Source code for kyu_7.easy_line.easyline

#  Created by Egor Kostan.
#  GitHub: https://github.com/ikostan
#  LinkedIn: https://www.linkedin.com/in/egor-kostan/

import math


def easy_line(n: int) -> int:
    """
    The function will take n (with: n>= 0) as parameter
    and will return the sum of the squares of the binomial
    coefficients on line n.

    :param n: the line number (with: n>= 0)
    :return:
    """
    if n < 0:
        raise ValueError('ERROR: invalid n ({}) value. n must be >= 0')

    if n == 0:
        return 1

    result = 0
    i = 0
    for row in range(n - 1, 2 * n):
        result += calc_combination_per_row_item(row, i)
        i += 1

    return result


def calc_combination_per_row_item(row: int, i: int) -> int:
    """
    Generates a specific combination from Pascal's Triangle row by specified index
    :param row: row
    :param i: index
    :return:
    """
    combination = int(math.factorial(row)) // (int(math.factorial(i)) * int(math.factorial(row - i)))
    # print(f'\n{row}! / ({i}! * ({row} - {i})!) = {combination}') # debug only
    return combination