

"""simple docstring"""




def 		A				(   snake_case__						, snake_case__						, snake_case__						, snake_case__			):




			'''simple docstring'''


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

def 		A				(   snake_case__						, snake_case__						, snake_case__						, snake_case__			):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__									=					[[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_:
												SCREAMING_SNAKE_CASE__									=					max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]						, dp[i - 1][w_]			)
									else:
												SCREAMING_SNAKE_CASE__									=					dp[i - 1][w_]

			return dp[n][w_], dp

def 		A				(   snake_case__						, snake_case__						, snake_case__			):




			'''simple docstring'''


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

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

			SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__									=					knapsack(lowercase_						, lowercase_						, lowercase_						, lowercase_			)
			SCREAMING_SNAKE_CASE__									=					set()
			_construct_solution(lowercase_						, lowercase_						, lowercase_						, lowercase_						, lowercase_			)

			return optimal_val, example_optional_set

def 		A				(   snake_case__						, snake_case__						, snake_case__						, snake_case__						, snake_case__			):




			'''simple docstring'''


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


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








def SCREAMING_SNAKE_CASE				(       lowercase_						)   ->       Any:



       """simple docstring"""

       A__       =    [0] * len(lowercase_						)
       A__       =    []
       A__       =    [1] * len(lowercase_						)

       for values in graph.values():
              for i in values:
                     indegree[i] += 1

       for i in range(len(lowercase_						)						):
              if indegree[i] == 0:
                     queue.append(lowercase_						)

       while queue:
              A__       =    queue.pop(0						)
              for x in graph[vertex]:
                     indegree[x] -= 1

                     if long_dist[vertex] + 1 > long_dist[x]:
                            A__       =    long_dist[vertex] + 1

                     if indegree[x] == 0:
                            queue.append(lowercase_						)

       print(max(lowercase_						)						)


# Adjacency list of Graph
_lowerCamelCase	:		Optional[int]							       =   {0: [2, 3, 4], 1: [2, 7], 2: [5], 3: [5, 7], 4: [7], 5: [6], 6: [7], 7: []}
longest_distance(graph)


