
'''simple docstring'''






import sys
from random import randint

class 							_snake_case     :
	"""simple docstring"""





	def __init__(						self				: Optional[int]					,						UpperCamelCase_				: List[str]					,						UpperCamelCase_				: int      ):
			lowerCAmelCase_   :       int    							=key
			lowerCAmelCase_   :       Dict    							=freq





	def __str__(						self				: Dict      ):
			return F'Node(key={self.key}, freq={self.freq})'







def 		SCREAMING_SNAKE_CASE__					(							_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ):
		if i > j or i < 0 or j > len(A__  ) - 1:
				return

		lowerCAmelCase_   :       int    							=root[i][j]
		if parent == -1:  # root does not have a parent
				print(f'{key[node]} is the root of the binary search tree.'  )
		elif is_left:
				print(f'{key[node]} is the left child of key {parent}.'  )
		else:
				print(f'{key[node]} is the right child of key {parent}.'  )

		print_binary_search_tree(A__  ,					A__  ,					A__  ,					node - 1  ,					key[node]  ,					A__  )
		print_binary_search_tree(A__  ,					A__  ,					node + 1  ,					A__  ,					key[node]  ,					A__  )







def 		SCREAMING_SNAKE_CASE__					(							_SCREAMING_SNAKE_CASE  ):
		nodes.sort(key=lambda _SCREAMING_SNAKE_CASE  : node.key  )

		lowerCAmelCase_   :       str    							=len(A__  )

		lowerCAmelCase_   :       Optional[int]    							=[nodes[i].key for i in range(A__  )]
		lowerCAmelCase_   :       List[Any]    							=[nodes[i].freq for i in range(A__  )]

		# This 2D array stores the overall tree cost (which's as minimized as possible);
		# for a single key, cost is equal to frequency of the key.
		lowerCAmelCase_   :       Optional[Any]    							=[[freqs[i] if i == j else 0 for j in range(A__  )] for i in range(A__  )]
		# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
		# array
		lowerCAmelCase_   :       int    							=[[freqs[i] if i == j else 0 for j in range(A__  )] for i in range(A__  )]
		# stores tree roots that will be used later for constructing binary search tree
		lowerCAmelCase_   :       int    							=[[i if i == j else 0 for j in range(A__  )] for i in range(A__  )]

		for interval_length in range(2  ,					n + 1  ):
				for i in range(n - interval_length + 1  ):
						lowerCAmelCase_   :       Optional[int]    							=i + interval_length - 1

						lowerCAmelCase_   :       str    							=sys.maxsize  # set the value to "infinity"
						lowerCAmelCase_   :       int    							=total[i][j - 1] + freqs[j]

						# Apply Knuth's optimization
						# Loop without optimization: for r in range(i, j + 1):
						for r in range(root[i][j - 1]  ,					root[i + 1][j] + 1  ):  # r is a temporal root
								lowerCAmelCase_   :       Optional[int]    							=dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
								lowerCAmelCase_   :       Dict    							=dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
								lowerCAmelCase_   :       Dict    							=left + total[i][j] + right

								if dp[i][j] > cost:
										lowerCAmelCase_   :       List[str]    							=cost
										lowerCAmelCase_   :       Dict    							=r

		print('''Binary search tree nodes:'''  )
		for node in nodes:
				print(A__  )

		print(f'\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.'  )
		print_binary_search_tree(A__  ,					A__  ,					0  ,					n - 1  ,					-1  ,					A__  )







def 		SCREAMING_SNAKE_CASE__					(							):
		lowerCAmelCase_   :       str    							=[Node(A__  ,					randint(1  ,					50  )  ) for i in range(10  ,					0  ,					-1  )]
		find_optimal_binary_search_tree(A__  )


if __name__ == "__main__":
							main()









"""simple docstring"""




SCREAMING_SNAKE_CASE_  :      Optional[int]							=      {0: [1, 2], 1: [0, 3], 2: [0], 3: [1], 4: [5, 6], 5: [4, 6], 6: [4, 5]}

SCREAMING_SNAKE_CASE_  :      str							=      {0: [1, 2, 3], 1: [0, 3], 2: [0], 3: [0, 1], 4: [], 5: []}



def 						UpperCAmelCase__ (					A__						,     A__						,     A__ )   ->   list:




   """simple docstring"""
   lowerCamelCase__						       =      True
   lowerCamelCase__						       =      []

   for neighbour in graph[vert]:
      if not visited[neighbour]:
         connected_verts += dfs(A__						,     A__						,     A__ )

   return [vert, *connected_verts]



def 						UpperCAmelCase__ (					A__ )   ->   list:




   """simple docstring"""
   lowerCamelCase__						       =      len(A__ )
   lowerCamelCase__						       =      graph_size * [False]
   lowerCamelCase__						       =      []

   for i in range(A__ ):
      if not visited[i]:
         lowerCamelCase__						       =      dfs(A__						,     A__						,     A__ )
         components_list.append(A__ )

   return components_list


if __name__ == "__main__":
     import doctest

     doctest.testmod()




