






"""simple docstring"""






def 					_A			(__a    ,				__a    ,				__a    ,				__a							) ->       int:
    """simple docstring"""






    if graph[path[curr_ind - 1]][next_ver] == 0:
        return False

    # 2. Validate that next vertex is not already in path
    return not any(vertex == next_ver for vertex in path							)



def 					_A			(__a    ,				__a    ,				__a							) ->       List[str]:
    """simple docstring"""






    if curr_ind == len(UpperCamelCase__							):
        # return whether path exists between current and starting vertices
        return graph[path[curr_ind - 1]][path[0]] == 1

    # Recursive Step
    for next_ver in range(0    ,				len(UpperCamelCase__							)							):
        if valid_connection(UpperCamelCase__    ,				UpperCamelCase__    ,				UpperCamelCase__    ,				UpperCamelCase__							):
            # Insert current vertex  into path as next transition
            SCREAMING_SNAKE_CASE_      :  List[Any]    						=		next_ver
            # Validate created path
            if util_hamilton_cycle(UpperCamelCase__    ,				UpperCamelCase__    ,				curr_ind + 1							):
                return True
            # Backtrack
            SCREAMING_SNAKE_CASE_      :  Union[str, Any]    						=		-1
    return False





def 					_A			(__a    ,				__a = 0							) ->       Optional[Any]:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_      :  Tuple    						=		[-1] * (len(UpperCamelCase__							) + 1)
    # initialize start and end of path with starting index
    SCREAMING_SNAKE_CASE_      :  List[Any]    						=		start_index
    # evaluate and if we find answer return path either return empty array
    return path if util_hamilton_cycle(UpperCamelCase__    ,				UpperCamelCase__    ,				1							) else []







"""simple docstring"""
from __future__ import annotations

import math





def  lowerCamelCase_						(UpperCamelCase__		:		int     ,       UpperCamelCase__		:		int     ,       UpperCamelCase__		:		bool     ,       UpperCamelCase__		:		list[int]     ,       UpperCamelCase__		:		float							):

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

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

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





def  lowerCamelCase_						():
    _UpperCAmelCase							:  Any											=    [90, 23, 6, 33, 21, 65, 123, 3_4423]
    _UpperCAmelCase							:  Any											=    math.log(len(UpperCamelCase__							)     ,       2							)
    print('''Optimal value : '''     ,       end=''''''							)
    print(minimax(0     ,       0     ,       UpperCamelCase__     ,       UpperCamelCase__     ,       UpperCamelCase__							)							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()


