Problem 26

In how many ways you choose a committee of 3 from a group of 12 people? The combination formula tells us C(12,3) = 220 possibilities.

Write a function to generate all combinations of a list.

combinations 2 ['a', 'b', 'c'] == [['a', 'b'], ['a', 'c'], ['b', 'c']]

Unit Test

import Html
import List


combinations : Int -> List a -> List (List a)
combinations n list =
    -- your implementation goes here
    [ [] ]


main : Html.Html a
main =
    Html.text
        <| case test of
            0 ->
                "Your implementation passed all tests."

            1 ->
                "Your implementation failed one test."

            x ->
                "Your implementation failed " ++ (toString x) ++ " tests."


test : Int
test =
    List.length
        <| List.filter ((==) False)
            [ combinations 1 (List.range 1 5) == [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ] ]
            , combinations 2 [ 'a', 'b', 'c' ] == [ [ 'a', 'b' ], [ 'a', 'c' ], [ 'b', 'c' ] ]
            , combinations 2 (List.range 1 3) == [ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ] ]
            , combinations 2 (List.range 1 4) == [ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 3, 4 ] ]
            , combinations 0 (List.range 1 10) == [ [] ]
            , combinations -1 (List.range 1 10) == [ [] ]
            , List.length (combinations 3 (List.range 1 12)) == 220
            , List.length (combinations 4 (List.range 1 15)) == 1365
            ]

Hint

1. Combinations of n number of elements can be generated from combinations of n-1.

Solution

Solutions