Balls-in-Bins Max Load Estimate

Problem

For n balls thrown independently and uniformly into n bins, the classic Poisson approximation for the expected maximum bin load is ln(n) / ln(ln(n)) for n >= 3. Return 1.0 for 1 <= n < 3 and 0.0 for n <= 0.

Hint

The maximum load grows like log n over log log n, far slower than the average load.

Test cases

case 1

in: [10]

expected: 2.7607859935346912

case 2

in: [100]

expected: 3.0154738238809906

case 3

in: [1000]

expected: 3.574249916581999

case 4

in: [2]

expected: 1

case 5

in: [0]

expected: 0

Starter codePython

import math


def max_load_estimate(bins):
    # Your code here
    pass

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