Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 191
(1) 1 2; 3; 4 5 6; 7;
(2) 5 4; 3; 1 2 7 6;
(3) 6 2; 4; 1 7 3 5;
(4) 4 2 6; 1 7; 3 5;
(1)
1 2
2
2 4
4
1
3 1
3
5 6 2
6
1 3
5 7
(2)
4 5
4
2 4
6
3
5 1
3
5
7
(3)
2 6
4
4
2
6 1 2
3
5 6
7
(4)
2 4
6
2
6
2 6
1
4
7
1
3 4
5
7
Fig. 4.50. Insertion of keys 1 to 7
These pictures make the third property of B-trees particularly obvious: all terminal nodes appear on the
same level. One is therefore inclined to compare these structures with garden hedges that have been
recently trimmed with hedge scissors.
The algorithm for the construction of SBB-trees is show below. It is based on a definition of the type
Node with the two components lh and rhindicating whether or not the left and right pointers are horizontal.
TYPE Node = RECORD
key, count: INTEGER;
left, right: POINTER TO Node;
lh, rh: BOOLEAN
END
The recursive procedure search again follows the pattern of the basic binary tree insertion algorithm. A
third parameter h is added; it indicates whether or not the subtree with root p has changed, and it
corresponds directly to the parameter h of the B-tree search program. We must note, however, the
consequence of representing pages as linked lists: a page is traversed by either one or two calls of the
search procedure. We must distinguish between the case of a subtree (indicated by a vertical pointer) that
has grown and a sibling node (indicated by a horizontal pointer) that has obtained another sibling and hence
requires a page split. The problem is easily solved by introducing a three-valued h with the following
meanings: