What is O value for naive random selection from finite set?

Question

This question on getting random values from a finite set got me thinking...

It\'s fairly common for people to want to retrieve X unique values from a set of Y values.

Answer 1

The worst case for this algorithm is clearly when you're choosing the full set of N items. This is equivalent to asking: On average, how many times must I roll an N-sided die before each side has come up at least once?

Answer: N * H_N, where H_N is the Nth harmonic number,

a value famously approximated by log(N).

This means the algorithm in question is N log N.

As a fun example, if you roll an ordinary 6-sided die until you see one of each number, it will take on average 6 H₆ = 14.7 rolls.