


def        snake_case_					(  snake_case					)  ->    Union[str, Any]:




       if collection == []:
              return []

       # get some information about the collection
       lowercase__:       Tuple        =       len(lowerCamelCase__					)
       lowercase__:       List[Any]        =       max(lowerCamelCase__					)
       lowercase__:       str        =       min(lowerCamelCase__					)

       # create the counting array
       lowercase__:       List[str]        =       coll_max + 1 - coll_min
       lowercase__:       Any        =       [0] * counting_arr_length

       # count how much a number appears in the collection
       for number in collection:
              counting_arr[number - coll_min] += 1

       # sum each position with it's predecessors. now, counting_arr[i] tells
       # us how many elements <= i has in the collection
       for i in range(1      ,							lowerCamelCase__					):
              lowercase__:       int        =       counting_arr[i] + counting_arr[i - 1]

       # create the output collection
       lowercase__:       Tuple        =       [0] * coll_len

       # place the elements in the output, respecting the original order (stable
       # sort) from end to begin, updating counting_arr
       for i in reversed(range(0      ,							lowerCamelCase__					)					):
              lowercase__:       Tuple        =       collection[i]
              counting_arr[collection[i] - coll_min] -= 1

       return ordered




def        snake_case_					(  snake_case					)  ->    List[Any]:
       return "".join([chr(lowerCamelCase__					) for i in counting_sort([ord(lowerCamelCase__					) for c in string]					)]					)


if __name__ == "__main__":
     # Test string sort
     assert counting_sort_string('''thisisthestring''') == "eghhiiinrsssttt"

     __lowerCAmelCase			=							input('''Enter numbers separated by a comma:\n''').strip()
     __lowerCAmelCase			=							[int(item) for item in user_input.split(''',''')]
     print(counting_sort(unsorted))






from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case = False					)  ->    list[float]:
       if radian_mode:
              return [magnitude * cos(snake_case					), magnitude * sin(snake_case					)]
       return [magnitude * cos(radians(snake_case					)					), magnitude * sin(radians(snake_case					)					)]




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case = 10**-1					)  ->    bool:
       lowercase__:       NDArray[floataa]        =       cross(snake_case      ,							snake_case					)
       lowercase__:       float        =       sum(snake_case					)
       return abs(snake_case					) < eps


if __name__ == "__main__":
 # Test to check if it works
 __lowerCAmelCase			=							array(
     [
         polar_force(718.4, 1_80 - 30),
         polar_force(879.54, 45),
         polar_force(1_00, -90),
     ]
 )

 __lowerCAmelCase			=							array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

 # Problem 1 in image_data/2D_problems.jpg
 __lowerCAmelCase			=							array(
     [
         polar_force(30 * 9.81, 15),
         polar_force(2_15, 1_80 - 45),
         polar_force(2_64, 90 - 30),
     ]
 )

 __lowerCAmelCase			=							array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

 # Problem in image_data/2D_problems_1.jpg
 __lowerCAmelCase			=							array([[0, -20_00], [0, -12_00], [0, 1_56_00], [0, -1_24_00]])

 __lowerCAmelCase			=							array([[0, 0], [6, 0], [10, 0], [12, 0]])

 assert in_static_equilibrium(forces, location)

 import doctest

 doctest.testmod()


