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pqueue.erl
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pqueue.erl
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%-*-Mode:erlang;coding:utf-8;tab-width:4;c-basic-offset:4;indent-tabs-mode:()-*-
% ex: set ft=erlang fenc=utf-8 sts=4 ts=4 sw=4 et nomod:
%%%
%%%------------------------------------------------------------------------
%%% @doc
%%% ==Static Priority Queue.==
%%% This priority queue implementation depends on a static number of priorities
%%% (-20 (high) to 20 (low)) so that tuple access times can be exploited for
%%% quick in/out priority queue operations. This implementation was created to
%%% avoid the slowness within the priority queue used by both RabbitMQ and Riak
%%% (https://github.com/basho/riak_core/blob/master/src/priority_queue.erl).
%%% @end
%%%
%%% MIT License
%%%
%%% Copyright (c) 2011-2020 Michael Truog <mjtruog at protonmail dot com>
%%%
%%% Permission is hereby granted, free of charge, to any person obtaining a
%%% copy of this software and associated documentation files (the "Software"),
%%% to deal in the Software without restriction, including without limitation
%%% the rights to use, copy, modify, merge, publish, distribute, sublicense,
%%% and/or sell copies of the Software, and to permit persons to whom the
%%% Software is furnished to do so, subject to the following conditions:
%%%
%%% The above copyright notice and this permission notice shall be included in
%%% all copies or substantial portions of the Software.
%%%
%%% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
%%% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
%%% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
%%% AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
%%% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
%%% FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
%%% DEALINGS IN THE SOFTWARE.
%%%
%%% @author Michael Truog <mjtruog at protonmail dot com>
%%% @copyright 2011-2020 Michael Truog
%%% @version 2.0.1 {@date} {@time}
%%%------------------------------------------------------------------------
-module(pqueue).
-author('mjtruog at protonmail dot com').
%% external interface
-export([in/2, % O(1)
in/3, % O(1)
is_empty/1, % O(1)
is_queue/1, % O(1)
join/2, % O(N) typically (?)
len/1, % O(N)
new/0, % O(1)
out/1, % O(1) amortized, O(N) worst case
out/2, % O(1) amortized, O(N) worst case
pout/1, % O(1) amortized, O(N) worst case
to_list/1, % O(N)
test/0]).
%%%------------------------------------------------------------------------
%%% External interface functions
%%%------------------------------------------------------------------------
-ifdef(ERLANG_OTP_VERSION_16).
-type pqueue() ::
{integer(),
{queue(), queue(), queue(), queue(), queue(), queue(), queue()},
{queue(), queue(), queue(), queue(), queue(), queue(), queue()},
{queue(), queue(), queue(), queue(), queue(), queue()},
queue(),
{queue(), queue(), queue(), queue(), queue(), queue()},
{queue(), queue(), queue(), queue(), queue(), queue(), queue()},
{queue(), queue(), queue(), queue(), queue(), queue(), queue()}} |
{'empty',
{queue(), queue(), queue(), queue(), queue(), queue(), queue()},
{queue(), queue(), queue(), queue(), queue(), queue(), queue()},
{queue(), queue(), queue(), queue(), queue(), queue()},
queue(),
{queue(), queue(), queue(), queue(), queue(), queue()},
{queue(), queue(), queue(), queue(), queue(), queue(), queue()},
{queue(), queue(), queue(), queue(), queue(), queue(), queue()}}.
-else.
-type pqueue() ::
{integer(),
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue(), queue:queue()},
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue(), queue:queue()},
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue()},
queue:queue(),
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue()},
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue(), queue:queue()},
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue(), queue:queue()}} |
{'empty',
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue(), queue:queue()},
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue(), queue:queue()},
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue()},
queue:queue(),
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue()},
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue(), queue:queue()},
{queue:queue(), queue:queue(), queue:queue(), queue:queue(),
queue:queue(), queue:queue(), queue:queue()}}.
-endif.
%%-------------------------------------------------------------------------
%% @doc
%% ===Append an item to the tail of the 0 priority queue.===
%% O(1)
%% @end
%%-------------------------------------------------------------------------
-spec in(term(), pqueue()) -> pqueue().
in(X, Q) ->
in(X, 0, Q).
%%-------------------------------------------------------------------------
%% @doc
%% ===Append an item to the tail of a specific priority queue.===
%% O(1)
%% @end
%%-------------------------------------------------------------------------
-spec in(term(), integer(), pqueue()) -> pqueue().
in(_, P, _)
when P < -20; P > 20 ->
erlang:exit(badarg);
in(X, P, {empty, _, _, _, _, _, _, _} = Q) ->
in_higher(P, Q, X);
in(X, P, {Pc, _, _, _, _, _, _, _} = Q)
when P < Pc ->
in_higher(P, Q, X);
in(X, P, Q) ->
in_lower(P, Q, X).
