-module(gleamy@leftist_heap).
-compile([no_auto_import, nowarn_unused_vars, nowarn_unused_function, nowarn_nomatch]).

-export([new/1, find_min/1, insert/2, delete_min/1, merge/2]).
-export_type([tree/1, heap/1]).

-type tree(GAJ) :: empty | {tree, integer(), GAJ, tree(GAJ), tree(GAJ)}.

-opaque heap(GAK) :: {heap, tree(GAK), fun((GAK, GAK) -> gleam@order:order())}.

-file("/home/julian/projects/gleamy_structures/src/gleamy/leftist_heap.gleam", 18).
-spec new(fun((GAL, GAL) -> gleam@order:order())) -> heap(GAL).
new(Compare) ->
    {heap, empty, Compare}.

-file("/home/julian/projects/gleamy_structures/src/gleamy/leftist_heap.gleam", 33).
-spec find_min(heap(GAQ)) -> {ok, GAQ} | {error, nil}.
find_min(Heap) ->
    case erlang:element(2, Heap) of
        {tree, _, X, _, _} ->
            {ok, X};

        empty ->
            {error, nil}
    end.

-file("/home/julian/projects/gleamy_structures/src/gleamy/leftist_heap.gleam", 72).
-spec make(GCC, tree(GCC), tree(GCC)) -> tree(GCC).
make(X, A, B) ->
    Rank_a = case A of
        {tree, R, _, _, _} ->
            R;

        empty ->
            0
    end,
    Rank_b = case B of
        {tree, R@1, _, _, _} ->
            R@1;

        empty ->
            0
    end,
    case Rank_a < Rank_b of
        true ->
            {tree, Rank_a + 1, X, B, A};

        _ ->
            {tree, Rank_b + 1, X, A, B}
    end.

-file("/home/julian/projects/gleamy_structures/src/gleamy/leftist_heap.gleam", 60).
-spec merge_trees(tree(GBD), tree(GBD), fun((GBD, GBD) -> gleam@order:order())) -> tree(GBD).
merge_trees(H1, H2, Compare) ->
    case {H1, H2} of
        {H, empty} ->
            H;

        {empty, H@1} ->
            H@1;

        {{tree, _, X, A1, B1}, {tree, _, Y, A2, B2}} ->
            case Compare(X, Y) of
                gt ->
                    make(Y, A2, merge_trees(H1, B2, Compare));

                _ ->
                    make(X, A1, merge_trees(B1, H2, Compare))
            end
    end.

-file("/home/julian/projects/gleamy_structures/src/gleamy/leftist_heap.gleam", 24).
-spec insert(heap(GAN), GAN) -> heap(GAN).
insert(Heap, Item) ->
    {heap,
        merge_trees(
            {tree, 1, Item, empty, empty},
            erlang:element(2, Heap),
            erlang:element(3, Heap)
        ),
        erlang:element(3, Heap)}.

-file("/home/julian/projects/gleamy_structures/src/gleamy/leftist_heap.gleam", 43).
-spec delete_min(heap(GAU)) -> {ok, {GAU, heap(GAU)}} | {error, nil}.
delete_min(Heap) ->
    case erlang:element(2, Heap) of
        {tree, _, X, A, B} ->
            {ok,
                {X,
                    {heap,
                        merge_trees(A, B, erlang:element(3, Heap)),
                        erlang:element(3, Heap)}}};

        empty ->
            {error, nil}
    end.

-file("/home/julian/projects/gleamy_structures/src/gleamy/leftist_heap.gleam", 55).
-spec merge(heap(GAZ), heap(GAZ)) -> heap(GAZ).
merge(Heap1, Heap2) ->
    Compare = erlang:element(3, Heap1),
    {heap,
        merge_trees(erlang:element(2, Heap1), erlang:element(2, Heap2), Compare),
        Compare}.