"""simple docstring"""


import random






def     __UpperCAmelCase					(			lowercase   ,lowercase   ,lowercase = False		):







  """simple docstring"""
  _UpperCAmelCase						 =      {i: [] for i in range(_lowerCamelCase		)}

  # if probability is greater or equal than 1, then generate a complete graph
  if probability >= 1:
    return complete_graph(_lowerCamelCase		)
  # if probability is lower or equal than 0, then return a graph without edges
  if probability <= 0:
    return graph

  # for each couple of nodes, add an edge from u to v
  # if the number randomly generated is greater than probability probability
  for i in range(_lowerCamelCase		):
    for j in range(i + 1   ,_lowerCamelCase		):
      if random.random() < probability:
        graph[i].append(_lowerCamelCase		)
        if not directed:
          # if the graph is undirected, add an edge in from j to i, either
          graph[j].append(_lowerCamelCase		)
  return graph






def     __UpperCAmelCase					(			lowercase		):







  """simple docstring"""
  return {
      i: [j for j in range(_lowerCamelCase		) if i != j] for i in range(_lowerCamelCase		)
  }


if __name__ == "__main__":
    import doctest

    doctest.testmod()



"""simple docstring"""


from __future__ import annotations

from random import choice






def     __UpperCAmelCase					(			lowercase		):







  """simple docstring"""
  return choice(lowercase		)






def     __UpperCAmelCase					(			lowercase   ,lowercase		):







  """simple docstring"""
  _UpperCAmelCase						 =      random_pivot(lowercase		)

  # partition based on pivot
  # linear time
  _UpperCAmelCase						 =      [e for e in lst if e < pivot]
  _UpperCAmelCase						 =      [e for e in lst if e > pivot]

  # if we get lucky, pivot might be the element we want.
  # we can easily see this:
  # small (elements smaller than k)
  # + pivot (kth element)
  # + big (elements larger than k)
  if len(lowercase		) == k - 1:
    return pivot
  # pivot is in elements bigger than k
  elif len(lowercase		) < k - 1:
    return kth_number(lowercase   ,k - len(lowercase		) - 1		)
  # pivot is in elements smaller than k
  else:
    return kth_number(lowercase   ,lowercase		)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