%%-------------------------------------------------------------------------
%% @doc
%% ===Check if the priority queue is empty.===
%% O(1)
%% @end
%%-------------------------------------------------------------------------
-spec is_empty(pqueue()) -> 'true' | 'false'.
is_empty({empty, _, _, _, _, _, _, _}) ->
true;
is_empty({_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}) ->
queue:is_empty(Qn20) and queue:is_empty(Qn19) and queue:is_empty(Qn18) and
queue:is_empty(Qn17) and queue:is_empty(Qn16) and queue:is_empty(Qn15) and
queue:is_empty(Qn14) and
queue:is_empty(Qn13) and queue:is_empty(Qn12) and queue:is_empty(Qn11) and
queue:is_empty(Qn10) and queue:is_empty(Qn9) and queue:is_empty(Qn8) and
queue:is_empty(Qn7) and
queue:is_empty(Qn6) and queue:is_empty(Qn5) and queue:is_empty(Qn4) and
queue:is_empty(Qn3) and queue:is_empty(Qn2) and queue:is_empty(Qn1) and
queue:is_empty(Q0) and
queue:is_empty(Qp1) and queue:is_empty(Qp2) and queue:is_empty(Qp3) and
queue:is_empty(Qp4) and queue:is_empty(Qp5) and queue:is_empty(Qp6) and
queue:is_empty(Qp7) and queue:is_empty(Qp8) and queue:is_empty(Qp9) and
queue:is_empty(Qp10) and queue:is_empty(Qp11) and queue:is_empty(Qp12) and
queue:is_empty(Qp13) and
queue:is_empty(Qp14) and queue:is_empty(Qp15) and queue:is_empty(Qp16) and
queue:is_empty(Qp17) and queue:is_empty(Qp18) and queue:is_empty(Qp19) and
queue:is_empty(Qp20).
%%-------------------------------------------------------------------------
%% @doc
%% ===Check if the priority queue type is as expected.===
%% O(1)
%% @end
%%-------------------------------------------------------------------------
-spec is_queue(pqueue()) -> 'true' | 'false'.
is_queue({Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14})
when tuple_size(Qsn14) == 7, tuple_size(Qsn7) == 7, tuple_size(Qsn1) == 6,
tuple_size(Qsp14) == 7, tuple_size(Qsp7) == 7, tuple_size(Qsp1) == 6 ->
(((Pc =:= empty) or is_integer(Pc)) and queue:is_queue(Q0));
is_queue(_) ->
false.
%%-------------------------------------------------------------------------
%% @doc
%% ===Join two priority queues.===
%% O(N)
%% @end
%%-------------------------------------------------------------------------
-spec join(pqueue(), pqueue()) -> pqueue().
join({P1c,
{Q1_n20, Q1_n19, Q1_n18, Q1_n17, Q1_n16, Q1_n15, Q1_n14},
{Q1_n13, Q1_n12, Q1_n11, Q1_n10, Q1_n9, Q1_n8, Q1_n7},
{Q1_n6, Q1_n5, Q1_n4, Q1_n3, Q1_n2, Q1_n1},
Q1_0,
{Q1_p1, Q1_p2, Q1_p3, Q1_p4, Q1_p5, Q1_p6},
{Q1_p7, Q1_p8, Q1_p9, Q1_p10, Q1_p11, Q1_p12, Q1_p13},
{Q1_p14, Q1_p15, Q1_p16, Q1_p17, Q1_p18, Q1_p19, Q1_p20}},
{P2c,
{Q2_n20, Q2_n19, Q2_n18, Q2_n17, Q2_n16, Q2_n15, Q2_n14},
{Q2_n13, Q2_n12, Q2_n11, Q2_n10, Q2_n9, Q2_n8, Q2_n7},
{Q2_n6, Q2_n5, Q2_n4, Q2_n3, Q2_n2, Q2_n1},
Q2_0,
{Q2_p1, Q2_p2, Q2_p3, Q2_p4, Q2_p5, Q2_p6},
{Q2_p7, Q2_p8, Q2_p9, Q2_p10, Q2_p11, Q2_p12, Q2_p13},
{Q2_p14, Q2_p15, Q2_p16, Q2_p17, Q2_p18, Q2_p19, Q2_p20}}) ->
{erlang:min(P1c, P2c),
{queue:join(Q1_n20, Q2_n20), queue:join(Q1_n19, Q2_n19),
queue:join(Q1_n18, Q2_n18), queue:join(Q1_n17, Q2_n17),
queue:join(Q1_n16, Q2_n16), queue:join(Q1_n15, Q2_n15),
queue:join(Q1_n14, Q2_n14)},
