






import sys
from random import randint

class        _SCREAMING_SNAKE_CASE			:





	def __init__(						self							:   List[str]					,    __lowerCamelCase							:   int					,    __lowerCamelCase							:   List[str]      ):
		UpperCamelCase	:Optional[int]		=      key
		UpperCamelCase	:int		=      freq





	def __str__(						self							:   Optional[Any]      ):
		return F"""Node(key={self.key}, freq={self.freq})"""

def   SCREAMING_SNAKE_CASE_				(				__magic_name__   :    Dict      ,     __magic_name__   :    Optional[int]      ,     __magic_name__   :    str      ,     __magic_name__   :    Dict      ,     __magic_name__   :    int      ,     __magic_name__   :    int   )						->     int:






	"""simple docstring"""



	if i > j or i < 0 or j > len(a_   ) - 1:
		return

	UpperCamelCase	:str		=      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_				(				__magic_name__   :    Optional[Any]   )						->     List[str]:






	"""simple docstring"""



	nodes.sort(key=lambda __magic_name__   : node.key   )

	UpperCamelCase	:List[Any]		=      len(a_   )

	UpperCamelCase	:Union[str, Any]		=      [nodes[i].key for i in range(a_   )]
	UpperCamelCase	:List[str]		=      [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.
	UpperCamelCase	: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
	UpperCamelCase	:Dict		=      [[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
	UpperCamelCase	:Any		=      [[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   ):
			UpperCamelCase	:Optional[int]		=      i + interval_length - 1

			UpperCamelCase	:List[Any]		=      sys.maxsize  # set the value to "infinity"
			UpperCamelCase	:str		=      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
				UpperCamelCase	:Any		=      dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
				UpperCamelCase	:int		=      dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
				UpperCamelCase	:List[Any]		=      left + total[i][j] + right

				if dp[i][j] > cost:
					UpperCamelCase	:Dict		=      cost
					UpperCamelCase	:Optional[int]		=      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_				(				)						->     Union[str, Any]:






	"""simple docstring"""



	UpperCamelCase	:Any		=      [Node(a_      ,     randint(1      ,     50   )   ) for i in range(10      ,     0      ,     -1   )]
	find_optimal_binary_search_tree(a_   )


if __name__ == "__main__":
	main()








'''simple docstring'''







import re






def  lowerCAmelCase__		(					a_  :     Optional[int]			)   -> Optional[Any]:
       def docstring_decorator(a_  :     Dict			):
              UpperCAmelCase__	:   Optional[int]												=	fn.__doc__
              UpperCAmelCase__	:   Dict												=	func_doc.split('''\n'''			)
              UpperCAmelCase__	:   Any												=	0
              while i < len(a_			) and re.search(r'''^\s*Examples?:\s*$'''			,						lines[i]			) is None:
                     i += 1
              if i < len(a_			):
                     UpperCAmelCase__	:   List[Any]												=	example_docstring
                     UpperCAmelCase__	:   int												=	'''\n'''.join(a_			)
              else:
                     raise ValueError(
                         f"""The function {fn} should have an empty 'Examples:' in its docstring as placeholder, """
                         f"""current docstring is:\n{func_doc}"""			)
              UpperCAmelCase__	:   Any												=	func_doc
              return fn

       return docstring_decorator