



from __future__ import annotations

import os
from collections.abc import Mapping

_lowercase     							=						tuple[int, int]
class 				__A					:





			def __init__(self							,    __magic_name__							,    __magic_name__				):
						lowerCamelCase__ :      set[int]								=		vertices
						lowerCamelCase__ :      dict[EdgeT, int]								=		{
						    (min(__magic_name__				), max(__magic_name__				)): weight for edge, weight in edges.items()
						}





			def        _snake_case    (self							,    __magic_name__							,    __magic_name__				):
						self.vertices.add(edge[0]				)
						self.vertices.add(edge[1]				)
						lowerCamelCase__ :      Union[str, Any]								=		weight





			def        _snake_case    (self				):
						lowerCamelCase__ :      Graph								=		Graph({min(self.vertices				)}							,    {}				)
						lowerCamelCase__ :      EdgeT
						lowerCamelCase__ :      int
						lowerCamelCase__ :      EdgeT
						lowerCamelCase__ :      int

						while len(subgraph.vertices				) < len(self.vertices				):
									lowerCamelCase__ :      Any								=		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:
																		lowerCamelCase__ :      int								=		edge
																		lowerCamelCase__ :      Optional[Any]								=		weight

									subgraph.add_edge(__magic_name__							,    __magic_name__				)

						return subgraph







def      _A				(UpperCamelCase		:      str = "p107_network.txt" )  ->int:



			'''simple docstring'''







			lowerCamelCase__ :      str								=		os.path.abspath(os.path.dirname(UpperCamelCase ) )
			lowerCamelCase__ :      str								=		os.path.join(UpperCamelCase      ,			UpperCamelCase )
			lowerCamelCase__ :      dict[EdgeT, int]								=		{}
			lowerCamelCase__ :      list[str]
			lowerCamelCase__ :      int
			lowerCamelCase__ :      int

			with open(UpperCamelCase ) as f:
						lowerCamelCase__ :      Any								=		f.read().strip().split("""\n""" )

			lowerCamelCase__ :      Dict								=		[line.split(""",""" ) for line in data]

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

			lowerCamelCase__ :      Graph								=		Graph(set(range(len(UpperCamelCase ) ) )      ,			UpperCamelCase )

			lowerCamelCase__ :      Graph								=		graph.prims_algorithm()

			lowerCamelCase__ :      int								=		sum(graph.edges.values() )
			lowerCamelCase__ :      int								=		sum(subgraph.edges.values() )

			return initial_total - optimal_total


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








from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase






def      _A				(UpperCamelCase		:      str )  ->None:



			'''simple docstring'''







			lowerCamelCase__							,lowerCamelCase__ :      List[str]								=		analyze_text(UpperCamelCase )
			lowerCamelCase__ :      Any								=		list(""" """ + ascii_lowercase )
			# what is our total sum of probabilities.
			lowerCamelCase__ :      str								=		sum(single_char_strings.values() )

			# one length string
			lowerCamelCase__ :      Union[str, Any]								=		0
			# for each alpha we go in our dict and if it is in it we calculate entropy
			for ch in my_alphas:
						if ch in single_char_strings:
									lowerCamelCase__ :      List[Any]								=		single_char_strings[ch]
									lowerCamelCase__ :      List[str]								=		my_str / all_sum
									my_fir_sum += prob * math.loga(UpperCamelCase )  # entropy formula.

    # print entropy
			print(f"{round(-1 * my_fir_sum ):.1f}" )

			# two len string
			lowerCamelCase__ :      str								=		sum(two_char_strings.values() )
			lowerCamelCase__ :      int								=		0
			# for each alpha (two in size) calculate entropy.
			for cha in my_alphas:
						for cha in my_alphas:
									lowerCamelCase__ :      str								=		cha + cha
									if sequence in two_char_strings:
												lowerCamelCase__ :      str								=		two_char_strings[sequence]
												lowerCamelCase__ :      int								=		int(UpperCamelCase ) / all_sum
												my_sec_sum += prob * math.loga(UpperCamelCase )

    # print second entropy
			print(f"{round(-1 * my_sec_sum ):.1f}" )

			# print the difference between them
			print(f"{round((-1 * my_sec_sum) - (-1 * my_fir_sum) ):.1f}" )






def      _A				(UpperCamelCase		:      str )  ->tuple[dict, dict]:



			'''simple docstring'''







			lowerCamelCase__ :      Optional[int]								=		Counter()  # type: ignore
			lowerCamelCase__ :      List[Any]								=		Counter()  # type: ignore
			single_char_strings[text[-1]] += 1

			# first case when we have space at start.
			two_char_strings[" " + text[0]] += 1
			for i in range(0      ,			len(UpperCamelCase ) - 1 ):
						single_char_strings[text[i]] += 1
						two_char_strings[text[i : i + 2]] += 1
			return single_char_strings, two_char_strings






def      _A				()  ->List[str]:



			'''simple docstring'''







			import doctest

			doctest.testmod()
			# text = (
			#     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
			#     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
			#     "jointure saw horrible. He private he on be imagine suppose. Fertile "
			#     "beloved evident through no service elderly is. Blind there if every no so "
			#     "at. Own neglected you preferred way sincerity delivered his attempted. To "
			#     "of message cottage windows do besides against uncivil.  Delightful "
			#     "unreserved impossible few estimating men favourable see entreaties. She "
			#     "propriety immediate was improving. He or entrance humoured likewise "
			#     "moderate. Much nor game son say feel. Fat make met can must form into "
			#     "gate. Me we offending prevailed discovery. "
			# )

			# calculate_prob(text)


if __name__ == "__main__":
				main()



