
class 				lowercase					:



		def __init__( self       )  ->					int:
				"""simple docstring"""
				UpperCamelCase		=     ''
				UpperCamelCase		=     ''
				UpperCamelCase		=     []



		def __UpperCamelCase ( self				,      A_				,      A_       )  ->					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]:
								UpperCamelCase		=     self.__min_dist_top_down_dp(m - 1				,      n - 1       )
						else:
								UpperCamelCase		=     self.__min_dist_top_down_dp(A_				,      n - 1       )
								UpperCamelCase		=     self.__min_dist_top_down_dp(m - 1				,      A_       )
								UpperCamelCase		=     self.__min_dist_top_down_dp(m - 1				,      n - 1       )
								UpperCamelCase		=     1 + min(A_				,      A_				,      A_       )

						return self.dp[m][n]



		def __UpperCamelCase ( self				,      A_				,      A_       )  ->					int:
				"""simple docstring"""
				UpperCamelCase		=     worda
				UpperCamelCase		=     worda
				UpperCamelCase		=     [[-1 for _ in range(len(A_       )       )] for _ in range(len(A_       )       )]

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



		def __UpperCamelCase ( self				,      A_				,      A_       )  ->					int:
				"""simple docstring"""
				UpperCamelCase		=     worda
				UpperCamelCase		=     worda
				UpperCamelCase		=     len(A_       )
				UpperCamelCase		=     len(A_       )
				UpperCamelCase		=     [[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
										UpperCamelCase		=     j
								elif j == 0:  # second string is empty
										UpperCamelCase		=     i
								elif worda[i - 1] == worda[j - 1]:  # last characters are equal
										UpperCamelCase		=     self.dp[i - 1][j - 1]
								else:
										UpperCamelCase		=     self.dp[i][j - 1]
										UpperCamelCase		=     self.dp[i - 1][j]
										UpperCamelCase		=     self.dp[i - 1][j - 1]
										UpperCamelCase		=     1 + min(A_				,      A_				,      A_       )
				return self.dp[m][n]


if __name__ == "__main__":
					_UpperCAmelCase					: Any      =       EditDistance()

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

					_UpperCAmelCase					: Optional[Any]      =       input("Enter the first string: ").strip()
					_UpperCAmelCase					: Optional[int]      =       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 ***************")


from __future__ import annotations

import os
from collections.abc import Mapping

_UpperCAmelCase					: Tuple      =       tuple[int, int]


class 				lowercase					:



		def __init__( self				,      A_				,      A_       )  ->					None:
				"""simple docstring"""
				UpperCamelCase		=     vertices
				UpperCamelCase		=     {
				    (min(A_       ), max(A_       )): weight for edge, weight in edges.items()
				}



		def __UpperCamelCase ( self				,      A_				,      A_       )  ->					None:
				"""simple docstring"""
				self.vertices.add(edge[0]       )
				self.vertices.add(edge[1]       )
				UpperCamelCase		=     weight



		def __UpperCamelCase ( self       )  ->					Graph:
				"""simple docstring"""
				UpperCamelCase		=     Graph({min(self.vertices       )}				,      {}       )
				UpperCamelCase		=     42
				UpperCamelCase		=     42
				UpperCamelCase		=     42
				UpperCamelCase		=     42

				while len(subgraph.vertices       ) < len(self.vertices       ):
						UpperCamelCase		=     max(self.edges.values()       ) + 1
						for edge, weight in self.edges.items():
								if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
										if weight < min_weight:
												UpperCamelCase		=     edge
												UpperCamelCase		=     weight

						subgraph.add_edge(A_				,      A_       )

				return subgraph






def       A       (					lowercase = "p107_network.txt" )   ->  int:
		'''simple docstring'''

		UpperCamelCase		=     os.path.abspath(os.path.dirname(lowercase ) )
		UpperCamelCase		=     os.path.join(lowercase    ,       lowercase )
		UpperCamelCase		=     {}
		UpperCamelCase		=     42
		UpperCamelCase		=     42
		UpperCamelCase		=     42

		with open(lowercase ) as f:
				UpperCamelCase		=     f.read().strip().split('\n' )

		UpperCamelCase		=     [line.split(',' ) for line in data]

		for edgea in range(1    ,       len(lowercase ) ):
				for edgea in range(lowercase ):
						if adjaceny_matrix[edgea][edgea] != "-":
								UpperCamelCase		=     int(adjaceny_matrix[edgea][edgea] )

		UpperCamelCase		=     Graph(set(range(len(lowercase ) ) )    ,       lowercase )

		UpperCamelCase		=     graph.prims_algorithm()

		UpperCamelCase		=     sum(graph.edges.values() )
		UpperCamelCase		=     sum(subgraph.edges.values() )

		return initial_total - optimal_total


if __name__ == "__main__":
					print(F'''{solution() = }''')
