





'''simple docstring'''

import sys





def 		UpperCamelCase							(				_lowerCamelCase   :   Dict			):
    A__							=     len(_lowerCamelCase			)
    A__							=     [[0 for x in range(_lowerCamelCase			)] for x in range(_lowerCamelCase			)]
    A__							=     [[0 for x in range(_lowerCamelCase			)] for x in range(_lowerCamelCase			)]

    for chain_length in range(2		,			_lowerCamelCase			):
        for a in range(1		,			n - chain_length + 1			):
            A__							=     a + chain_length - 1

            A__							=     sys.maxsize
            for c in range(_lowerCamelCase		,			_lowerCamelCase			):
                A__							=     (
                    matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
                )
                if cost < matrix[a][b]:
                    A__							=     cost
                    A__							=     c
    return matrix, sol





def 		UpperCamelCase							(				_lowerCamelCase   :   Tuple		,			_lowerCamelCase   :   Optional[Any]		,			_lowerCamelCase   :   Dict			):
    if i == j:
        print("A" + str(_lowerCamelCase			)		,			end=" "			)
    else:
        print("("		,			end=" "			)
        print_optiomal_solution(_lowerCamelCase		,			_lowerCamelCase		,			optimal_solution[i][j]			)
        print_optiomal_solution(_lowerCamelCase		,			optimal_solution[i][j] + 1		,			_lowerCamelCase			)
        print(")"		,			end=" "			)





def 		UpperCamelCase							(				):
    A__							=     [30, 35, 15, 5, 10, 20, 25]
    A__							=     len(_lowerCamelCase			)
    # Size of matrix created from above array will be
    # 30*35 35*15 15*5 5*10 10*20 20*25
    A__,      A__							=     matrix_chain_order(_lowerCamelCase			)

    print("No. of Operation required: " + str(matrix[1][n - 1]			)			)
    print_optiomal_solution(_lowerCamelCase		,			1		,			n - 1			)


if __name__ == "__main__":
  main()










'''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()



