



'''simple docstring'''





import random




def 							lowerCamelCase	(					_snake_case	:    Any  ,_snake_case	:    Optional[Any]  ,_snake_case	:    Optional[int]							):





    '''simple docstring'''


    lowercase__									=    a[left_index]
    lowercase__									=    left_index + 1
    for j in range(left_index + 1  ,_snake_case							):
        if a[j] < pivot:
            lowercase__							,							lowercase__									=    a[i], a[j]
            i += 1
    lowercase__							,							lowercase__									=    a[i - 1], a[left_index]
    return i - 1




def 							lowerCamelCase	(					_snake_case	:    str  ,_snake_case	:    Union[str, Any]  ,_snake_case	:    Optional[int]							):





    '''simple docstring'''


    if left < right:
        lowercase__									=    random.randint(_snake_case  ,right - 1							)
        lowercase__							,							lowercase__									=    (
            a[left],
            a[pivot],
        )  # switches the pivot with the left most bound
        lowercase__									=    partition(_snake_case  ,_snake_case  ,_snake_case							)
        quick_sort_random(
            _snake_case  ,_snake_case  ,_snake_case							)  # recursive quicksort to the left of the pivot point
        quick_sort_random(
            _snake_case  ,pivot_index + 1  ,_snake_case							)  # recursive quicksort to the right of the pivot point




def 							lowerCamelCase	(					):





    '''simple docstring'''


    lowercase__									=    input("Enter numbers separated by a comma:\n"							).strip()
    lowercase__									=    [int(_snake_case							) for item in user_input.split(","							)]

    quick_sort_random(_snake_case  ,0  ,len(_snake_case							)							)

    print(_snake_case							)


if __name__ == "__main__":
 main()









'''simple docstring'''





from __future__ import annotations

import math




def 							lowerCamelCase	(					_snake_case	:    float  ,_snake_case	:    int							):





    '''simple docstring'''


    lowercase__									=    u
    for i in range(1  ,_snake_case							):
        lowercase__									=    temp * (u - i)
    return temp




def 							lowerCamelCase	(					):





    '''simple docstring'''


    lowercase__									=    int(input("enter the numbers of values: "							)							)
    lowercase__									=    []
    for _ in range(_snake_case							):
        y.append([]							)
    for i in range(_snake_case							):
        for j in range(_snake_case							):
            y[i].append(_snake_case							)
            lowercase__									=    0

    print("enter the values of parameters in a list: "							)
    lowercase__									=    list(map(_snake_case  ,input().split()							)							)

    print("enter the values of corresponding parameters: "							)
    for i in range(_snake_case							):
        lowercase__									=    float(input()							)

    lowercase__									=    int(input("enter the value to interpolate: "							)							)
    lowercase__									=    (value - x[0]) / (x[1] - x[0])

    # for calculating forward difference table

    for i in range(1  ,_snake_case							):
        for j in range(n - i							):
            lowercase__									=    y[j + 1][i - 1] - y[j][i - 1]

    lowercase__									=    y[0][0]
    for i in range(1  ,_snake_case							):
        summ += (ucal(_snake_case  ,_snake_case							) * y[0][i]) / math.factorial(_snake_case							)

    print(f'''the value at {value} is {summ}'''							)


if __name__ == "__main__":
 main()




