solution(a ,  a ,  i - 1 ,  a ,  a							)
              else:
                     optimal_set.add(a							)
                     _construct_solution(a ,  a ,  i - 1 ,  j - wt[i - 1] ,  a							)


if __name__ == "__main__":
   SCREAMING_SNAKE_CASE__:Tuple			=	[3, 2, 4, 4]
   SCREAMING_SNAKE_CASE__:List[str]			=	[4, 3, 2, 3]
   SCREAMING_SNAKE_CASE__:List[str]			=	4
   SCREAMING_SNAKE_CASE__:List[str]			=	6
   SCREAMING_SNAKE_CASE__:Optional[Any]			=	[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
   SCREAMING_SNAKE_CASE__	,      SCREAMING_SNAKE_CASE__:Optional[int]			=	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
   SCREAMING_SNAKE_CASE__	,      SCREAMING_SNAKE_CASE__:Optional[Any]			=	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)
