Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 145
(*input phase*)
NEW(head); tail := head; Texts.Scan(S);
WHILE S.class = Texts.Int DO
x := S.i; Texts.Scan(S); y := S.i; p := find(x); q := find(y);
NEW(t); t.id := q; t.next := p.trail;
p.trail := t; INC(q.count); Texts.Scan(S)
END
head
tail
key
count
1
0
2
1
4
2
6
1
10
2
8
2
3
2
5
2
7
0
9
1
next
trail
id
next
id
next
Fig. 4.15. List structure generated by TopSort program
After the data structure of Fig. 4.15 has been constructed in this input phase, the actual process of
topological sorting can be taken up as described above. But since it consists of repeatedly selecting an
element with a zero count of predecessors, it seems sensible to first gather all such elements in a linked
chain. Since we note that the original chain of leaders will afterwards no longer be needed, the same field
called next may be used again to link the zero predecessor leaders. This operation of replacing one chain
by another chain occurs frequently in list processing. It is expressed in detail here, and for reasons of
convenience it constructs the new chain in reverse order.
(*search for leaders without predecessors*)
p := head; head := NIL;
WHILE p # tail DO
q := p; p := q.next;
IF q.count = 0 THEN (*insert q^ in new chain*)
q.next := head; head := q
END
END
Referring to Fig. 4.15, we see that the next chain of leaders is replaced by the one of Fig. 4.16 in which
the pointers not depicted are left unchanged.
1
0
7
0 head
NIL