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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;
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