%%%----------------------------------------------------------------------
%%% File    : treap.erl
%%% Author  : Alexey Shchepin <alexey@process-one.net>
%%% Purpose : Treaps implementation
%%% Created : 22 Apr 2008 by Alexey Shchepin <alexey@process-one.net>
%%%
%%%
%%% Copyright (C) 2002-2015   ProcessOne
%%%
%%% This program is free software; you can redistribute it and/or
%%% modify it under the terms of the GNU General Public License as
%%% published by the Free Software Foundation; either version 2 of the
%%% License, or (at your option) any later version.
%%%
%%% This program is distributed in the hope that it will be useful,
%%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%%% General Public License for more details.
%%%
%%% You should have received a copy of the GNU General Public License
%%% along with this program; if not, write to the Free Software
%%% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
%%% 02111-1307 USA
%%%
%%%----------------------------------------------------------------------

-module(treap).

-export([empty/0, insert/4, delete/2, delete_root/1,
	 get_root/1, lookup/2, is_empty/1, fold/3, from_list/1,
	 to_list/1]).

-type hashkey() :: {non_neg_integer(), any()}.

-type treap() :: {hashkey(), any(), any(), treap(), treap()} | nil.

-export_type([treap/0]).

empty() -> nil.

insert(Key, Priority, Value, Tree) ->
    HashKey = {erlang:phash2(Key), Key},
    insert1(Tree, HashKey, Priority, Value).

insert1(nil, HashKey, Priority, Value) ->
    {HashKey, Priority, Value, nil, nil};
insert1({HashKey1, Priority1, Value1, Left, Right} =
	    Tree,
	HashKey, Priority, Value) ->
    if HashKey < HashKey1 ->
	   heapify({HashKey1, Priority1, Value1,
		    insert1(Left, HashKey, Priority, Value), Right});
       HashKey > HashKey1 ->
	   heapify({HashKey1, Priority1, Value1, Left,
		    insert1(Right, HashKey, Priority, Value)});
       Priority == Priority1 ->
	   {HashKey, Priority, Value, Left, Right};
       true ->
	   insert1(delete_root(Tree), HashKey, Priority, Value)
    end.

heapify({_HashKey, _Priority, _Value, nil, nil} =
	    Tree) ->
    Tree;
heapify({HashKey, Priority, Value, nil = Left,
	 {HashKeyR, PriorityR, ValueR, LeftR, RightR}} =
	    Tree) ->
    if PriorityR > Priority ->
	   {HashKeyR, PriorityR, ValueR,
	    {HashKey, Priority, Value, Left, LeftR}, RightR};
       true -> Tree
    end;
heapify({HashKey, Priority, Value,
	 {HashKeyL, PriorityL, ValueL, LeftL, RightL},
	 nil = Right} =
	    Tree) ->
    if PriorityL > Priority ->
	   {HashKeyL, PriorityL, ValueL, LeftL,
	    {HashKey, Priority, Value, RightL, Right}};
       true -> Tree
    end;
heapify({HashKey, Priority, Value,
	 {HashKeyL, PriorityL, ValueL, LeftL, RightL} = Left,
	 {HashKeyR, PriorityR, ValueR, LeftR, RightR} = Right} =
	    Tree) ->
    if PriorityR > Priority ->
	   {HashKeyR, PriorityR, ValueR,
	    {HashKey, Priority, Value, Left, LeftR}, RightR};
       PriorityL > Priority ->
	   {HashKeyL, PriorityL, ValueL, LeftL,
	    {HashKey, Priority, Value, RightL, Right}};
       true -> Tree
    end.

delete(Key, Tree) ->
    HashKey = {erlang:phash2(Key), Key},
    delete1(HashKey, Tree).

delete1(_HashKey, nil) -> nil;
delete1(HashKey,
	{HashKey1, Priority1, Value1, Left, Right} = Tree) ->
    if HashKey < HashKey1 ->
	   {HashKey1, Priority1, Value1, delete1(HashKey, Left),
	    Right};
       HashKey > HashKey1 ->
	   {HashKey1, Priority1, Value1, Left,
	    delete1(HashKey, Right)};
       true -> delete_root(Tree)
    end.

delete_root({HashKey, Priority, Value, Left, Right}) ->
    case {Left, Right} of
      {nil, nil} -> nil;
      {_, nil} -> Left;
      {nil, _} -> Right;
      {{HashKeyL, PriorityL, ValueL, LeftL, RightL},
       {HashKeyR, PriorityR, ValueR, LeftR, RightR}} ->
	  if PriorityL > PriorityR ->
		 {HashKeyL, PriorityL, ValueL, LeftL,
		  delete_root({HashKey, Priority, Value, RightL, Right})};
	     true ->
		 {HashKeyR, PriorityR, ValueR,
		  delete_root({HashKey, Priority, Value, Left, LeftR}),
		  RightR}
	  end
    end.

is_empty(nil) -> true;
is_empty({_HashKey, _Priority, _Value, _Left,
	  _Right}) ->
    false.

get_root({{_Hash, Key}, Priority, Value, _Left,
	  _Right}) ->
    {Key, Priority, Value}.

lookup(Key, Tree) ->
    HashKey = {erlang:phash2(Key), Key},
    lookup1(Tree, HashKey).

lookup1(nil, _HashKey) -> error;
lookup1({HashKey1, Priority1, Value1, Left, Right},
	HashKey) ->
    if HashKey < HashKey1 -> lookup1(Left, HashKey);
       HashKey > HashKey1 -> lookup1(Right, HashKey);
       true -> {ok, Priority1, Value1}
    end.

fold(_F, Acc, nil) -> Acc;
fold(F, Acc,
     {{_Hash, Key}, Priority, Value, Left, Right}) ->
    Acc1 = F({Key, Priority, Value}, Acc),
    Acc2 = fold(F, Acc1, Left),
    fold(F, Acc2, Right).

to_list(Tree) -> to_list(Tree, []).

to_list(nil, Acc) -> Acc;
to_list(Tree, Acc) ->
    Root = get_root(Tree),
    to_list(delete_root(Tree), [Root | Acc]).

from_list(List) -> from_list(List, nil).

from_list([{Key, Priority, Value} | Tail], Tree) ->
    from_list(Tail, insert(Key, Priority, Value, Tree));
from_list([], Tree) -> Tree.
