Binomial Coefficient

Problem

Compute the binomial coefficient n choose k, the number of ways to choose k items from n distinct items, returning 0 when k < 0 or k > n.

Use the multiplicative formula result = result * (n - k + i) // i for i from 1 to k after replacing k with min(k, n - k). Each step divides exactly, so the result stays an integer.

Hint

Reduce k to min(k, n - k) first so the loop and the numbers stay small.

Test cases

case 1

in: [5,2]

expected: 10

case 2

in: [0,0]

expected: 1

case 3

in: [10,3]

expected: 120

case 4

in: [5,6]

expected: 0

case 5

in: [52,5]

expected: 2598960

Starter codePython

def binomial(n, k):
    # Your code here
    pass

5 test cases · run your code against them in the editor