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# RandomShuffle

## Problem

For some gaming applications, e.g. Poker, we would need a fair random shuffle. There are two basics algorithms for this both described by Knuth. The more well known Knuth/Fisher-Yates shuffle is O(n) but requires destructive updates. The shuffle listed is O(n log n) but works well for any functional language.

## Solution

We associate each element in the list with a random number. The list is then sorted based on the generated number. We repeat this process log(n) times to ensure a fair shuffle.

```
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% shuffle(List1) -> List2
%% Takes a list and randomly shuffles it. Relies on random:uniform
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

shuffle(List) ->
%% Determine the log n portion then randomize the list.
randomize(round(math:log(length(List)) + 0.5), List).

randomize(1, List) ->
randomize(List);
randomize(T, List) ->
lists:foldl(fun(_E, Acc) ->
randomize(Acc)
end, randomize(List), lists:seq(1, (T - 1))).

randomize(List) ->
D = lists:map(fun(A) ->
{random:uniform(), A}
end, List),
{_, D1} = lists:unzip(lists:keysort(1, D)),
D1.

```

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