Expected Largest Spacing

Problem

Place n points independently and uniformly on [0, 1]. The n + 1 spacings including the two end gaps form a Dirichlet(1, ..., 1) vector whose largest component has expectation:

E[max spacing] = H_(n+1) / (n + 1)

where H_m is the m-th harmonic number. Return 0.0 for negative n.

Hint

For a uniform Dirichlet vector with m components the expected maximum is H_m / m.

Test cases

case 1

in: [0]

expected: 1

case 2

in: [1]

expected: 0.75

case 3

in: [2]

expected: 0.611111111111111

case 4

in: [4]

expected: 0.45666666666666667

Starter codePython

def expected_largest_spacing(n):
    # Your code here
    pass

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