



'''simple docstring'''
from __future__ import annotations

import os
from collections.abc import Mapping

snake_case_					:      Any    			=    tuple[int, int]






class 				lowercase__      :





	def __init__(					self   :							Tuple					,lowerCamelCase__   :							Union[str, Any]					,lowerCamelCase__   :							Dict					):







							'''simple docstring'''
							_UpperCamelCase   :						List[str]												=  vertices
							_UpperCamelCase   :						Any												=  {
							    (min(UpperCAmelCase_					), max(UpperCAmelCase_					)): weight for edge, weight in edges.items()
							}





	def       UpperCamelCase_    (					self   :							List[Any]					,lowerCamelCase__   :							List[Any]					,lowerCamelCase__   :							Optional[Any]					):







							'''simple docstring'''
							self.vertices.add(edge[0]					)
							self.vertices.add(edge[1]					)
							_UpperCamelCase   :						str												=  weight





	def       UpperCamelCase_    (					self   :							str					):







							'''simple docstring'''
							_UpperCamelCase   :						Union[str, Any]												=  Graph({min(self.vertices					)}					,{}					)
							_UpperCamelCase   :						Union[str, Any]												=  42
							_UpperCamelCase   :						Union[str, Any]												=  42
							_UpperCamelCase   :						str												=  42
							_UpperCamelCase   :						Union[str, Any]												=  42

							while len(subgraph.vertices					) < len(self.vertices					):
													_UpperCamelCase   :						int												=  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   :						int												=  edge
																															_UpperCamelCase   :						Tuple												=  weight

													subgraph.add_edge(UpperCAmelCase_					,UpperCAmelCase_					)

							return subgraph






def A__       (	UpperCAmelCase_ = "p107_network.txt"				):
						_UpperCamelCase   :						Optional[Any]												=  os.path.abspath(os.path.dirname(_snake_case				)				)
						_UpperCamelCase   :						List[Any]												=  os.path.join(_snake_case    ,    _snake_case				)
						_UpperCamelCase   :						Optional[Any]												=  {}
						_UpperCamelCase   :						List[Any]												=  4_2
						_UpperCamelCase   :						List[str]												=  4_2
						_UpperCamelCase   :						Dict												=  4_2

						with open(_snake_case				) as f:
												_UpperCamelCase   :						Dict												=  f.read().strip().split('\n'				)

						_UpperCamelCase   :						int												=  [line.split(','				) for line in data]

						for edgea in range(1    ,    len(_snake_case				)				):
												for edgea in range(_snake_case				):
																		if adjaceny_matrix[edgea][edgea] != "-":
																								_UpperCamelCase   :						List[str]												=  int(adjaceny_matrix[edgea][edgea]				)

						_UpperCamelCase   :						Dict												=  Graph(set(range(len(_snake_case				)				)				)    ,    _snake_case				)

						_UpperCamelCase   :						str												=  graph.prims_algorithm()

						_UpperCamelCase   :						Tuple												=  sum(graph.edges.values()				)
						_UpperCamelCase   :						Union[str, Any]												=  sum(subgraph.edges.values()				)

						return initial_total - optimal_total


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







'''simple docstring'''





from __future__ import annotations

import math




def 							lowerCamelCase	(					_snake_case	:    float  ,_snake_case	:    int							):





    '''simple docstring'''


    lowercase__									=    u
    for i in range(1  ,_snake_case							):
        lowercase__									=    temp * (u - i)
    return temp




def 							lowerCamelCase	(					):





    '''simple docstring'''


    lowercase__									=    int(input("enter the numbers of values: "							)							)
    lowercase__									=    []
    for _ in range(_snake_case							):
        y.append([]							)
    for i in range(_snake_case							):
        for j in range(_snake_case							):
            y[i].append(_snake_case							)
            lowercase__									=    0

    print("enter the values of parameters in a list: "							)
    lowercase__									=    list(map(_snake_case  ,input().split()							)							)

    print("enter the values of corresponding parameters: "							)
    for i in range(_snake_case							):
        lowercase__									=    float(input()							)

    lowercase__									=    int(input("enter the value to interpolate: "							)							)
    lowercase__									=    (value - x[0]) / (x[1] - x[0])

    # for calculating forward difference table

    for i in range(1  ,_snake_case							):
        for j in range(n - i							):
            lowercase__									=    y[j + 1][i - 1] - y[j][i - 1]

    lowercase__									=    y[0][0]
    for i in range(1  ,_snake_case							):
        summ += (ucal(_snake_case  ,_snake_case							) * y[0][i]) / math.factorial(_snake_case							)

    print(f'''the value at {value} is {summ}'''							)


if __name__ == "__main__":
 main()




