

from __future__ import annotations

from math import ceil, floor, sqrt




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_ = 2_0_0_0_0_0_0			)->						int:



    """simple docstring"""






    UpperCamelCase_			  =						[0]
    UpperCamelCase_			  =						42

    for idx in range(1			,						ceil(sqrt(target * 2			) * 1.1			)			):
        triangle_numbers.append(triangle_numbers[-1] + idx			)

    # we want this to be as close as possible to target
    UpperCamelCase_			  =						0
    # the area corresponding to the grid that gives the product closest to target
    UpperCamelCase_			  =						0
    # an estimate of b, using the quadratic formula
    UpperCamelCase_			  =						42
    # the largest integer less than b_estimate
    UpperCamelCase_			  =						42
    # the largest integer less than b_estimate
    UpperCamelCase_			  =						42
    # the triangle number corresponding to b_floor
    UpperCamelCase_			  =						42
    # the triangle number corresponding to b_ceil
    UpperCamelCase_			  =						42

    for idx_a, triangle_a in enumerate(triangle_numbers[1:]			,						1			):
        UpperCamelCase_			  =						(-1 + sqrt(1 + 8 * target / triangle_a			)) / 2
        UpperCamelCase_			  =						floor(SCREAMING_SNAKE_CASE_			)
        UpperCamelCase_			  =						ceil(SCREAMING_SNAKE_CASE_			)
        UpperCamelCase_			  =						triangle_numbers[b_floor]
        UpperCamelCase_			  =						triangle_numbers[b_ceil]

        if abs(target - triangle_b_first_guess * triangle_a			) < abs(
            target - best_product			):
            UpperCamelCase_			  =						triangle_b_first_guess * triangle_a
            UpperCamelCase_			  =						idx_a * b_floor

        if abs(target - triangle_b_second_guess * triangle_a			) < abs(
            target - best_product			):
            UpperCamelCase_			  =						triangle_b_second_guess * triangle_a
            UpperCamelCase_			  =						idx_a * b_ceil

    return area


if __name__ == "__main__":
 print(F'''{solution() = }''')



from __future__ import annotations

import math




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)->						int:



    """simple docstring"""






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

    if len(SCREAMING_SNAKE_CASE_			) == 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			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						minimax(depth + 1			,						node_index * 2 + 1			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						)

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




def 			lowerCAmelCase(      )->						None:



    """simple docstring"""






    UpperCamelCase_			  =						[9_0, 2_3, 6, 3_3, 2_1, 6_5, 1_2_3, 3_4_4_2_3]
    UpperCamelCase_			  =						math.log(len(SCREAMING_SNAKE_CASE_			)			,						2			)
    print("Optimal value : "			,						end=""			)
    print(minimax(0			,						0			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()
