August 23, 2024
P26 - Generate the combinations of K distinct objects chosen from the N elements of a list.
In how many ways can a committee of 3 be chosen from a group of 12 people? We all know that there areC(12,3) = 220possibilities (C(N,K)denotes the well-known binomial coefficient). For pure mathematicians, this result may be great. But we want to really generate all the possibilities.
Example:
> p26:combinations(2, [1,2,3,4]).
[[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]erlang
%Generate the combinations of K distinct objects chosen from the N elements of a list.
-module(p26).
-export([combinations/2]).
combinations(0, Ls) ->
[Ls];
combinations(1, Ls) ->
lists:map(fun(X) -> [X] end, Ls);
combinations(_, []) ->
[];
combinations(N, [Head | Tail]) ->
Sub = combinations(N-1, Tail),
lists:map(fun(Sl) -> [Head | Sl] end, Sub) ++ combinations(N, Tail) .
% length(p26:combinations(3, [1,2,3,4,5,6,7,8,9,10,11,12])).
% 220
%
%
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