Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 63
whereby after each step the next (least) item may be picked off the top of the heap. Once more, the
question arises about where to store the emerging top elements and whether or not an in situ sort would be
possible. Of course there is such a solution: In each step take the last component (say x) off the heap, store
the top element of the heap in the now free location of x, and let x sift down into its proper position. The
necessary n-1 steps are illustrated on the heap of Table 2.7. The process is described with the aid of the
procedure sift as follows:
R := n-1;
WHILE R > 0 DO
x := a[0]; a[0] := a[R]; a[R] := x;
DEC(R); sift(1, R)
END
06 42 12 55 94 18 44 67
12 42 18 55 94 67 44 | 06
18 42 44 55 94 67 | 12 06
42 55 44 67 94 | 18 12 06
44 55 94 67 | 42 18 12 06
55 67 94 | 44 42 18 12 06
67 94 | 55 44 42 18 12 06
94 | 67 55 44 42 18 12 06
Table 2.7. Example of a HeapSort Process.
The example of Table 2.7 shows that the resulting order is actually inverted. This, however, can easily
be remedied by changing the direction of the ordering relations in the sift procedure. This results in the
following procedure HeapSort. (Note that sift should actually be declared local to HeapSort.)
PROCEDURE sift (L, R: INTEGER); (* ADenS2_Sorts *)
VAR i, j: INTEGER; x: Item;
BEGIN
i := L; j := 2*i+1; x := a[i];
IF (j < R) & (a[j] < a[j+1]) THEN j := j+1 END;
WHILE (j 0 DO
DEC(L); sift(L, R)
END;
WHILE R > 0 DO
x := a[0]; a[0] := a[R]; a[R] := x;
DEC(R); sift(L, R)
END
END HeapSort