






'''simple docstring'''




from __future__ import annotations

class   _UpperCAmelCase     :




   """simple docstring"""

   def __init__(						self					:      List[str] , __UpperCAmelCase					:      int						):





         '''simple docstring'''





         _A     	=      data
         _A     	=      None
         _A     	=      None





def    __lowercase		(     __lowercase			)			->		None:  # In Order traversal of the tree

      '''simple docstring'''


      if tree:
            display(tree.left			)
            print(tree.data			)
            display(tree.right			)

def    __lowercase		(     __lowercase			)			->		int:

      '''simple docstring'''


      return 1 + max(depth_of_tree(tree.left			)  ,    depth_of_tree(tree.right			)			) if tree else 0

def    __lowercase		(     __lowercase			)			->		bool:

      '''simple docstring'''


      if not tree:
            return True
      if tree.left and tree.right:
            return is_full_binary_tree(tree.left			) and is_full_binary_tree(tree.right			)
      else:
            return not tree.left and not tree.right

def    __lowercase		(     )			->		None:  # Main function for testing.

      '''simple docstring'''


      _A     	=      Node(1			)
      _A     	=      Node(2			)
      _A     	=      Node(3			)
      _A     	=      Node(4			)
      _A     	=      Node(5			)
      _A     	=      Node(6			)
      _A     	=      Node(7			)
      _A     	=      Node(8			)
      _A     	=      Node(9			)

      print(is_full_binary_tree(__UpperCAmelCase			)			)
      print(depth_of_tree(__UpperCAmelCase			)			)
      print("Tree is: "			)
      display(__UpperCAmelCase			)


if __name__ == "__main__":
    main()










'''simple docstring'''

from random import randint
from tempfile import TemporaryFile

import numpy as np







def a_     (    __UpperCAmelCase				,							__UpperCAmelCase				,							__UpperCAmelCase					)				->					int:





			"""simple docstring"""







			snake_case:    int      							=0
			if start < end:
						snake_case:    Tuple      							=randint(__UpperCAmelCase				,							__UpperCAmelCase					)
						snake_case:    Optional[Any]      							=a[end]
						snake_case:    List[Any]      							=a[pivot]
						snake_case:    int      							=temp

						snake_case							,  snake_case:    Optional[int]      							=_in_place_partition(__UpperCAmelCase				,							__UpperCAmelCase				,							__UpperCAmelCase					)
						count += _in_place_quick_sort(__UpperCAmelCase				,							__UpperCAmelCase				,							p - 1					)
						count += _in_place_quick_sort(__UpperCAmelCase				,							p + 1				,							__UpperCAmelCase					)
			return count







def a_     (    __UpperCAmelCase				,							__UpperCAmelCase				,							__UpperCAmelCase					)				->					Optional[int]:





			"""simple docstring"""







			snake_case:    Tuple      							=0
			snake_case:    Tuple      							=randint(__UpperCAmelCase				,							__UpperCAmelCase					)
			snake_case:    List[Any]      							=a[end]
			snake_case:    List[str]      							=a[pivot]
			snake_case:    Dict      							=temp
			snake_case:    Union[str, Any]      							=start - 1
			for index in range(__UpperCAmelCase				,							__UpperCAmelCase					):
						count += 1
						if a[index] < a[end]:  # check if current val is less than pivot value
									snake_case:    Optional[Any]      							=new_pivot_index + 1
									snake_case:    Dict      							=a[new_pivot_index]
									snake_case:    Union[str, Any]      							=a[index]
									snake_case:    List[Any]      							=temp

			snake_case:    Union[str, Any]      							=a[new_pivot_index + 1]
			snake_case:    Tuple      							=a[end]
			snake_case:    Union[str, Any]      							=temp
			return new_pivot_index + 1, count


a							   =				TemporaryFile()
a							   =				100  # 1000 elements are to be sorted


a   ,      a							   =				0, 1  # mean and standard deviation
a							   =				np.random.normal(mu, sigma, p)
np.save(outfile, X)
print('The array is')
print(X)


outfile.seek(0)  # using the same array
a							   =				np.load(outfile)
a							   =				len(M) - 1
a							   =				_in_place_quick_sort(M, 0, r)

print(
    'No of Comparisons for 100 elements selected from a standard normal distribution'
    'is :'
)







print(z)




