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

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

-spec new(fun((FLR, FLR) -> gleam@order:order())) -> heap(FLR).
new(Compare) ->
    {heap, empty, Compare}.

-spec find_min(heap(FLW)) -> {ok, FLW} | {error, nil}.
find_min(Heap) ->
    case erlang:element(2, Heap) of
        {tree, _, X, _, _} ->
            {ok, X};

        empty ->
            {error, nil}
    end.

-spec make(FNH, tree(FNH), tree(FNH)) -> tree(FNH).
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.

-spec merge_trees(tree(FMJ), tree(FMJ), fun((FMJ, FMJ) -> gleam@order:order())) -> tree(FMJ).
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.

-spec insert(heap(FLT), FLT) -> heap(FLT).
insert(Heap, Item) ->
    {heap,
        merge_trees(
            {tree, 1, Item, empty, empty},
            erlang:element(2, Heap),
            erlang:element(3, Heap)
        ),
        erlang:element(3, Heap)}.

-spec delete_min(heap(FMA)) -> {ok, {FMA, heap(FMA)}} | {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.

-spec merge(heap(FMF), heap(FMF)) -> heap(FMF).
merge(Heap1, Heap2) ->
    Compare = erlang:element(3, Heap1),
    {heap,
        merge_trees(erlang:element(2, Heap1), erlang:element(2, Heap2), Compare),
        Compare}.