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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;