File : g-hesorg.adb
1 ------------------------------------------------------------------------------
2 -- --
3 -- GNAT RUN-TIME COMPONENTS --
4 -- --
5 -- G N A T . H E A P _ S O R T _ G --
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_G 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) is
48
49 Max : Natural := N;
50 -- Current Max index in tree being sifted
51
52 procedure Sift (S : Positive);
53 -- This procedure sifts up node S, i.e. converts the subtree rooted
54 -- at node S into a heap, given the precondition that any sons of
55 -- S are already heaps. On entry, the contents of node S is found
56 -- in the temporary (index 0), the actual contents of node S on
57 -- entry are irrelevant. This is just a minor optimization to avoid
58 -- what would otherwise be two junk moves in phase two of the sort.
59
60 ----------
61 -- Sift --
62 ----------
63
64 procedure Sift (S : Positive) is
65 C : Positive := S;
66 Son : Positive;
67 Father : Positive;
68 -- Note: by making the above all Positive, we ensure that a test
69 -- against zero for the temporary location can be resolved on the
70 -- basis of types when the routines are inlined.
71
72 begin
73 -- This is where the optimization is done, normally we would do a
74 -- comparison at each stage between the current node and the larger
75 -- of the two sons, and continue the sift only if the current node
76 -- was less than this maximum. In this modified optimized version,
77 -- we assume that the current node will be less than the larger
78 -- son, and unconditionally sift up. Then when we get to the bottom
79 -- of the tree, we check parents to make sure that we did not make
80 -- a mistake. This roughly cuts the number of comparisons in half,
81 -- since it is almost always the case that our assumption is correct.
82
83 -- Loop to pull up larger sons
84
85 loop
86 Son := 2 * C;
87
88 if Son < Max then
89 if Lt (Son, Son + 1) then
90 Son := Son + 1;
91 end if;
92 elsif Son > Max then
93 exit;
94 end if;
95
96 Move (Son, C);
97 C := Son;
98 end loop;
99
100 -- Loop to check fathers
101
102 while C /= S loop
103 Father := C / 2;
104
105 if Lt (Father, 0) then
106 Move (Father, C);
107 C := Father;
108 else
109 exit;
110 end if;
111 end loop;
112
113 -- Last step is to pop the sifted node into place
114
115 Move (0, C);
116 end Sift;
117
118 -- Start of processing for Sort
119
120 begin
121 -- Phase one of heapsort is to build the heap. This is done by
122 -- sifting nodes N/2 .. 1 in sequence.
123
124 for J in reverse 1 .. N / 2 loop
125 Move (J, 0);
126 Sift (J);
127 end loop;
128
129 -- In phase 2, the largest node is moved to end, reducing the size
130 -- of the tree by one, and the displaced node is sifted down from
131 -- the top, so that the largest node is again at the top.
132
133 while Max > 1 loop
134 Move (Max, 0);
135 Move (1, Max);
136 Max := Max - 1;
137 Sift (1);
138 end loop;
139
140 end Sort;
141
142 end GNAT.Heap_Sort_G;