


"""simple docstring"""

# Algorithm for the pigeonhole sorting









def lowerCAmelCase_      (				UpperCamelCase__	: Union[str, Any] ):






 """simple docstring"""







 __lowercase									=	min(UpperCamelCase__ )  # min() finds the minimum value
 __lowercase									=	max(UpperCamelCase__ )  # max() finds the maximum value

 __lowercase									=	max_val - min_val + 1  # size is difference of max and min values plus one

 # list of pigeonholes of size equal to the variable size
 __lowercase									=	[0] * size

 # Populate the pigeonholes.
 for x in a:
  assert isinstance(UpperCamelCase__				,   UpperCamelCase__ ), "integers only please"
  holes[x - min_val] += 1

 # Putting the elements back into the array in an order.
 __lowercase									=	0
 for count in range(UpperCamelCase__ ):
  while holes[count] > 0:
   holes[count] -= 1
   __lowercase									=	count + min_val
   i += 1


def lowerCAmelCase_      (				):






 """simple docstring"""







 __lowercase									=	[8, 3, 2, 7, 4, 6, 8]
 pigeonhole_sort(UpperCamelCase__ )
 print("""Sorted order is:"""				,   """ """.join(UpperCamelCase__ ) )


if __name__ == "__main__":
       main()




"""simple docstring"""

from collections.abc import Callable

import numpy as np


def lowerCAmelCase_      (				UpperCamelCase__	: Callable				,   UpperCamelCase__	: float				,   UpperCamelCase__	: float				,   UpperCamelCase__	: float				,   UpperCamelCase__	: float ):






 """simple docstring"""







 __lowercase									=	int(np.ceil((x_end - xa) / step_size ) )
 __lowercase									=	np.zeros((n + 1,) )
 __lowercase									=	ya
 __lowercase									=	xa

 for k in range(UpperCamelCase__ ):
  __lowercase									=	y[k] + step_size * ode_func(UpperCamelCase__				,   y[k] )
  x += step_size

 return y


if __name__ == "__main__":
       import doctest

       doctest.testmod()