{queue:join(Q1_n13, Q2_n13), queue:join(Q1_n12, Q2_n12),
queue:join(Q1_n11, Q2_n11), queue:join(Q1_n10, Q2_n10),
queue:join(Q1_n9, Q2_n9), queue:join(Q1_n8, Q2_n8),
queue:join(Q1_n7, Q2_n7)},
{queue:join(Q1_n6, Q2_n6), queue:join(Q1_n5, Q2_n5),
queue:join(Q1_n4, Q2_n4), queue:join(Q1_n3, Q2_n3),
queue:join(Q1_n2, Q2_n2), queue:join(Q1_n1, Q2_n1)},
queue:join(Q1_0, Q2_0),
{queue:join(Q1_p1, Q2_p1), queue:join(Q1_p2, Q2_p2),
queue:join(Q1_p3, Q2_p3), queue:join(Q1_p4, Q2_p4),
queue:join(Q1_p5, Q2_p5), queue:join(Q1_p6, Q2_p6)},
{queue:join(Q1_p7, Q2_p7), queue:join(Q1_p8, Q2_p8),
queue:join(Q1_p9, Q2_p9), queue:join(Q1_p10, Q2_p10),
queue:join(Q1_p11, Q2_p11), queue:join(Q1_p12, Q2_p12),
queue:join(Q1_p13, Q2_p13)},
{queue:join(Q1_p14, Q2_p14), queue:join(Q1_p15, Q2_p15),
queue:join(Q1_p16, Q2_p16), queue:join(Q1_p17, Q2_p17),
queue:join(Q1_p18, Q2_p18), queue:join(Q1_p19, Q2_p19),
queue:join(Q1_p20, Q2_p20)}}.
%%-------------------------------------------------------------------------
%% @doc
%% ===Determine the length of a priority queue.===
%% O(N)
%% @end
%%-------------------------------------------------------------------------
-spec len(pqueue()) -> non_neg_integer().
len({_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}) ->
queue:len(Qn20) + queue:len(Qn19) + queue:len(Qn18) + queue:len(Qn17) +
queue:len(Qn16) + queue:len(Qn15) + queue:len(Qn14) +
queue:len(Qn13) + queue:len(Qn12) + queue:len(Qn11) + queue:len(Qn10) +
queue:len(Qn9) + queue:len(Qn8) + queue:len(Qn7) +
queue:len(Qn6) + queue:len(Qn5) + queue:len(Qn4) + queue:len(Qn3) +
queue:len(Qn2) + queue:len(Qn1) +
queue:len(Q0) +
queue:len(Qp1) + queue:len(Qp2) + queue:len(Qp3) + queue:len(Qp4) +
queue:len(Qp5) + queue:len(Qp6) +
queue:len(Qp7) + queue:len(Qp8) + queue:len(Qp9) + queue:len(Qp10) +
queue:len(Qp11) + queue:len(Qp12) + queue:len(Qp13) +
queue:len(Qp14) + queue:len(Qp15) + queue:len(Qp16) + queue:len(Qp17) +
queue:len(Qp18) + queue:len(Qp19) + queue:len(Qp20).
%%-------------------------------------------------------------------------
%% @doc
%% ===Create a new priority queue.===
%% O(1)
%% @end
%%-------------------------------------------------------------------------
-spec new() -> pqueue().
new() ->
{empty, % current priority
erlang:make_tuple(7, queue:new()), % priority [-20..-14]
erlang:make_tuple(7, queue:new()), % priority [-13.. -7]
erlang:make_tuple(6, queue:new()), % priority [ -6.. -1]
queue:new(), % priority 0 (default)
erlang:make_tuple(6, queue:new()), % priority [ 1.. 6]
erlang:make_tuple(7, queue:new()), % priority [ 7.. 13]
erlang:make_tuple(7, queue:new())}. % priority [ 14.. 20]
%%-------------------------------------------------------------------------
%% @doc
%% ===Take an item from the head of the priority queue.===
%% O(1) amortized, O(N) worst case
%% @end
%%-------------------------------------------------------------------------
-spec out(pqueue()) ->
{{'value', term()}, pqueue()} | {'empty', pqueue()}.
out({empty, _, _, _, _, _, _, _} = Q) ->
{empty, Q};
out({Pc, _, _, _, _, _, _, _} = Q) ->
out_current(Pc, Q, nopriority).
