-module(list_utils).
-export([double/1, evens/1, sort/1, list_at/2, median/1, count/2, mode/1]).

% Transforming list elements
% Define an Erlang function double/1 to double the elements of a list of numbers.
double([]) -> [];
double([X|Xs]) -> [2*X | double(Xs)].

% Filtering lists
% Define a function evens/1 that extracts the even numbers from a list of integers.
evens([]) -> [];
evens([X|Xs]) when X rem 2 == 0 ->[X | evens(Xs)];
evens([X|Xs]) when X rem 2 > 0 -> evens(Xs).

% Sort the list
sort([]) -> [];
sort([X]) -> [X];
sort([X,Y]) when X =< Y -> [X,Y];
sort([X,Y]) when X > Y -> [Y,X];
sort(X) ->
    {X1, X2} = lists:split(length(X) div 2, X),
    lists:merge(sort(X1), sort(X2)).

% Return the element at position Index
list_at(X, Index) -> list_at(X, Index, 0).
list_at([X|_], Index, Index) -> X;
list_at([_|Xs], Index, CurrentIndex)
    when CurrentIndex < Index ->
            list_at(Xs, Index, CurrentIndex + 1).

% Median
median(X) ->
    XLength = length(X),
    MiddlePosition = XLength div 2,
    XSorted = sort(X),
    list_at(XSorted, MiddlePosition).

% Count the number of occurrences of Item in X
count(X, Item) -> count(X, Item, 0).
count([], _, Acc) -> Acc;
count([X|Xs], X, Acc) -> count(Xs, X, 1+Acc);
count([_|Xs], Item, Acc) -> count(Xs, Item, Acc).

% Mode
mode(X) ->
    XUniq = sets:to_list(sets:from_list(X)),
    mode(XUniq, X, nil, -1).

mode([], _XOccurrences, ItemMax, _Max) -> ItemMax;
mode([X|Xs], XOccurrences, ItemMax, Max) ->
    XCount = count(XOccurrences, X),
    if
        XCount > Max -> mode(Xs, XOccurrences, X, XCount);
        XCount =< Max -> mode(Xs, XOccurrences, ItemMax, Max)
    end.