File : g-heasor.adb
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- --
13 -- ware Foundation; either version 3, or (at your option) any later ver- --
14 -- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
15 -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
16 -- or FITNESS FOR A PARTICULAR PURPOSE. --
17 -- --
18 -- --
19 -- --
20 -- --
21 -- --
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
32 package 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
130 end GNAT.Heap_Sort;