Longest Incresing Subsequence

-module(lis_dc).
-author({pranjal, pandit}).
-export([test/1]).

tree(List) ->
    lists:foldl(
        fun(Elem, AccIn) ->
            {Tree, V} = AccIn,
            case is_tuple(Elem) of
            true ->
                {OldKey, OldValue} = Elem,
                {mytrees:insert(OldKey, {OldValue, V}, Tree), V+1};
            false ->
                {mytrees:insert(Elem, V, Tree), V+1}
            end
        end,
    {mytrees:empty(), 0}, List).

insert(Tree, []) -> Tree;
insert(Tree, [{K, V} | Tail]) ->
    insert(mytrees:insert(K, V, Tree), Tail).

update(Tree, []) -> Tree;
update(Tree, [{K, V} | Tail]) ->
    update(mytrees:update(K, V, Tree), Tail).


delete(Tree, []) -> Tree;
delete(Tree, [K | Tail]) ->
    delete(mytrees:delete(K, Tree), Tail).

test(List) ->
    {Tree, _} = tree(List),
    {Tree1, _} = tree(mytrees:to_list(Tree)),
    Left = Middle = mytrees:empty(),
    Left1 = mytrees:insert(0, length(List)-1, Left),
    Middle1 = mytrees:insert(lists:append(["0", "-", integer_to_list(length(List)-1)]) , 1, Middle),
    {Result, _,_,_} = lists:foldl(
        fun(Elem, AccIn) ->
            {Listqq, Leftqq, Middleqq, Treeqq} = AccIn,
            {value, {_, B}} = mytrees:lookup(Elem, Treeqq),
            case mytrees:lookup(B, Leftqq) of
            {value, Vzero} ->
                case mytrees:lookup(Vzero, Leftqq) of
                {value, Vnext} ->
                    {_, MV}=mytrees:lookup(lists:append(["0", "-", integer_to_list(Vzero)]), Middleqq),
                    L1 = delete( Leftqq, [Vzero] ),
                    L2 = update( L1, [{0, Vnext}] ),
                    M1 = delete( Middleqq, [lists:append(["0", "-", integer_to_list(Vzero)]),
                        lists:append([integer_to_list(Vzero), "-", integer_to_list(Vnext)])] ),
                    M2 = insert( M1, [{lists:append(["0", "-", integer_to_list(Vnext)]), MV+1}] ),
                    {mytrees:insert(Elem, MV, Listqq), L2, M2, Treeqq};
                {neighbours, {{A1 , B1}, single}} ->
                    {_, MV}=mytrees:lookup(lists:append([integer_to_list(A1), "-", integer_to_list(B1)]), Middleqq),
                    M1 = update( Middleqq, [{lists:append([integer_to_list(A1), "-", integer_to_list(B1)]), MV+1}] ),
                    {mytrees:insert(Elem, MV, Listqq), Leftqq, M1, Treeqq}
                end;
            {neighbours, {L, R}} ->
                case {L,R} of
                {{LK, LV}, single} ->
                    {_, MV}=mytrees:lookup(lists:append([integer_to_list(LK), "-", integer_to_list(LV)]), Middleqq),
                    M1 = delete( Middleqq, [lists:append([integer_to_list(LK), "-", integer_to_list(LV)])] ),
                    M2 = insert( M1, [{lists:append([integer_to_list(LK), "-", integer_to_list(B)]), MV},
                        {lists:append([integer_to_list(B), "-", integer_to_list(LV)]), MV+1}] ),
                    L1 = update( Leftqq, [{LK, B}] ),
                    L2 = insert( L1,  [{B, LV}]),
                    {mytrees:insert(Elem, MV, Listqq), L2, M2, Treeqq};
                {{LK, LV}, plus_inf} ->
                    {_, MV}=mytrees:lookup(lists:append([integer_to_list(LK), "-", integer_to_list(LV)]), Middleqq),
                    M1 = delete( Middleqq, [lists:append([integer_to_list(LK), "-", integer_to_list(LV)])] ),
                    M2 = insert( M1, [{lists:append([integer_to_list(LK), "-", integer_to_list(B)]), MV},
                        {lists:append([integer_to_list(B), "-", integer_to_list(LV)]), MV+1}] ),
                    L1 = update( Leftqq, [{LK, B}] ),
                    L2 = insert( L1,  [{B, LV}]),
                    {mytrees:insert(Elem, MV, Listqq), L2, M2, Treeqq};

                {{LK, LV}, {RK, RV}} ->
                    {_, MV}=mytrees:lookup(lists:append([integer_to_list(LK), "-", integer_to_list(LV)]), Middleqq),
                    {_, MV1}=mytrees:lookup(lists:append([integer_to_list(RK), "-", integer_to_list(RV)]), Middleqq),
                    M1 = delete( Middleqq, [lists:append([integer_to_list(LK), "-", integer_to_list(LV)]),
                        lists:append([integer_to_list(RK), "-", integer_to_list(RV)]) ]),
                    M2 = insert( M1, [{lists:append([integer_to_list(LK), "-", integer_to_list(B)]), MV},
                        {lists:append([integer_to_list(B), "-", integer_to_list(RV)]), MV1}] ),
                    L1 = update( Leftqq, [{LK, B}] ),
                    L2 = delete( L1, [RK] ),
                    L3 = insert( L2, [{B, RV}] ),
                    {mytrees:insert(Elem, MV, Listqq), L3, M2, Treeqq}

                end
            end
        end,
    {mytrees:empty(), Left1, Middle1, Tree1} , List),
    mytrees:to_list(Result).