
"""simple docstring"""
from collections.abc import Callable

_a   :      int       =				Callable[[float], float]  # type alias for a real -> real function
def 					a__ ( a :					RealFunc							,  a :					RealFunc							,  a :					int							,  ):

  """simple docstring"""







  _snake_case  :    int            = float(a		)
  while True:
    try:
      _snake_case  :    int            = prev_guess - function(a		) / derivative(a		)
    except ZeroDivisionError:
      raise ZeroDivisionError("Could not find root"		) from None
    if abs(prev_guess - next_guess		) < 10**-5:
      return next_guess
    _snake_case  :    List[str]            = next_guess
def 					a__ ( a :					float		):

  """simple docstring"""







  return (x**3) - (2 * x) - 5
def 					a__ ( a :					float		):

  """simple docstring"""







  return 3 * (x**2) - 2


if __name__ == "__main__":
    print(newton(f, fa, 3))



"""simple docstring"""
from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
_a   :      List[str]       =				{
    """1""": ["""2""", """3""", """4""", """5"""],
    """2""": ["""1""", """3""", """4""", """5"""],
    """3""": ["""1""", """2""", """4""", """5""", """10"""],
    """4""": ["""1""", """2""", """3""", """5""", """6"""],
    """5""": ["""1""", """2""", """3""", """4""", """7"""],
    """6""": ["""7""", """8""", """9""", """10""", """4"""],
    """7""": ["""6""", """8""", """9""", """10""", """5"""],
    """8""": ["""6""", """7""", """9""", """10"""],
    """9""": ["""6""", """7""", """8""", """10"""],
    """10""": ["""6""", """7""", """8""", """9""", """3"""],
}
def 					a__ ( a :					dict[str, list[str]]		):

  """simple docstring"""







  _snake_case  :    List[Any]            = {node: {node} for node in graph}

  _snake_case  :    str            = {node: graph[node][:] for node in graph}

  while len(a		) > 2:
    # Choose a random edge.
    _snake_case  :    str            = random.choice(list(graph_copy.keys()		)		)
    _snake_case  :    Union[str, Any]            = random.choice(graph_copy[u]		)

    # Contract edge (u, v) to new node uv
    _snake_case  :    Union[str, Any]            = u + v
    _snake_case  :    Union[str, Any]            = list(set(graph_copy[u] + graph_copy[v]		)		)
    uv_neighbors.remove(a		)
    uv_neighbors.remove(a		)
    _snake_case  :    Union[str, Any]            = uv_neighbors
    for neighbor in uv_neighbors:
      graph_copy[neighbor].append(a		)

    _snake_case  :    Dict            = set(contracted_nodes[u].union(contracted_nodes[v]		)		)

    # Remove nodes u and v.
    del graph_copy[u]
    del graph_copy[v]
    for neighbor in uv_neighbors:
      if u in graph_copy[neighbor]:
        graph_copy[neighbor].remove(a		)
      if v in graph_copy[neighbor]:
        graph_copy[neighbor].remove(a		)

    # Find cutset.
  _snake_case  :    List[Any]            = [contracted_nodes[node] for node in graph_copy]
  return {
      (node, neighbor)
      for node in groups[0]
      for neighbor in graph[node]
      if neighbor in groups[1]
  }


if __name__ == "__main__":
    print(partition_graph(TEST_GRAPH))

