gcc/ada/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) 1995-2005, AdaCore                     --
  10 --                                                                          --
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  20 -- Boston, MA 02110-1301, USA.                                              --
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  22 -- As a special exception,  if other files  instantiate  generics from this --
  23 -- unit, or you link  this unit with other files  to produce an executable, --
  24 -- this  unit  does not  by itself cause  the resulting  executable  to  be --
  25 -- covered  by the  GNU  General  Public  License.  This exception does not --
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  27 -- covered by the  GNU Public License.                                      --
  28 --                                                                          --
  29 -- GNAT was originally developed  by the GNAT team at  New York University. --
  30 -- Extensive contributions were provided by Ada Core Technologies Inc.      --
  31 --                                                                          --
  32 ------------------------------------------------------------------------------
  33
  34 package body GNAT.Heap_Sort is
  35
  36    ----------
  37    -- Sort --
  38    ----------
  39
  40    --  We are using the classical heapsort algorithm (i.e. Floyd's Treesort3)
  41    --  as described by Knuth ("The Art of Programming", Volume III, first
  42    --  edition, section 5.2.3, p. 145-147) with the modification that is
  43    --  mentioned in exercise 18. For more details on this algorithm, see
  44    --  Robert B. K. Dewar PhD thesis "The use of Computers in the X-ray
  45    --  Phase Problem". University of Chicago, 1968, which was the first
  46    --  publication of the modification, which reduces the number of compares
  47    --  from 2NlogN to NlogN.
  48
  49    procedure Sort (N : Natural; Xchg : Xchg_Procedure; Lt : Lt_Function) is
  50       Max : Natural := N;
  51       --  Current Max index in tree being sifted. Note that we make Max
  52       --  Natural rather than Positive so that the case of sorting zero
  53       --  elements is correctly handled (i.e. does nothing at all).
  54
  55       procedure Sift (S : Positive);
  56       --  This procedure sifts up node S, i.e. converts the subtree rooted
  57       --  at node S into a heap, given the precondition that any sons of
  58       --  S are already heaps.
  59
  60       ----------
  61       -- Sift --
  62       ----------
  63
  64       procedure Sift (S : Positive) is
  65          C      : Positive := S;
  66          Son    : Positive;
  67          Father : Positive;
  68
  69       begin
  70          --  This is where the optimization is done, normally we would do a
  71          --  comparison at each stage between the current node and the larger
  72          --  of the two sons, and continue the sift only if the current node
  73          --  was less than this maximum. In this modified optimized version,
  74          --  we assume that the current node will be less than the larger
  75          --  son, and unconditionally sift up. Then when we get to the bottom
  76          --  of the tree, we check parents to make sure that we did not make
  77          --  a mistake. This roughly cuts the number of comparisons in half,
  78          --  since it is almost always the case that our assumption is correct.
  79
  80          --  Loop to pull up larger sons
  81
  82          loop
  83             Son := C + C;
  84
  85             if Son < Max then
  86                if Lt (Son, Son + 1) then
  87                   Son := Son + 1;
  88                end if;
  89             elsif Son > Max then
  90                exit;
  91             end if;
  92
  93             Xchg (Son, C);
  94             C := Son;
  95          end loop;
  96
  97          --  Loop to check fathers
  98
  99          while C /= S loop
 100             Father := C / 2;
 101
 102             if Lt (Father, C) then
 103                Xchg (Father, C);
 104                C := Father;
 105             else
 106                exit;
 107             end if;
 108          end loop;
 109       end Sift;
 110
 111    --  Start of processing for Sort
 112
 113    begin
 114       --  Phase one of heapsort is to build the heap. This is done by
 115       --  sifting nodes N/2 .. 1 in sequence.
 116
 117       for J in reverse 1 .. N / 2 loop
 118          Sift (J);
 119       end loop;
 120
 121       --  In phase 2, the largest node is moved to end, reducing the size
 122       --  of the tree by one, and the displaced node is sifted down from
 123       --  the top, so that the largest node is again at the top.
 124
 125       while Max > 1 loop
 126          Xchg (1, Max);
 127          Max := Max - 1;
 128          Sift (1);
 129       end loop;
 130    end Sort;
 131
 132 end GNAT.Heap_Sort;