




from __future__ import annotations

# This is the precision for this function which can be altered.
# It is recommended for users to keep this number greater than or equal to 10.
_lowerCamelCase      			=						10




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						int	,					__UpperCamelCase      :						int	,					__UpperCamelCase      :						list[int]	,					__UpperCamelCase      :						int				)  ->							int:
    for i in range(__UpperCamelCase	,					__UpperCamelCase				):
        if array[i] == target:
            return i
    return -1




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						list[int]	,					__UpperCamelCase      :						int				)  ->							int:
    UpperCAmelCase_										=					0
    UpperCAmelCase_										=					len(__UpperCamelCase				)
    while left <= right:
        if right - left < precision:
            return lin_search(__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase				)

        UpperCAmelCase_										=					(left + right) // 3 + 1
        UpperCAmelCase_										=					2 * (left + right) // 3 + 1

        if array[one_third] == target:
            return one_third
        elif array[two_third] == target:
            return two_third

        elif target < array[one_third]:
            UpperCAmelCase_										=					one_third - 1
        elif array[two_third] < target:
            UpperCAmelCase_										=					two_third + 1

        else:
            UpperCAmelCase_										=					one_third + 1
            UpperCAmelCase_										=					two_third - 1
    else:
        return -1




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						int	,					__UpperCamelCase      :						int	,					__UpperCamelCase      :						list[int]	,					__UpperCamelCase      :						int				)  ->							int:
    if left < right:
        if right - left < precision:
            return lin_search(__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase				)
        UpperCAmelCase_										=					(left + right) // 3 + 1
        UpperCAmelCase_										=					2 * (left + right) // 3 + 1

        if array[one_third] == target:
            return one_third
        elif array[two_third] == target:
            return two_third

        elif target < array[one_third]:
            return rec_ternary_search(__UpperCamelCase	,					one_third - 1	,					__UpperCamelCase	,					__UpperCamelCase				)
        elif array[two_third] < target:
            return rec_ternary_search(two_third + 1	,					__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase				)
        else:
            return rec_ternary_search(one_third + 1	,					two_third - 1	,					__UpperCamelCase	,					__UpperCamelCase				)
    else:
        return -1


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 _lowerCamelCase      			=						input('Enter numbers separated by comma:\n').strip()
 _lowerCamelCase      			=						[int(item.strip()) for item in user_input.split(',')]
 assert collection == sorted(collection), F"List must be ordered.\n{collection}."
 _lowerCamelCase      			=						int(input('Enter the number to be found in the list:\n').strip())
 _lowerCamelCase      			=						ite_ternary_search(collection, target)
 _lowerCamelCase      			=						rec_ternary_search(0, len(collection) - 1, collection, target)
 if resulta != -1:
  print(F"Iterative search: {target} found at positions: {resulta}")
  print(F"Recursive search: {target} found at positions: {resulta}")
 else:
  print('Not found')











from __future__ import annotations

_lowerCamelCase      			=						list[list[int]]

# assigning initial values to the grid
_lowerCamelCase      			=						[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
_lowerCamelCase      			=						[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix	,					__UpperCamelCase      :						int	,					__UpperCamelCase      :						int	,					__UpperCamelCase      :						int				)  ->							bool:
    for i in range(9				):
        if grid[row][i] == n or grid[i][column] == n:
            return False

    for i in range(3				):
        for j in range(3				):
            if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
                return False

    return True




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix				)  ->							tuple[int, int] | None:
    for i in range(9				):
        for j in range(9				):
            if grid[i][j] == 0:
                return i, j
    return None




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix				)  ->							Matrix | None:
    if location := find_empty_location(__UpperCamelCase				):
        UpperCAmelCase_			,							UpperCAmelCase_										=					location
    else:
        # If the location is ``None``, then the grid is solved.
        return grid

    for digit in range(1	,					10				):
        if is_safe(__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase				):
            UpperCAmelCase_										=					digit

            if sudoku(__UpperCamelCase				) is not None:
                return grid

            UpperCAmelCase_										=					0

    return None




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix				)  ->							None:
    for row in grid:
        for cell in row:
            print(__UpperCamelCase	,					end=''' '''				)
        print()


if __name__ == "__main__":
 # make a copy of grid so that you can compare with the unmodified grid
 for example_grid in (initial_grid, no_solution):
  print('\nExample grid:\n' + '=' * 20)
  print_solution(example_grid)
  print('\nExample grid solution:')
  _lowerCamelCase      			=						sudoku(example_grid)
  if solution is not None:
   print_solution(solution)
  else:
   print('Cannot find a solution.')





