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------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- G N A T . H E A P _ S O R T _ A --
-- --
-- B o d y --
-- --
-- Copyright (C) 1995-2021, AdaCore --
-- --
-- GNAT is free software; you can redistribute it and/or modify it under --
-- terms of the GNU General Public License as published by the Free Soft- --
-- ware Foundation; either version 3, or (at your option) any later ver- --
-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
-- or FITNESS FOR A PARTICULAR PURPOSE. --
-- --
-- As a special exception under Section 7 of GPL version 3, you are granted --
-- additional permissions described in the GCC Runtime Library Exception, --
-- version 3.1, as published by the Free Software Foundation. --
-- --
-- You should have received a copy of the GNU General Public License and --
-- a copy of the GCC Runtime Library Exception along with this program; --
-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
-- <http://www.gnu.org/licenses/>. --
-- --
-- GNAT was originally developed by the GNAT team at New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc. --
-- --
------------------------------------------------------------------------------
pragma Compiler_Unit_Warning;
package body GNAT.Heap_Sort_A is
----------
-- Sort --
----------
-- We are using the classical heapsort algorithm (i.e. Floyd's Treesort3)
-- as described by Knuth ("The Art of Programming", Volume III, first
-- edition, section 5.2.3, p. 145-147) with the modification that is
-- mentioned in exercise 18. For more details on this algorithm, see
-- Robert B. K. Dewar PhD thesis "The use of Computers in the X-ray
-- Phase Problem". University of Chicago, 1968, which was the first
-- publication of the modification, which reduces the number of compares
-- from 2NlogN to NlogN.
procedure Sort (N : Natural; Move : Move_Procedure; Lt : Lt_Function) is
Max : Natural := N;
-- Current Max index in tree being sifted
procedure Sift (S : Positive);
-- This procedure sifts up node S, i.e. converts the subtree rooted
-- at node S into a heap, given the precondition that any sons of
-- S are already heaps. On entry, the contents of node S is found
-- in the temporary (index 0), the actual contents of node S on
-- entry are irrelevant. This is just a minor optimization to avoid
-- what would otherwise be two junk moves in phase two of the sort.
procedure Sift (S : Positive) is
C : Positive := S;
Son : Positive;
Father : Positive;
begin
-- This is where the optimization is done, normally we would do a
-- comparison at each stage between the current node and the larger
-- of the two sons, and continue the sift only if the current node
-- was less than this maximum. In this modified optimized version,
-- we assume that the current node will be less than the larger
-- son, and unconditionally sift up. Then when we get to the bottom
-- of the tree, we check parents to make sure that we did not make
-- a mistake. This roughly cuts the number of comparisons in half,
-- since it is almost always the case that our assumption is correct.
-- Loop to pull up larger sons
loop
Son := 2 * C;
exit when Son > Max;
if Son < Max and then Lt (Son, Son + 1) then
Son := Son + 1;
end if;
Move (Son, C);
C := Son;
end loop;
-- Loop to check fathers
while C /= S loop
Father := C / 2;
if Lt (Father, 0) then
Move (Father, C);
C := Father;
else
exit;
end if;
end loop;
-- Last step is to pop the sifted node into place
Move (0, C);
end Sift;
-- Start of processing for Sort
begin
-- Phase one of heapsort is to build the heap. This is done by
-- sifting nodes N/2 .. 1 in sequence.
for J in reverse 1 .. N / 2 loop
Move (J, 0);
Sift (J);
end loop;
-- In phase 2, the largest node is moved to end, reducing the size
-- of the tree by one, and the displaced node is sifted down from
-- the top, so that the largest node is again at the top.
while Max > 1 loop
Move (Max, 0);
Move (1, Max);
Max := Max - 1;
Sift (1);
end loop;
end Sort;
end GNAT.Heap_Sort_A;
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