Secretary Optimal Success Probability

Problem

Exact optimal success probability for the secretary problem with n applicants, maximizing over the number of applicants to reject:

P(k) = (k - 1) / n * sum from j = k to n of 1 / (j - 1).

Return 1.0 for n = 1 and 0.0 for n <= 0.

Hint

The best applicant is hired when the first record after the rejection phase is the global best.

case 1

in: [1]

expected: 1

case 2

in: [2]

expected: 0.5

case 3

in: [3]

expected: 0.5

case 4

in: [10]

expected: 0.39869047619047615

case 5

in: [100]

expected: 0.3710427787126428

Starter codePython

def secretary_success_probability(n):
    # Your code here
    pass

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