[Haskell-cafe] Strange random choice algorithm

[Sebastian Fischer]

On Jan 30, 2010, at 8:59 PM, michael rice wrote:

> I'm not sure where I got this PICK function from, and don't  
> understand why it's written as it is, so I wanted to test it for  
> randomness. It seems random enough.

We can convince ourselves using reason instead of tests. An element is  
selected by the algorithm if it is picked and no later element is  
picked afterwards. It doesn't matter which elements are picked before.  
The n-th element of the given list replaces the current selection with  
probability (1/n). Hence, the probability that the n-th element is  
selected in the end is (1/n)*(1-1/(n+1))*...*(1-1/m) if there are m  
elements. For example, if there are 9 elements, the probability of  
selecting the 7th is 1/7 * 7/8 * 8/9 which is 1/9 because the 7 and 8  
are canceled out. This happens for all elements and, thus, every  
element is selected with probability 1/9.

Anyway,

     pick xs = do n <- randomRIO (1,length xs)
                  return (xs!!(n-1))

would have been clearer.. It queries the random number generator only  
once but walks through the list twice.

Sebastian


-- 
Underestimating the novelty of the future is a time-honored tradition.
(D.G.)