randomSample

[Jason House]

Andrei Alexandrescu Wrote:

> I'm writing a range to select a random sampling of a forward range. The 
> number of elements in the forward range is already known.
> 
> The strategy is: at any moment, I know I need to select k random samples 
> out of n. To implement popFront, I generate a random number in [0, n - 
> k]. That's the probability that the next item in the input will be part 
> of the selection. If the random number is 0, then the element got 
> selected. Otherwise, I must ignore that guy so I popFront the input 
> range, decrease n by one, and repeat.
> 
> This seems reasonable but somehow the selection comes skewed: the 
> elements towards the beginning of the range are less represented than 
> the ones towards the end. Where am I wrong?
> 
> 
> Andrei

You have your probability wrong. The selection probability is k/n. Pick a number in [0,n) and pick the element if the result is in [0,k). If you do select an item, decrement k. Always decrement n when popping, regardless of if the element is selected.