%%-------------------------------------------------------------------------
%% @doc
%% ===Take an item of a specific priority from the head of the queue.===
%% O(1) amortized, O(N) worst case
%% @end
%%-------------------------------------------------------------------------
-spec out(integer(), pqueue()) ->
{{'value', term()}, pqueue()} | {'empty', pqueue()}.
out(P, _)
when P < -20; P > 20 ->
erlang:exit(badarg);
out(_, {empty, _, _, _, _, _, _, _} = Q) ->
{empty, Q};
out(P, Q) ->
out_specific(P, Q).
%%-------------------------------------------------------------------------
%% @doc
%% ===Take an item from the head of the priority queue.===
%% Includes the priority in the return value.
%% O(1) amortized, O(N) worst case
%% @end
%%-------------------------------------------------------------------------
-spec pout(pqueue()) ->
{{'value', term(), integer()}, pqueue()} | {'empty', pqueue()}.
pout({empty, _, _, _, _, _, _, _} = Q) ->
{empty, Q};
pout({Pc, _, _, _, _, _, _, _} = Q) ->
out_current(Pc, Q, priority).
%%-------------------------------------------------------------------------
%% @doc
%% ===Convert the priority queue to a list.===
%% O(N)
%% @end
%%-------------------------------------------------------------------------
-spec to_list(pqueue()) -> list(term()).
to_list({_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}) ->
queue:to_list(Qn20) ++ queue:to_list(Qn19) ++ queue:to_list(Qn18) ++
queue:to_list(Qn17) ++ queue:to_list(Qn16) ++ queue:to_list(Qn15) ++
queue:to_list(Qn14) ++
queue:to_list(Qn13) ++ queue:to_list(Qn12) ++ queue:to_list(Qn11) ++
queue:to_list(Qn10) ++ queue:to_list(Qn9) ++ queue:to_list(Qn8) ++
queue:to_list(Qn7) ++
queue:to_list(Qn6) ++ queue:to_list(Qn5) ++ queue:to_list(Qn4) ++
queue:to_list(Qn3) ++ queue:to_list(Qn2) ++ queue:to_list(Qn1) ++
queue:to_list(Q0) ++
queue:to_list(Qp1) ++ queue:to_list(Qp2) ++ queue:to_list(Qp3) ++
queue:to_list(Qp4) ++ queue:to_list(Qp5) ++ queue:to_list(Qp6) ++
queue:to_list(Qp7) ++ queue:to_list(Qp8) ++ queue:to_list(Qp9) ++
queue:to_list(Qp10) ++ queue:to_list(Qp11) ++ queue:to_list(Qp12) ++
queue:to_list(Qp13) ++
queue:to_list(Qp14) ++ queue:to_list(Qp15) ++ queue:to_list(Qp16) ++
queue:to_list(Qp17) ++ queue:to_list(Qp18) ++ queue:to_list(Qp19) ++
queue:to_list(Qp20).
%%-------------------------------------------------------------------------
%% @doc
%% ===Regression test.===
%% @end
%%-------------------------------------------------------------------------
test() ->
Q0 = pqueue:new(),
true = pqueue:is_queue(Q0),
Q1 = pqueue:in(20, 20, Q0),
Q2 = pqueue:in(19, 19, Q1),
Q3 = pqueue:in(18, 18, Q2),
Q4 = pqueue:in(17, 17, Q3),
Q5 = pqueue:in(16, 16, Q4),
Q6 = pqueue:in(15, 15, Q5),
Q7 = pqueue:in(14, 14, Q6),
Q8 = pqueue:in(13, 13, Q7),
Q9 = pqueue:in(12, 12, Q8),
Q10 = pqueue:in(11, 11, Q9),
Q11 = pqueue:in(10, 10, Q10),
Q12 = pqueue:in(9, 9, Q11),
Q13 = pqueue:in(8, 8, Q12),
Q14 = pqueue:in(7, 7, Q13),
Q15 = pqueue:in(6, 6, Q14),
Q16 = pqueue:in(5, 5, Q15),
Q17 = pqueue:in(4, 4, Q16),
Q18 = pqueue:in(3, 3, Q17),
