

from dataclasses import dataclass

_a:      str								=     "0.1"
_a:      List[Any]								=     "Lucia Harcekova"

@dataclass
class   __UpperCamelCase      :
	SCREAMING_SNAKE_CASE__      			=       42
	SCREAMING_SNAKE_CASE__      			=       42
	SCREAMING_SNAKE_CASE__      			=       42




	def __repr__(						self		:  Any							):


		'''simple docstring'''







		return F"({self.offset}, {self.length}, {self.indicator})"


class   __UpperCamelCase      :




	def __init__(						self		:  str						,		lowerCAmelCase		:  int = 13						,		lowerCAmelCase		:  int = 6							):


		'''simple docstring'''







		UpperCAmelCase_    			=     window_size
		UpperCAmelCase_    			=     lookahead_buffer_size
		UpperCAmelCase_    			=     self.window_size - self.lookahead_buffer_size




	def  __A   (						self		:  int						,		lowerCAmelCase		:  str							):


		'''simple docstring'''







		UpperCAmelCase_    			=     []
		UpperCAmelCase_    			=     ''

		# while there are still characters in text to compress
		while text:
			# find the next encoding phrase
			# - triplet with offset, length, indicator (the next encoding character)
			UpperCAmelCase_    			=     self._find_encoding_token(_snake_case						,		_snake_case							)

			# update the search buffer:
			# - add new characters from text into it
			# - check if size exceed the max search buffer size, if so, drop the
			#   oldest elements
			search_buffer += text[: token.length + 1]
			if len(_snake_case							) > self.search_buffer_size:
				UpperCAmelCase_    			=     search_buffer[-self.search_buffer_size :]

			# update the text
			UpperCAmelCase_    			=     text[token.length + 1 :]

			# append the token to output
			output.append(_snake_case							)

		return output




	def  __A   (						self		:  Any						,		lowerCAmelCase		:  list[Token]							):


		'''simple docstring'''







		UpperCAmelCase_    			=     ''

		for token in tokens:
			for _ in range(token.length							):
				output += output[-token.offset]
			output += token.indicator

		return output




	def  __A   (						self		:  int						,		lowerCAmelCase		:  str						,		lowerCAmelCase		:  str							):


		'''simple docstring'''







		if not text:
			raise ValueError("We need some text to work with."							)

		# Initialise result parameters to default values
		UpperCAmelCase_    			=     0, 0

		if not search_buffer:
			return Token(_snake_case						,		_snake_case						,		text[length]							)

		for i, character in enumerate(_snake_case							):
			UpperCAmelCase_    			=     len(_snake_case							) - i
			if character == text[0]:
				UpperCAmelCase_    			=     self._match_length_from_index(_snake_case						,		_snake_case						,		0						,		_snake_case							)
				# if the found length is bigger than the current or if it's equal,
				# which means it's offset is smaller: update offset and length
				if found_length >= length:
					UpperCAmelCase_    			=     found_offset, found_length

		return Token(_snake_case						,		_snake_case						,		text[length]							)




	def  __A   (						self		:  List[Any]						,		lowerCAmelCase		:  str						,		lowerCAmelCase		:  str						,		lowerCAmelCase		:  int						,		lowerCAmelCase		:  int							):


		'''simple docstring'''







		if not text or text[text_index] != window[window_index]:
			return 0
		return 1 + self._match_length_from_index(
		    _snake_case						,		window + text[text_index]						,		text_index + 1						,		window_index + 1							)


if __name__ == "__main__":
				from doctest import testmod

				testmod()
				# Initialize compressor class
				_a:      Union[str, Any]								=     LZaaCompressor(window_size=13, lookahead_buffer_size=6)

				# Example
				_a:      List[str]								=     "cabracadabrarrarrad"
				_a:      Any								=     lzaa_compressor.compress(TEXT)
				print(lzaa_compressor.compress("""ababcbababaa"""))
				_a:      Union[str, Any]								=     lzaa_compressor.decompress(compressed_text)
				assert decompressed_text == TEXT, "The LZ77 algorithm returned the invalid result."


# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint

class   __UpperCamelCase      :




	def __init__(						self		:  Optional[Any]						,		lowerCAmelCase		:  Any						,		lowerCAmelCase		:  Optional[Any]							):


		'''simple docstring'''







		UpperCAmelCase_    			=     key
		UpperCAmelCase_    			=     freq




	def __str__(						self		:  List[str]							):


		'''simple docstring'''







		return F"Node(key={self.key}, freq={self.freq})"



def  __lowerCAmelCase (  A    ,       A    ,       A    ,       A    ,       A    ,       A      ):
	if i > j or i < 0 or j > len(A      ) - 1:
		return

	UpperCAmelCase_    			=     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  __lowerCAmelCase (  A      ):
	nodes.sort(key=lambda A      : node.key      )

	UpperCAmelCase_    			=     len(A      )

	UpperCAmelCase_    			=     [nodes[i].key for i in range(A      )]
	UpperCAmelCase_    			=     [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_    			=     [[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_    			=     [[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_    			=     [[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_    			=     i + interval_length - 1

			UpperCAmelCase_    			=     sys.maxsize  # set the value to "infinity"
			UpperCAmelCase_    			=     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_    			=     dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
				UpperCAmelCase_    			=     dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
				UpperCAmelCase_    			=     left + total[i][j] + right

				if dp[i][j] > cost:
					UpperCAmelCase_    			=     cost
					UpperCAmelCase_    			=     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  __lowerCAmelCase (  ):
	# A sample binary search tree
	UpperCAmelCase_    			=     [Node(A    ,       randint(1    ,       50      )      ) for i in range(10    ,       0    ,       -1      )]
	find_optimal_binary_search_tree(A      )


if __name__ == "__main__":
				main()