Prentice.Hall.Introduction.to.Java.Programming,.Brief.Version.9th.(2014).[sharethefiles.com]

oot
parentOfu
u
Figure 47.13
The nodes along the path may become empty as result of a transfer and
fusion operation.
If the node is a nonleaf node, locate the rightmost element in the left
subtree of the node (lines 25–26), get the path that leads to the
rightmost element from the root (line 29), replace e in the node with
the rightmost element (line 31), and invoke validate to fix the
rightmost node if it is empty (line 34).
The validate(E e, Tree24Node u, ArrayList path)
checks whether u is empty and performs a transfer or fusion operation
to fix the empty node. The validate method exits when node is not empty
(line 43). Otherwise, consider one of the following cases:
1. If u has a left sibling with more than one element, perform a
transfer on u with its left sibling (line 49).
2. Otherwise, if u has a right sibling with more than one element,
perform a transfer on u with its right sibling (line 52).
3. Otherwise, if u has a left sibling, perform a fusion on u with
its left sibling (line 55) and reset u to parentOfu (line 56).
4. Otherwise, u must have a right sibling. Perform a fusion on u
with its right sibling (line 59) and reset u to parentOfu (line
60).
Only one of the preceding cases is executed. Afterward, a new iteration
starts to perform a transfer or fusion operation on a new node u if
needed. Figure 47.14 shows the steps of deleting elements 20, 15, 3, 6,
and 34 are deleted from a 2-4 tree in Figure 47.9(k).
20
16
15
27 34
15
27 34
3 16 24 25 29 50
3
24 25
29 50
(a) Delete 20 (b) Replace 20 with 16
12