Birthday Threshold Search

Problem

Smallest number of people n such that the probability of at least one shared birthday reaches target_prob, with days equally likely birthdays:

P(n) = 1 - product from i = 0 to n - 1 of (1 - i / days).

Return 0 for days <= 0 or target_prob outside (0, 1].

Hint

Grow the probability multiplicatively instead of recomputing the whole product.

case 1

in: [365,0.5]

expected: 23

case 2

in: [365,0.99]

expected: 57

case 3

in: [365,0.01]

expected: 4

case 4

in: [1,0.5]

expected: 2

Starter codePython

def birthday_threshold(days, target_prob):
    # Your code here
    pass

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