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Functional Programming in Erlang: 2.27
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-module(morelists). | |
-export([concat/1, concat_test/0, insertion_sort/1, | |
join/2, join_test/0, member/2, member_test/0, | |
merge_sort/1, perms/1, perms_test/0, quicksort/1, | |
sort_tests/0, test/0]). | |
join([], Y) -> Y; | |
join([X | Xs], Y) -> [X | join(Xs, Y)]. | |
join_test() -> "hello" = join("hel", "lo"), ok. | |
concat([]) -> []; | |
concat([X | Xs]) -> join(X, concat(Xs)). | |
concat_test() -> | |
"goodbye" = concat(["goo", "d", "", "by", "e"]), ok. | |
member(_, []) -> false; | |
member(X, [Y | _]) when X == Y -> true; | |
member(X, [_ | Ys]) -> member(X, Ys). | |
member_test() -> | |
true = member(2, [2, 0, 0, 1]), | |
false = member(20, [2, 0, 0, 1]), | |
ok. | |
merge_sort([]) -> []; | |
merge_sort([X]) -> [X]; | |
merge_sort(Xs) -> | |
{L, R} = split(Xs, [], [], left), | |
merge(merge_sort(L), merge_sort(R)). | |
split([], L, R, _) -> {L, R}; | |
split([X | Xs], L, R, left) -> | |
split(Xs, [X | L], R, right); | |
split([X | Xs], L, R, right) -> | |
split(Xs, L, [X | R], left). | |
merge(L, []) -> L; | |
merge([], R) -> R; | |
merge([L | Ls], [R | Rs]) when L < R -> | |
[L | merge(Ls, [R | Rs])]; | |
merge(L, [R | Rs]) -> [R | merge(L, Rs)]. | |
quicksort([]) -> []; | |
quicksort([X | Xs]) -> | |
{LT, GTE} = split_by_pivot(X, Xs, [], []), | |
join(quicksort(LT), [X | quicksort(GTE)]). | |
split_by_pivot(_, [], LT, GTE) -> {LT, GTE}; | |
split_by_pivot(P, [X | Xs], LT, GTE) when X < P -> | |
split_by_pivot(P, Xs, [X | LT], GTE); | |
split_by_pivot(P, [X | Xs], LT, GTE) -> | |
split_by_pivot(P, Xs, LT, [X | GTE]). | |
insertion_sort([]) -> []; | |
insertion_sort([X | Xs]) -> | |
insert_in_place(X, insertion_sort(Xs)). | |
insert_in_place(N, []) -> [N]; | |
insert_in_place(N, [X | Xs]) when N < X -> [N, X | Xs]; | |
insert_in_place(N, [X | Xs]) -> | |
[X | insert_in_place(N, Xs)]. | |
sort_tests() -> | |
[0, 1, 2, 3, 4, 4, 5, 7] = insertion_sort([4, 2, 5, 7, | |
3, 1, 0, 4]), | |
[0, 1, 2, 3, 4, 4, 5, 7] = merge_sort([4, 2, 5, 7, 3, 1, | |
0, 4]), | |
[0, 1, 2, 3, 4, 4, 5, 7] = quicksort([4, 2, 5, 7, 3, 1, | |
0, 4]), | |
ok. | |
perms([]) -> [[]]; | |
perms(L) -> element(1, gen_perms(length(L), L)). | |
% Heap's algorthim: https://en.wikipedia.org/wiki/Heap%27s_algorithm | |
gen_perms(1, A) -> {[A], A}; | |
gen_perms(K, A) -> | |
{L1, A2} = gen_perms(K - 1, A), | |
{L2, A3} = gen_perms(K, A2, 0), | |
{L1 ++ L2, A3}. | |
gen_perms(K, A, I) -> | |
A2 = case K rem 2 of | |
0 -> swap(A, I, K - 1); | |
1 -> swap(A, 0, K - 1) | |
end, | |
case I + 1 < K - 1 of | |
true -> | |
{L1, A3} = gen_perms(K - 1, A2), | |
{L2, A4} = gen_perms(K, A3, I + 1), | |
{L1 ++ L2, A4}; | |
false -> gen_perms(K - 1, A2) | |
end. | |
% helper function for Heap's algorithm: swap elements I & J of a list | |
swap([X | Xs], 0, J) -> | |
{L, [R | Rs]} = lists:split(J - 1, Xs), | |
[R | L] ++ [X | Rs]; | |
swap([X | Xs], I, J) -> [X | swap(Xs, I - 1, J - 1)]. | |
swap_test() -> | |
[4, 2, 3, 1] = swap([1, 2, 3, 4], 0, 3), ok. | |
perms_test() -> | |
[[1, 2, 3], [2, 1, 3], [3, 1, 2], [1, 3, 2], [2, 3, 1], | |
[3, 2, 1]] = | |
perms([1, 2, 3]), | |
ok. | |
test() -> swap_test(), perms_test(), ok. |
Wow that was fast, I will go over it Tomorrow, I am done for today.
My implementation is at https://gist.github.com/viniciusd/25372491ec2aa8368292fbf6e2788d7c#file-permutations-erl
But it is generating duplicates, I have no idea why. Probably spent all my energy today and need some recharging 😅
I tried adapting the algorithm to Erlang's 1-based lists
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Thanks for the bug report @viniciusd ! What an embarrassing test 😊.
I wasn't preserving the mutations to
A
in the recursive call togenerate
.I've revised the code, please take a look and let me know what you think.