

from __future__ import annotations

from dataclasses import dataclass

@dataclass
class 							UpperCAmelCase_						:
							"""simple docstring"""







							UpperCAmelCase__			:		float
							UpperCAmelCase__			:		TreeNode | None             =       None
							UpperCAmelCase__			:		TreeNode | None             =       None



def   __UpperCAmelCase					(      __a :     TreeNode | None      )     ->	bool:

					"""simple docstring"""

					def is_valid_tree(__a :     TreeNode | None      ) -> bool:
										if node is None:
															return True

										if not isinstance(__a						,__a      ):
															return False

										try:
															float(node.data      )
										except (TypeError, ValueError):
															return False

										return is_valid_tree(node.left      ) and is_valid_tree(node.right      )

					if not is_valid_tree(__a      ):
										raise ValueError(
										    '''Each node should be type of TreeNode and data should be float.'''      )

					def is_binary_search_tree_recursive_check(
					    __a :     TreeNode | None						,__a :     float						,__a :     float      ) -> bool:

										if node is None:
															return True

										return (
										    left_bound < node.data < right_bound
										    and is_binary_search_tree_recursive_check(node.left						,__a						,node.data      )
										    and is_binary_search_tree_recursive_check(
										        node.right						,node.data						,__a      )
										)

					return is_binary_search_tree_recursive_check(__a						,-float('''inf'''      )						,float('''inf'''      )      )


if __name__ == "__main__":
			import doctest

			doctest.testmod()






from random import randint
from tempfile import TemporaryFile

import numpy as np



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

					"""simple docstring"""

					_a      :       int   =						0
					if start < end:
										_a      :       Tuple   =						randint(__a						,__a      )
										_a      :       Tuple   =						a[end]
										_a      :       List[str]   =						a[pivot]
										_a      :       Any   =						temp

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



def   __UpperCAmelCase					(      __a :     List[Any]						,__a :     Tuple						,__a :     Dict      )     ->	Dict:

					"""simple docstring"""

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

					_a      :       Union[str, Any]   =						a[new_pivot_index + 1]
					_a      :       Tuple   =						a[end]
					_a      :       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)