Q19 = pqueue:in(2, 2, Q18),
Q20 = pqueue:in(1, 1, Q19),
Q21 = pqueue:in(0, 0, Q20),
Q22 = pqueue:in(-1, -1, Q21),
Q23 = pqueue:in(-2, -2, Q22),
Q24 = pqueue:in(-3, -3, Q23),
Q25 = pqueue:in(-4, -4, Q24),
Q26 = pqueue:in(-5, -5, Q25),
Q27 = pqueue:in(-6, -6, Q26),
Q28 = pqueue:in(-7, -7, Q27),
Q29 = pqueue:in(-8, -8, Q28),
Q30 = pqueue:in(-9, -9, Q29),
Q31 = pqueue:in(-10, -10, Q30),
Q32 = pqueue:in(-11, -11, Q31),
Q33 = pqueue:in(-12, -12, Q32),
Q34 = pqueue:in(-13, -13, Q33),
Q35 = pqueue:in(-14, -14, Q34),
Q36 = pqueue:in(-15, -15, Q35),
Q37 = pqueue:in(-16, -16, Q36),
Q38 = pqueue:in(-17, -17, Q37),
Q39 = pqueue:in(-18, -18, Q38),
Q40 = pqueue:in(-19, -19, Q39),
Q41 = pqueue:in(-20, -20, Q40),
Q42 = pqueue:in(-20, -20, Q41),
Q43 = pqueue:in(-19, -19, Q42),
Q44 = pqueue:in(-18, -18, Q43),
Q45 = pqueue:in(-17, -17, Q44),
Q46 = pqueue:in(-16, -16, Q45),
Q47 = pqueue:in(-15, -15, Q46),
Q48 = pqueue:in(-14, -14, Q47),
Q49 = pqueue:in(-13, -13, Q48),
Q50 = pqueue:in(-12, -12, Q49),
Q51 = pqueue:in(-11, -11, Q50),
Q52 = pqueue:in(-10, -10, Q51),
Q53 = pqueue:in(-9, -9, Q52),
Q54 = pqueue:in(-8, -8, Q53),
Q55 = pqueue:in(-7, -7, Q54),
Q56 = pqueue:in(-6, -6, Q55),
Q57 = pqueue:in(-5, -5, Q56),
Q58 = pqueue:in(-4, -4, Q57),
Q59 = pqueue:in(-3, -3, Q58),
Q60 = pqueue:in(-2, -2, Q59),
Q61 = pqueue:in(-1, -1, Q60),
Q62 = pqueue:in(0, 0, Q61),
Q63 = pqueue:in(1, 1, Q62),
Q64 = pqueue:in(2, 2, Q63),
Q65 = pqueue:in(3, 3, Q64),
Q66 = pqueue:in(4, 4, Q65),
Q67 = pqueue:in(5, 5, Q66),
Q68 = pqueue:in(6, 6, Q67),
Q69 = pqueue:in(7, 7, Q68),
Q70 = pqueue:in(8, 8, Q69),
Q71 = pqueue:in(9, 9, Q70),
Q72 = pqueue:in(10, 10, Q71),
Q73 = pqueue:in(11, 11, Q72),
Q74 = pqueue:in(12, 12, Q73),
Q75 = pqueue:in(13, 13, Q74),
Q76 = pqueue:in(14, 14, Q75),
Q77 = pqueue:in(15, 15, Q76),
Q78 = pqueue:in(16, 16, Q77),
Q79 = pqueue:in(17, 17, Q78),
Q80 = pqueue:in(18, 18, Q79),
Q81 = pqueue:in(19, 19, Q80),
Q82 = pqueue:in(20, 20, Q81),
true = pqueue:is_queue(Q82),
82 = pqueue:len(Q82),
[-20, -20, -19, -19, -18, -18, -17, -17, -16, -16, -15, -15, -14, -14,
-13, -13, -12, -12, -11, -11, -10, -10, -9, -9, -8, -8, -7, -7, -6, -6,
-5, -5, -4, -4, -3, -3, -2, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4,
5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14,
15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20] = pqueue:to_list(Q82),
{{value, -20}, Q83} = pqueue:out(Q82),
{{value, -20}, Q84} = pqueue:out(Q83),
{{value, -19}, Q85} = pqueue:out(Q84),
{{value, -19}, Q86} = pqueue:out(Q85),
{{value, -18}, Q87} = pqueue:out(Q86),
{{value, -18}, Q88} = pqueue:out(Q87),
{{value, 0}, Q89} = pqueue:out(0, Q88),
{{value, 0}, Q90} = pqueue:out(0, Q89),
{empty, _} = pqueue:out(0, Q90),
{{value, -17, -17}, Q91} = pqueue:pout(Q90),
{{value, -17, -17}, Q92} = pqueue:pout(Q91),
{{value, -16, -16}, Q93} = pqueue:pout(Q92),
{{value, -16, -16}, Q94} = pqueue:pout(Q93),
{{value, -15, -15}, Q95} = pqueue:pout(Q94),
{{value, -15, -15}, Q96} = pqueue:pout(Q95),
{{value, -14, -14}, Q97} = pqueue:pout(Q96),
{{value, -14, -14}, Q98} = pqueue:pout(Q97),
