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------------------------------------------------------------------------------
--                                                                          --
--                         GNAT RUN-TIME COMPONENTS                         --
--                                                                          --
--                       G N A T . H E A P _ S O R T                        --
--                                                                          --
--                                 B o d y                                  --
--                                                                          --
--                     Copyright (C) 1995-2010, 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.      --
--                                                                          --
------------------------------------------------------------------------------
 
package body GNAT.Heap_Sort 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; Xchg : Xchg_Procedure; Lt : Lt_Function) is
      Max : Natural := N;
      --  Current Max index in tree being sifted. Note that we make Max
      --  Natural rather than Positive so that the case of sorting zero
      --  elements is correctly handled (i.e. does nothing at all).
 
      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.
 
      ----------
      -- Sift --
      ----------
 
      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 := C + C;
 
            if Son < Max then
               if Lt (Son, Son + 1) then
                  Son := Son + 1;
               end if;
            elsif Son > Max then
               exit;
            end if;
 
            Xchg (Son, C);
            C := Son;
         end loop;
 
         --  Loop to check fathers
 
         while C /= S loop
            Father := C / 2;
 
            if Lt (Father, C) then
               Xchg (Father, C);
               C := Father;
            else
               exit;
            end if;
         end loop;
      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
         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
         Xchg (1, Max);
         Max := Max - 1;
         Sift (1);
      end loop;
   end Sort;
 
end GNAT.Heap_Sort;