Recursion exercise in Erlang.

pieces.erl

-module( pieces ).
% I export fac and binomial so I can play in the shell.
-export( [ fac/1, binomial/2, pieces/2, test2d/0, test3d/0 ] ).

% Hopefully tail-recursive factorial. I’ve been reading ahead ;)
fac( N ) ->
    fac( 1, N ).

fac( Acc, 0 ) ->
    Acc;
fac( Acc, N ) when N > 0 ->
    fac( Acc * N, N - 1 ).

% Binomial that accepts K > N (probably doesn’t follow the let it fail philosophy)
binomial( N, K ) when N >= 0, K > N ->
    0;
binomial( N, K ) when N >= 0 ->
    fac:fac( N ) / ( fac:fac( K ) * ( fac:fac( N - K ) ) ).

% Function derived from https://en.wikipedia.org/wiki/Cake_number
pieces( 0, Cuts ) ->
    binomial( Cuts, 0 );
pieces( Dimensions, Cuts ) ->
    binomial( Cuts, Dimensions ) + pieces( Dimensions - 1, Cuts ).

testSequence( Expected, Function ) ->
    Result = lists:map( Function, lists:seq( 0, length( Expected ) - 1 ) ),
    Result == Expected.

% Expected values from https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence
test2d() ->
    Expected = [ 1, 2, 4, 7, 11, 16, 22, 29, 37 ],
    testSequence( Expected, fun( N ) -> pieces( 2, N ) end ).

% Expected values from https://en.wikipedia.org/wiki/Cake_number
test3d() ->
    Expected = [ 1, 2, 4, 8, 15, 26, 42, 64, 93 ],
    testSequence( Expected, fun( N ) -> pieces( 3, N ) end ).