{{value, -13, -13}, Q99} = pqueue:pout(Q98),
{{value, -13, -13}, Q100} = pqueue:pout(Q99),
{{value, -12, -12}, Q101} = pqueue:pout(Q100),
{{value, -12, -12}, Q102} = pqueue:pout(Q101),
{{value, -11, -11}, Q103} = pqueue:pout(Q102),
{{value, -11, -11}, Q104} = pqueue:pout(Q103),
{{value, -10, -10}, Q105} = pqueue:pout(Q104),
{{value, -10, -10}, Q106} = pqueue:pout(Q105),
{{value, -9, -9}, Q107} = pqueue:pout(Q106),
{{value, -9, -9}, Q108} = pqueue:pout(Q107),
{{value, -8, -8}, Q109} = pqueue:pout(Q108),
{{value, -8, -8}, Q110} = pqueue:pout(Q109),
{{value, -7, -7}, Q111} = pqueue:pout(Q110),
{{value, -7, -7}, Q112} = pqueue:pout(Q111),
{{value, -6, -6}, Q113} = pqueue:pout(Q112),
{{value, -6, -6}, Q114} = pqueue:pout(Q113),
{{value, -5, -5}, Q115} = pqueue:pout(Q114),
{{value, -5, -5}, Q116} = pqueue:pout(Q115),
{{value, -4, -4}, Q117} = pqueue:pout(Q116),
{{value, -4, -4}, Q118} = pqueue:pout(Q117),
{{value, -3, -3}, Q119} = pqueue:pout(Q118),
{{value, -3, -3}, Q120} = pqueue:pout(Q119),
{{value, -2, -2}, Q121} = pqueue:pout(Q120),
{{value, -2, -2}, Q122} = pqueue:pout(Q121),
{{value, -1, -1}, Q123} = pqueue:pout(Q122),
{{value, -1, -1}, Q124} = pqueue:pout(Q123),
{{value, 1, 1}, Q125} = pqueue:pout(Q124),
{{value, 1, 1}, Q126} = pqueue:pout(Q125),
{{value, 2, 2}, Q127} = pqueue:pout(Q126),
{{value, 2, 2}, Q128} = pqueue:pout(Q127),
{{value, 3, 3}, Q129} = pqueue:pout(Q128),
{{value, 3, 3}, Q130} = pqueue:pout(Q129),
{{value, 4, 4}, Q131} = pqueue:pout(Q130),
{{value, 4, 4}, Q132} = pqueue:pout(Q131),
{{value, 5, 5}, Q133} = pqueue:pout(Q132),
{{value, 5, 5}, Q134} = pqueue:pout(Q133),
{{value, 6, 6}, Q135} = pqueue:pout(Q134),
{{value, 6, 6}, Q136} = pqueue:pout(Q135),
{{value, 7, 7}, Q137} = pqueue:pout(Q136),
{{value, 7, 7}, Q138} = pqueue:pout(Q137),
{{value, 8, 8}, Q139} = pqueue:pout(Q138),
{{value, 8, 8}, Q140} = pqueue:pout(Q139),
{{value, 9, 9}, Q141} = pqueue:pout(Q140),
{{value, 9, 9}, Q142} = pqueue:pout(Q141),
{{value, 10, 10}, Q143} = pqueue:pout(Q142),
{{value, 10, 10}, Q144} = pqueue:pout(Q143),
{{value, 11, 11}, Q145} = pqueue:pout(Q144),
{{value, 11, 11}, Q146} = pqueue:pout(Q145),
{{value, 12, 12}, Q147} = pqueue:pout(Q146),
{{value, 12, 12}, Q148} = pqueue:pout(Q147),
{{value, 13, 13}, Q149} = pqueue:pout(Q148),
{{value, 13, 13}, Q150} = pqueue:pout(Q149),
{{value, 14, 14}, Q151} = pqueue:pout(Q150),
{{value, 14, 14}, Q152} = pqueue:pout(Q151),
{{value, 15, 15}, Q153} = pqueue:pout(Q152),
{{value, 15, 15}, Q154} = pqueue:pout(Q153),
{{value, 16, 16}, Q155} = pqueue:pout(Q154),
{{value, 16, 16}, Q156} = pqueue:pout(Q155),
{{value, 17, 17}, Q157} = pqueue:pout(Q156),
{{value, 17, 17}, Q158} = pqueue:pout(Q157),
{{value, 18, 18}, Q159} = pqueue:pout(Q158),
{{value, 18, 18}, Q160} = pqueue:pout(Q159),
{{value, 19, 19}, Q161} = pqueue:pout(Q160),
{{value, 19, 19}, Q162} = pqueue:pout(Q161),
{{value, 20, 20}, Q163} = pqueue:pout(Q162),
{{value, 20, 20}, Q164} = pqueue:pout(Q163),
true = pqueue:is_empty(Q164),
{empty, Q165} = pqueue:pout(Q164),
true = pqueue:is_empty(Q165),
ok.
