


'''simple docstring'''

from __future__ import annotations

from random import choice






def __UpperCamelCase   (			__lowerCamelCase		: Tuple				)      ->     List[Any]:







     '''simple docstring'''






     return choice(__lowerCamelCase				)






def __UpperCamelCase   (			__lowerCamelCase		: list[int]      ,  __lowerCamelCase		: int				)      ->     int:







     '''simple docstring'''






     _a						=		random_pivot(__lowerCamelCase				)

     # partition based on pivot
     # linear time
     _a						=		[e for e in lst if e < pivot]
     _a						=		[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(__lowerCamelCase				) == k - 1:
          return pivot
     # pivot is in elements bigger than k
     elif len(__lowerCamelCase				) < k - 1:
          return kth_number(__lowerCamelCase      ,  k - len(__lowerCamelCase				) - 1				)
     # pivot is in elements smaller than k
     else:
          return kth_number(__lowerCamelCase      ,  __lowerCamelCase				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()





'''simple docstring'''

from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst






def __UpperCamelCase   (			)      ->     Tuple:







     '''simple docstring'''






     _a			,			_a						=		9, 14  # noqa: F841
     _a						=		[
         [0, 1, 4],
         [0, 7, 8],
         [1, 2, 8],
         [7, 8, 7],
         [7, 6, 1],
         [2, 8, 2],
         [8, 6, 6],
         [2, 3, 7],
         [2, 5, 4],
         [6, 5, 2],
         [3, 5, 14],
         [3, 4, 9],
         [5, 4, 10],
         [1, 7, 11],
     ]

     _a						=		defaultdict(__lowerCamelCase				)
     for nodea, nodea, cost in edges:
          adjancency[nodea].append([nodea, cost]				)
          adjancency[nodea].append([nodea, cost]				)

     _a						=		mst(__lowerCamelCase				)

     _a						=		[
         [7, 6, 1],
         [2, 8, 2],
         [6, 5, 2],
         [0, 1, 4],
         [2, 5, 4],
         [2, 3, 7],
         [0, 7, 8],
         [3, 4, 9],
     ]

     for answer in expected:
          _a						=		tuple(answer[:2]				)
          _a						=		tuple(edge[::-1]				)
          assert edge in result or reverse in result

