





'''simple docstring'''

from collections.abc import Callable

import numpy as np





def 		UpperCamelCase							(				_lowerCamelCase   :   Callable		,			_lowerCamelCase   :   float		,			_lowerCamelCase   :   float		,			_lowerCamelCase   :   float		,			_lowerCamelCase   :   float			):
    A__							=     int(np.ceil((x_end - xa) / step_size			)			)
    A__							=     np.zeros((n + 1,)			)
    A__							=     ya
    A__							=     xa

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

    return y


if __name__ == "__main__":
  import doctest

  doctest.testmod()










'''simple docstring'''

from __future__ import annotations

import math





def 		UpperCamelCase							(				_lowerCamelCase   :   int		,			_lowerCamelCase   :   int		,			_lowerCamelCase   :   bool		,			_lowerCamelCase   :   list[int]		,			_lowerCamelCase   :   float			):

    if depth < 0:
        raise ValueError("Depth cannot be less than 0"			)

    if len(_lowerCamelCase			) == 0:
        raise ValueError("Scores cannot be empty"			)

    if depth == height:
        return scores[node_index]

    if is_max:
        return max(
            minimax(depth + 1		,			node_index * 2		,			_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)		,			minimax(depth + 1		,			node_index * 2 + 1		,			_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)		,			)

    return min(
        minimax(depth + 1		,			node_index * 2		,			_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)		,			minimax(depth + 1		,			node_index * 2 + 1		,			_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)		,			)





def 		UpperCamelCase							(				):
    A__							=     [90, 23, 6, 33, 21, 65, 1_23, 3_44_23]
    A__							=     math.log(len(_lowerCamelCase			)		,			2			)
    print("Optimal value : "		,			end=""			)
    print(minimax(0		,			0		,			_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)			)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()