%%%------------------------------------------------------------------------
%%% Private functions
%%%------------------------------------------------------------------------
in_higher(-20, {_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-20,
{queue:in(X, Qn20), Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-19, {_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-19,
{Qn20, queue:in(X, Qn19), Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-18, {_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-18,
{Qn20, Qn19, queue:in(X, Qn18), Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-17, {_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-17,
{Qn20, Qn19, Qn18, queue:in(X, Qn17), Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-16, {_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-16,
{Qn20, Qn19, Qn18, Qn17, queue:in(X, Qn16), Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-15, {_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-15,
{Qn20, Qn19, Qn18, Qn17, Qn16, queue:in(X, Qn15), Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-14, {_,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-14,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, queue:in(X, Qn14)},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-13, {_, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-13, Qsn14,
{queue:in(X, Qn13), Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-12, {_, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-12, Qsn14,
{Qn13, queue:in(X, Qn12), Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-11, {_, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-11, Qsn14,
{Qn13, Qn12, queue:in(X, Qn11), Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-10, {_, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-10, Qsn14,
{Qn13, Qn12, Qn11, queue:in(X, Qn10), Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-9, {_, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-9, Qsn14,
{Qn13, Qn12, Qn11, Qn10, queue:in(X, Qn9), Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-8, {_, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-8, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, queue:in(X, Qn8), Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-7, {_, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-7, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, queue:in(X, Qn7)},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_higher(-6, {_, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-6, Qsn14, Qsn7,
{queue:in(X, Qn6), Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_higher(-5, {_, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-5, Qsn14, Qsn7,
{Qn6, queue:in(X, Qn5), Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_higher(-4, {_, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-4, Qsn14, Qsn7,
{Qn6, Qn5, queue:in(X, Qn4), Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_higher(-3, {_, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-3, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, queue:in(X, Qn3), Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_higher(-2, {_, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-2, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, queue:in(X, Qn2), Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_higher(-1, {_, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{-1, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, queue:in(X, Qn1)},
Q0, Qsp1, Qsp7, Qsp14};
in_higher(0, {_, Qsn14, Qsn7, Qsn1,
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{0, Qsn14, Qsn7, Qsn1,
queue:in(X, Q0),
Qsp1, Qsp7, Qsp14};
in_higher(1, {_, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{1, Qsn14, Qsn7, Qsn1, Q0,
{queue:in(X, Qp1), Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14};
in_higher(2, {_, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{2, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, queue:in(X, Qp2), Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14};
in_higher(3, {_, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{3, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, queue:in(X, Qp3), Qp4, Qp5, Qp6},
Qsp7, Qsp14};
in_higher(4, {_, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{4, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, queue:in(X, Qp4), Qp5, Qp6},
Qsp7, Qsp14};
in_higher(5, {_, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{5, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, queue:in(X, Qp5), Qp6},
Qsp7, Qsp14};
in_higher(6, {_, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{6, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, queue:in(X, Qp6)},
Qsp7, Qsp14};
in_higher(7, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{7, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{queue:in(X, Qp7), Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14};
in_higher(8, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{8, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, queue:in(X, Qp8), Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14};
in_higher(9, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{9, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, queue:in(X, Qp9), Qp10, Qp11, Qp12, Qp13},
Qsp14};
in_higher(10, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{10, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, queue:in(X, Qp10), Qp11, Qp12, Qp13},
Qsp14};
in_higher(11, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{11, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, queue:in(X, Qp11), Qp12, Qp13},
Qsp14};
in_higher(12, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{12, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, queue:in(X, Qp12), Qp13},
Qsp14};
in_higher(13, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{13, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, queue:in(X, Qp13)},
Qsp14};
in_higher(14, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}, X) ->
{14, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{queue:in(X, Qp14), Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}};
in_higher(15, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}, X) ->
{15, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, queue:in(X, Qp15), Qp16, Qp17, Qp18, Qp19, Qp20}};
in_higher(16, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}, X) ->
{16, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, queue:in(X, Qp16), Qp17, Qp18, Qp19, Qp20}};
in_higher(17, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}, X) ->
{17, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, queue:in(X, Qp17), Qp18, Qp19, Qp20}};
in_higher(18, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}, X) ->
{18, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, queue:in(X, Qp18), Qp19, Qp20}};
in_higher(19, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}, X) ->
{19, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, Qp18, queue:in(X, Qp19), Qp20}};
in_higher(20, {_, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, Qp20}}, X) ->
{20, Qsn14, Qsn7, Qsn1, Q0, Qsp1, Qsp7,
{Qp14, Qp15, Qp16, Qp17, Qp18, Qp19, queue:in(X, Qp20)}}.
