

"""simple docstring"""




def 					lowerCAmelCase  (   __UpperCamelCase ):
 '''simple docstring'''





 if len(snake_case__ ) == 0 or not all(len(snake_case__ ) == 2 for pair in coordinates ):
  raise ValueError("""The program cannot work out a fitting polynomial.""" )

 if len({tuple(snake_case__ ) for pair in coordinates} ) != len(snake_case__ ):
  raise ValueError("""The program cannot work out a fitting polynomial.""" )

 UpperCAmelCase__   :					Any   				=   {x for x, _ in coordinates}
 if len(snake_case__ ) == 1:
  return F"x={coordinates[0][0]}"

 if len(snake_case__ ) != len(snake_case__ ):
  raise ValueError("""The program cannot work out a fitting polynomial.""" )

 UpperCAmelCase__   :					Union[str, Any]   				=   len(snake_case__ )

 UpperCAmelCase__   :					Optional[Any]   				=   0
 UpperCAmelCase__   :					Dict   				=   []
 # put the x and x to the power values in a matrix
 while count_of_line < x:
  UpperCAmelCase__   :					str   				=   0
  UpperCAmelCase__   :					int   				=   coordinates[count_of_line][0]
  UpperCAmelCase__   :					Optional[Any]   				=   []
  while count_in_line < x:
   count_line.append(a ** (x - (count_in_line + 1)) )
   count_in_line += 1
  matrix.append(snake_case__ )
  count_of_line += 1

 UpperCAmelCase__   :					Optional[int]   				=   0
 # put the y values into a vector
 UpperCAmelCase__   :					List[str]   				=   []
 while count_of_line < x:
  vector.append(coordinates[count_of_line][1] )
  count_of_line += 1

 UpperCAmelCase__   :					Optional[Any]   				=   0

 while count < x:
  UpperCAmelCase__   :					Dict   				=   0
  while zahlen < x:
   if count == zahlen:
    zahlen += 1
   if zahlen == x:
    break
   UpperCAmelCase__   :					List[Any]   				=   matrix[zahlen][count] / matrix[count][count]
   for counting_columns, item in enumerate(matrix[count] ):
    # manipulating all the values in the matrix
    matrix[zahlen][counting_columns] -= item * bruch
   # manipulating the values in the vector
   vector[zahlen] -= vector[count] * bruch
   zahlen += 1
  count += 1

 UpperCAmelCase__   :					Optional[int]   				=   0
 # make solutions
 UpperCAmelCase__   :					Dict   				=   []
 while count < x:
  solution.append(str(vector[count] / matrix[count][count] ) )
  count += 1

 UpperCAmelCase__   :					Any   				=   0
 UpperCAmelCase__   :					Dict   				=   """f(x)="""

 while count < x:
  UpperCAmelCase__   :					List[str]   				=   solution[count].split("""E""" )
  if len(snake_case__ ) > 1:
   UpperCAmelCase__   :					Dict   				=   F"{remove_e[0]}*10^{remove_e[1]}"
  solved += F"x^{x - (count + 1)}*{solution[count]}"
  if count + 1 != x:
   solved += "+"
  count += 1

 return solved


if __name__ == "__main__":
      print(points_to_polynomial([]))
      print(points_to_polynomial([[]]))
      print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
      print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
      print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
      print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
      print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
      print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
      print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
      print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))








"""simple docstring"""




import hashlib
import importlib.util
import json
import os
import pathlib
from types import ModuleType

import pytest
import requests

__UpperCAmelCase	=			pathlib.Path.cwd().joinpath('project_euler')
__UpperCAmelCase	=			pathlib.Path.cwd().joinpath(
    'scripts', 'project_euler_answers.json'
)

with open(PROJECT_EULER_ANSWERS_PATH) as file_handle:
      __UpperCAmelCase	=			json.load(file_handle)
def 					lowerCAmelCase  (   __UpperCamelCase ):
 '''simple docstring'''





 UpperCAmelCase__   :					Dict   				=   importlib.util.spec_from_file_location(file_path.name							,      str(__UpperCamelCase ) )
 UpperCAmelCase__   :					Optional[Any]   				=   importlib.util.module_from_spec(__UpperCamelCase )  # type: ignore
 spec.loader.exec_module(__UpperCamelCase )  # type: ignore
 return module
def 					lowerCAmelCase  (   ):
 '''simple docstring'''





 UpperCAmelCase__   :					Dict   				=   []
 for problem_dir_path in PROJECT_EULER_DIR_PATH.iterdir():
  if problem_dir_path.is_file() or problem_dir_path.name.startswith("""_""" ):
   continue
  for file_path in problem_dir_path.iterdir():
   if file_path.suffix != ".py" or file_path.name.startswith(("""_""", """test""") ):
    continue
   solution_file_paths.append(__UpperCamelCase )
 return solution_file_paths
def 					lowerCAmelCase  (   ):
 '''simple docstring'''





 with open(os.environ["""GITHUB_EVENT_PATH"""] ) as file:
  UpperCAmelCase__   :					List[Any]   				=   json.load(__UpperCamelCase )
 return event["pull_request"]["url"] + "/files"
def 					lowerCAmelCase  (   ):
 '''simple docstring'''





 UpperCAmelCase__   :					Tuple   				=   []
 UpperCAmelCase__   :					List[str]   				=   {
     """Accept""": """application/vnd.github.v3+json""",
     """Authorization""": """token """ + os.environ["""GITHUB_TOKEN"""],
 }
 UpperCAmelCase__   :					Tuple   				=   requests.get(get_files_url()							,      headers=__UpperCamelCase ).json()
 for file in files:
  UpperCAmelCase__   :					List[str]   				=   pathlib.Path.cwd().joinpath(file["""filename"""] )
  if (
      filepath.suffix != ".py"
      or filepath.name.startswith(("""_""", """test""") )
      or not filepath.name.startswith("""sol""" )
  ):
   continue
  solution_file_paths.append(__UpperCamelCase )
 return solution_file_paths
def 					lowerCAmelCase  (   ):
 '''simple docstring'''





 if os.environ.get("""CI""" ) and os.environ.get("""GITHUB_EVENT_NAME""" ) == "pull_request":
  # Return only if there are any, otherwise default to all solutions
  if filepaths := added_solution_file_path():
   return filepaths
 return all_solution_file_paths()




@pytest.mark.parametrize(
    """solution_path"""							,      collect_solution_file_paths()							,      ids=lambda __UpperCamelCase : F"{path.parent.name}/{path.name}"							,      )
def 					lowerCAmelCase  (   __UpperCamelCase ):
 '''simple docstring'''





 UpperCAmelCase__   :					str   				=   solution_path.parent.name[8:].zfill(3 )
 UpperCAmelCase__   :					str   				=   PROBLEM_ANSWERS[problem_number]
 UpperCAmelCase__   :					int   				=   convert_path_to_module(__UpperCamelCase )
 UpperCAmelCase__   :					str   				=   str(solution_module.solution() )  # type: ignore
 UpperCAmelCase__   :					Optional[Any]   				=   hashlib.shaaaa(answer.encode() ).hexdigest()
 assert (
     answer == expected
 ), F"Expected solution to {problem_number} to have hash {expected}, got {answer}"





