



def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__    ,			snake_case__					)	->     Optional[Any]:



				"""simple docstring"""





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







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__    ,			snake_case__					)	->     Dict:



				"""simple docstring"""





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

				return dp[n][w_], dp







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__					)	->     Optional[int]:



				"""simple docstring"""





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

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

				lowerCAmelCase__  ,   lowerCAmelCase__		  =  knapsack(snake_case__    ,			snake_case__    ,			snake_case__    ,			snake_case__					)
				lowerCAmelCase__		  =  set()
				_construct_solution(snake_case__    ,			snake_case__    ,			snake_case__    ,			snake_case__    ,			snake_case__					)

				return optimal_val, example_optional_set







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__    ,			snake_case__    ,			snake_case__					)	->     Any:



				"""simple docstring"""





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


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





import numpy as np


class 	__snake_case   :
		def __init__(							self						):







						"""simple docstring"""
						lowerCAmelCase__		  =  (0, 0)
						lowerCAmelCase__		  =  None
						lowerCAmelCase__		  =  0
						lowerCAmelCase__		  =  0
						lowerCAmelCase__		  =  0
		def __eq__(							self    ,a_						):







						"""simple docstring"""
						return self.position == cell.position



		def 						SCREAMING_SNAKE_CASE_					(							self						):







						"""simple docstring"""
						print(self.position						)



class 	__snake_case   :
		def __init__(							self    ,a_=(5, 5)						):







						"""simple docstring"""
						lowerCAmelCase__		  =  np.zeros(a_						)
						lowerCAmelCase__		  =  world_size[0]
						lowerCAmelCase__		  =  world_size[1]
		def 						SCREAMING_SNAKE_CASE_					(							self						):







						"""simple docstring"""
						print(self.w						)



		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_						):







						"""simple docstring"""
						lowerCAmelCase__		  =  [
						    (-1, -1),
						    (-1, 0),
						    (-1, 1),
						    (0, -1),
						    (0, 1),
						    (1, -1),
						    (1, 0),
						    (1, 1),
						]
						lowerCAmelCase__		  =  cell.position[0]
						lowerCAmelCase__		  =  cell.position[1]
						lowerCAmelCase__		  =  []
						for n in neughbour_cord:
										lowerCAmelCase__		  =  current_x + n[0]
										lowerCAmelCase__		  =  current_y + n[1]
										if 0 <= x < self.world_x_limit and 0 <= y < self.world_y_limit:
														lowerCAmelCase__		  =  Cell()
														lowerCAmelCase__		  =  (x, y)
														lowerCAmelCase__		  =  cell
														neighbours.append(a_						)
						return neighbours







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__					)	->     int:



				"""simple docstring"""





				lowerCAmelCase__		  =  []
				lowerCAmelCase__		  =  []
				_open.append(snake_case__					)

				while _open:
								lowerCAmelCase__		  =  np.argmin([n.f for n in _open]					)
								lowerCAmelCase__		  =  _open[min_f]
								_closed.append(_open.pop(snake_case__					)					)
								if current == goal:
												break
								for n in world.get_neigbours(snake_case__					):
												for c in _closed:
																if c == n:
																				continue
												lowerCAmelCase__		  =  current.g + 1
												lowerCAmelCase__  ,   lowerCAmelCase__		  =  n.position
												lowerCAmelCase__  ,   lowerCAmelCase__		  =  goal.position
												lowerCAmelCase__		  =  (ya - ya) ** 2 + (xa - xa) ** 2
												lowerCAmelCase__		  =  n.h + n.g

												for c in _open:
																if c == n and c.f < n.f:
																				continue
												_open.append(snake_case__					)
				lowerCAmelCase__		  =  []
				while current.parent is not None:
								path.append(current.position					)
								lowerCAmelCase__		  =  current.parent
				path.append(current.position					)
				return path[::-1]


if __name__ == "__main__":
	_lowerCAmelCase	:   str    =   Gridworld()
	# Start position and goal
	_lowerCAmelCase	:   List[Any]    =   Cell()
	_lowerCAmelCase	:   List[str]    =   (0, 0)
	_lowerCAmelCase	:   Optional[int]    =   Cell()
	_lowerCAmelCase	:   int    =   (4, 4)
	print(f"""path from {start.position} to {goal.position}""")
	_lowerCAmelCase	:   Optional[int]    =   astar(world, start, goal)
	#   Just for visual reasons.
	for i in s:
		_lowerCAmelCase	:   int    =   1
	print(world.w)
