





'''simple docstring'''



class 							__lowercase       :







	'''simple docstring'''

	def __init__(self )							->							Optional[int]:







				'''simple docstring'''





				__lowercase										=							''''''
				__lowercase										=							''''''
				__lowercase										=							[]


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase )							->							int:







				'''simple docstring'''





				if m == -1:
							return n + 1
				elif n == -1:
							return m + 1
				elif self.dp[m][n] > -1:
							return self.dp[m][n]
				else:
							if self.worda[m] == self.worda[n]:
										__lowercase										=							self.__min_dist_top_down_dp(m - 1     ,n - 1 )
							else:
										__lowercase										=							self.__min_dist_top_down_dp(_lowerCamelCase     ,n - 1 )
										__lowercase										=							self.__min_dist_top_down_dp(m - 1     ,_lowerCamelCase )
										__lowercase										=							self.__min_dist_top_down_dp(m - 1     ,n - 1 )
										__lowercase										=							1 + min(_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase )

							return self.dp[m][n]


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase )							->							int:







				'''simple docstring'''





				__lowercase										=							worda
				__lowercase										=							worda
				__lowercase										=							[[-1 for _ in range(len(_lowerCamelCase ) )] for _ in range(len(_lowerCamelCase ) )]

				return self.__min_dist_top_down_dp(len(_lowerCamelCase ) - 1     ,len(_lowerCamelCase ) - 1 )


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase )							->							int:







				'''simple docstring'''





				__lowercase										=							worda
				__lowercase										=							worda
				__lowercase										=							len(_lowerCamelCase )
				__lowercase										=							len(_lowerCamelCase )
				__lowercase										=							[[0 for _ in range(n + 1 )] for _ in range(m + 1 )]

				for i in range(m + 1 ):
							for j in range(n + 1 ):
										if i == 0:  # first string is empty
													__lowercase										=							j
										elif j == 0:  # second string is empty
													__lowercase										=							i
										elif worda[i - 1] == worda[j - 1]:  # last characters are equal
													__lowercase										=							self.dp[i - 1][j - 1]
										else:
													__lowercase										=							self.dp[i][j - 1]
													__lowercase										=							self.dp[i - 1][j]
													__lowercase										=							self.dp[i - 1][j - 1]
													__lowercase										=							1 + min(_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase )
				return self.dp[m][n]


if __name__ == "__main__":
	_SCREAMING_SNAKE_CASE					=    EditDistance()

	print('''****************** Testing Edit Distance DP Algorithm ******************''')
	print()

	_SCREAMING_SNAKE_CASE					=    input('''Enter the first string: ''').strip()
	_SCREAMING_SNAKE_CASE					=    input('''Enter the second string: ''').strip()

	print()
	print(f'''The minimum edit distance is: {solver.min_dist_top_down(Sa, Sa)}''')
	print(f'''The minimum edit distance is: {solver.min_dist_bottom_up(Sa, Sa)}''')
	print()
	print('''*************** End of Testing Edit Distance DP Algorithm ***************''')












'''simple docstring'''



from __future__ import annotations

from typing import Any






class 							__lowercase       :







	'''simple docstring'''

	def __init__(self     ,_lowerCamelCase )							->							None:







				'''simple docstring'''





				__lowercase										=							num_of_nodes
				__lowercase										=							[]
				__lowercase										=							{}


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase )							->							None:







				'''simple docstring'''





				self.m_edges.append([u_node, v_node, weight] )


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase )							->							int:







				'''simple docstring'''





				if self.m_component[u_node] == u_node:
							return u_node
				return self.find_component(self.m_component[u_node] )


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase )							->							None:







				'''simple docstring'''





				if self.m_component[u_node] != u_node:
							for k in self.m_component:
										__lowercase										=							self.find_component(_lowerCamelCase )


	def 						_UpperCAmelCase     (self     ,_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase )							->							None:







				'''simple docstring'''





				if component_size[u_node] <= component_size[v_node]:
							__lowercase										=							v_node
							component_size[v_node] += component_size[u_node]
							self.set_component(_lowerCamelCase )

				elif component_size[u_node] >= component_size[v_node]:
							__lowercase										=							self.find_component(_lowerCamelCase )
							component_size[u_node] += component_size[v_node]
							self.set_component(_lowerCamelCase )


	def 						_UpperCAmelCase     (self )							->							None:







				'''simple docstring'''





				__lowercase										=							[]
				__lowercase										=							0

				__lowercase										=							[-1] * self.m_num_of_nodes

				# A list of components (initialized to all of the nodes)
				for node in range(self.m_num_of_nodes ):
							self.m_component.update({node: node} )
							component_size.append(1 )

				__lowercase										=							self.m_num_of_nodes

				while num_of_components > 1:
							for edge in self.m_edges:
										__lowercase						,		__lowercase						,		__lowercase										=							edge

										__lowercase										=							self.m_component[u]
										__lowercase										=							self.m_component[v]

										if u_component != v_component:

													for component in (u_component, v_component):
																if (
																    minimum_weight_edge[component] == -1
																    or minimum_weight_edge[component][2] > w
																):
																			__lowercase										=							[u, v, w]

							for edge in minimum_weight_edge:
										if isinstance(_lowerCamelCase     ,_lowerCamelCase ):
													__lowercase						,		__lowercase						,		__lowercase										=							edge

													__lowercase										=							self.m_component[u]
													__lowercase										=							self.m_component[v]

													if u_component != v_component:
																mst_weight += w
																self.union(_lowerCamelCase     ,_lowerCamelCase     ,_lowerCamelCase )
																print(f"Added edge [{u} - {v}]\nAdded weight: {w}\n" )
																num_of_components -= 1

							__lowercase										=							[-1] * self.m_num_of_nodes
				print(f"The total weight of the minimal spanning tree is: {mst_weight}" )





def    _lowerCAmelCase						(				):
			pass


if __name__ == "__main__":
	import doctest

	doctest.testmod()





