





from __future__ import annotations

import os
from collections.abc import Mapping

lowercase_					     =	tuple[int, int]
class        SCREAMING_SNAKE_CASE     :


   def __init__(					self    :       Tuple    ,  a    :       set[int]    ,  a    :       Mapping[EdgeT, int] )->     Dict:





     """simple docstring"""







     lowercase__			    =						vertices
     lowercase__			    =						{
         (min(_snake_case ), max(_snake_case )): weight for edge, weight in edges.items()
     }


   def  SCREAMING_SNAKE_CASE_							(					self    :       Optional[Any]    ,  a    :       EdgeT    ,  a    :       int )->     Any:





     """simple docstring"""







     self.vertices.add(edge[0] )
     self.vertices.add(edge[1] )
     lowercase__			    =						weight


   def  SCREAMING_SNAKE_CASE_							(					self    :       List[str] )->     List[str]:





     """simple docstring"""







     lowercase__			    =						Graph({min(self.vertices )}    ,  {} )
     lowercase__			    =						42
     lowercase__			    =						42
     lowercase__			    =						42
     lowercase__			    =						42

     while len(subgraph.vertices ) < len(self.vertices ):
       lowercase__			    =						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:
             lowercase__			    =						edge
             lowercase__			    =						weight

       subgraph.add_edge(_snake_case    ,  _snake_case )

     return subgraph






def     __UpperCamelCase						(_SCREAMING_SNAKE_CASE = "p107_network.txt"	)       ->     int:
  lowercase__			    =						os.path.abspath(os.path.dirname(__UpperCamelCase	)	)
  lowercase__			    =						os.path.join(__UpperCamelCase	,		__UpperCamelCase	)
  lowercase__			    =						{}
  lowercase__			    =						42
  lowercase__			    =						42
  lowercase__			    =						42

  with open(__UpperCamelCase	) as f:
    lowercase__			    =						f.read().strip().split('\n'	)

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

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

  lowercase__			    =						Graph(set(range(len(__UpperCamelCase	)	)	)	,		__UpperCamelCase	)

  lowercase__			    =						graph.prims_algorithm()

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

  return initial_total - optimal_total


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










from __future__ import annotations

import math
from collections.abc import Callable




def     __UpperCamelCase						(_SCREAMING_SNAKE_CASE	,		_SCREAMING_SNAKE_CASE	,		_SCREAMING_SNAKE_CASE	,		_SCREAMING_SNAKE_CASE = 100	,		)       ->     float:
  lowercase__			    =						x_start
  lowercase__			    =						fnc(_SCREAMING_SNAKE_CASE	)
  lowercase__			    =						0.0

  for _ in range(_SCREAMING_SNAKE_CASE	):
    # Approximates curve as a sequence of linear lines and sums their length
    lowercase__			    =						(x_end - x_start) / steps + xa
    lowercase__			    =						fnc(_SCREAMING_SNAKE_CASE	)
    length += math.hypot(xa - xa	,		fxa - fxa	)

    # Increment step
    lowercase__			    =						xa
    lowercase__			    =						fxa

  return length


if __name__ == "__main__":




      def     __UpperCamelCase						(_SCREAMING_SNAKE_CASE	)       ->     str:
        return math.sin(10 * x	)

      print("""f(x) = sin(10 * x)""")
      print("""The length of the curve from x = -10 to x = 10 is:""")
      lowercase_					     =	10
      while i <= 100_000:
            print(f'''With {i} steps: {line_length(f, -10, 10, i)}''')
            i *= 10


