1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT RUN-TIME COMPONENTS                         --
4--                                                                          --
5--                       G N A T . H E A P _ S O R T                        --
6--                                                                          --
7--                                 B o d y                                  --
8--                                                                          --
9--                     Copyright (C) 1995-2010, AdaCore                     --
10--                                                                          --
11-- GNAT is free software;  you can  redistribute it  and/or modify it under --
12-- terms of the  GNU General Public License as published  by the Free Soft- --
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14-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
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16-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
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20-- version 3.1, as published by the Free Software Foundation.               --
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22-- You should have received a copy of the GNU General Public License and    --
23-- a copy of the GCC Runtime Library Exception along with this program;     --
24-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
25-- <http://www.gnu.org/licenses/>.                                          --
26--                                                                          --
27-- GNAT was originally developed  by the GNAT team at  New York University. --
28-- Extensive contributions were provided by Ada Core Technologies Inc.      --
29--                                                                          --
30------------------------------------------------------------------------------
31
32package body GNAT.Heap_Sort is
33
34   ----------
35   -- Sort --
36   ----------
37
38   --  We are using the classical heapsort algorithm (i.e. Floyd's Treesort3)
39   --  as described by Knuth ("The Art of Programming", Volume III, first
40   --  edition, section 5.2.3, p. 145-147) with the modification that is
41   --  mentioned in exercise 18. For more details on this algorithm, see
42   --  Robert B. K. Dewar PhD thesis "The use of Computers in the X-ray
43   --  Phase Problem". University of Chicago, 1968, which was the first
44   --  publication of the modification, which reduces the number of compares
45   --  from 2NlogN to NlogN.
46
47   procedure Sort (N : Natural; Xchg : Xchg_Procedure; Lt : Lt_Function) is
48      Max : Natural := N;
49      --  Current Max index in tree being sifted. Note that we make Max
50      --  Natural rather than Positive so that the case of sorting zero
51      --  elements is correctly handled (i.e. does nothing at all).
52
53      procedure Sift (S : Positive);
54      --  This procedure sifts up node S, i.e. converts the subtree rooted
55      --  at node S into a heap, given the precondition that any sons of
56      --  S are already heaps.
57
58      ----------
59      -- Sift --
60      ----------
61
62      procedure Sift (S : Positive) is
63         C      : Positive := S;
64         Son    : Positive;
65         Father : Positive;
66
67      begin
68         --  This is where the optimization is done, normally we would do a
69         --  comparison at each stage between the current node and the larger
70         --  of the two sons, and continue the sift only if the current node
71         --  was less than this maximum. In this modified optimized version,
72         --  we assume that the current node will be less than the larger
73         --  son, and unconditionally sift up. Then when we get to the bottom
74         --  of the tree, we check parents to make sure that we did not make
75         --  a mistake. This roughly cuts the number of comparisons in half,
76         --  since it is almost always the case that our assumption is correct.
77
78         --  Loop to pull up larger sons
79
80         loop
81            Son := C + C;
82
83            if Son < Max then
84               if Lt (Son, Son + 1) then
85                  Son := Son + 1;
86               end if;
87            elsif Son > Max then
88               exit;
89            end if;
90
91            Xchg (Son, C);
92            C := Son;
93         end loop;
94
95         --  Loop to check fathers
96
97         while C /= S loop
98            Father := C / 2;
99
100            if Lt (Father, C) then
101               Xchg (Father, C);
102               C := Father;
103            else
104               exit;
105            end if;
106         end loop;
107      end Sift;
108
109   --  Start of processing for Sort
110
111   begin
112      --  Phase one of heapsort is to build the heap. This is done by
113      --  sifting nodes N/2 .. 1 in sequence.
114
115      for J in reverse 1 .. N / 2 loop
116         Sift (J);
117      end loop;
118
119      --  In phase 2, the largest node is moved to end, reducing the size
120      --  of the tree by one, and the displaced node is sifted down from
121      --  the top, so that the largest node is again at the top.
122
123      while Max > 1 loop
124         Xchg (1, Max);
125         Max := Max - 1;
126         Sift (1);
127      end loop;
128   end Sort;
129
130end GNAT.Heap_Sort;
131