[Haskell-cafe] Linear shuffle

Ben Rudiak-Gould Benjamin.Rudiak-Gould at cl.cam.ac.uk
Sat Jan 15 11:38:41 EST 2005

Marcin 'Qrczak' Kowalczyk wrote:

 >Henning Thielemann <iakd0 at clusterf.urz.uni-halle.de> writes:
 >>I did some shuffling based on mergesort [...]
 >I think it doesn't guarantee equal probabilities of all permutations.

It doesn't (proof: it has a bounded runtime, which can't be true of a 
perfect shuffling algorithm based on coin flips). But it looks pretty 
good. I think that iterating this algorithm n times is equivalent to 
assigning a random n-bit number to each list element and sorting, which 
is equivalent to Chris Okasaki's approach with one iteration and an 
array of size 2^n.

Henning Thielemann <iakd0 at clusterf.urz.uni-halle.de> writes:

 >It even works for infinite lists.

In the sense that it doesn't diverge if you evaluate any finite prefix 
of the list, yes. In the sense that it does a good job of shuffling the 
list, no.

-- Ben

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