in_lower(-20, {Pc,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc,
{queue:in(X, Qn20), Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-19, {Pc,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc,
{Qn20, queue:in(X, Qn19), Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-18, {Pc,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc,
{Qn20, Qn19, queue:in(X, Qn18), Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-17, {Pc,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc,
{Qn20, Qn19, Qn18, queue:in(X, Qn17), Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-16, {Pc,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc,
{Qn20, Qn19, Qn18, Qn17, queue:in(X, Qn16), Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-15, {Pc,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc,
{Qn20, Qn19, Qn18, Qn17, Qn16, queue:in(X, Qn15), Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-14, {Pc,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, Qn14},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc,
{Qn20, Qn19, Qn18, Qn17, Qn16, Qn15, queue:in(X, Qn14)},
Qsn7, Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-13, {Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14,
{queue:in(X, Qn13), Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-12, {Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14,
{Qn13, queue:in(X, Qn12), Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-11, {Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14,
{Qn13, Qn12, queue:in(X, Qn11), Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-10, {Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14,
{Qn13, Qn12, Qn11, queue:in(X, Qn10), Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-9, {Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, queue:in(X, Qn9), Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-8, {Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, queue:in(X, Qn8), Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-7, {Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, Qn7},
Qsn1, Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14,
{Qn13, Qn12, Qn11, Qn10, Qn9, Qn8, queue:in(X, Qn7)},
Qsn1, Q0, Qsp1, Qsp7, Qsp14};
in_lower(-6, {Pc, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7,
{queue:in(X, Qn6), Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_lower(-5, {Pc, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7,
{Qn6, queue:in(X, Qn5), Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_lower(-4, {Pc, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7,
{Qn6, Qn5, queue:in(X, Qn4), Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_lower(-3, {Pc, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, queue:in(X, Qn3), Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_lower(-2, {Pc, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, queue:in(X, Qn2), Qn1},
Q0, Qsp1, Qsp7, Qsp14};
in_lower(-1, {Pc, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, Qn1},
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7,
{Qn6, Qn5, Qn4, Qn3, Qn2, queue:in(X, Qn1)},
Q0, Qsp1, Qsp7, Qsp14};
in_lower(0, {Pc, Qsn14, Qsn7, Qsn1,
Q0, Qsp1, Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1,
queue:in(X, Q0),
Qsp1, Qsp7, Qsp14};
in_lower(1, {Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0,
{queue:in(X, Qp1), Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14};
in_lower(2, {Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, queue:in(X, Qp2), Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14};
in_lower(3, {Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, queue:in(X, Qp3), Qp4, Qp5, Qp6},
Qsp7, Qsp14};
in_lower(4, {Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, queue:in(X, Qp4), Qp5, Qp6},
Qsp7, Qsp14};
in_lower(5, {Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, queue:in(X, Qp5), Qp6},
Qsp7, Qsp14};
in_lower(6, {Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, Qp6},
Qsp7, Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0,
{Qp1, Qp2, Qp3, Qp4, Qp5, queue:in(X, Qp6)},
Qsp7, Qsp14};
in_lower(7, {Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{queue:in(X, Qp7), Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14};
in_lower(8, {Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, queue:in(X, Qp8), Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14};
in_lower(9, {Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, queue:in(X, Qp9), Qp10, Qp11, Qp12, Qp13},
Qsp14};
in_lower(10, {Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, queue:in(X, Qp10), Qp11, Qp12, Qp13},
Qsp14};
in_lower(11, {Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, queue:in(X, Qp11), Qp12, Qp13},
Qsp14};
in_lower(12, {Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, Qp12, Qp13},
Qsp14}, X) ->
{Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,
{Qp7, Qp8, Qp9, Qp10, Qp11, queue:in(X, Qp12), Qp13},
Qsp14};
in_lower(13, {Pc, Qsn14, Qsn7, Qsn1, Q0, Qsp1,