- Prelim:
- Before you can delete an entry, you must find that entry first
- Preliminary Delete procedure:
Entry remove(Key k) { e = keySearch(k, root); // Find entry containing key k // starting with the root node if ( e == null ) return; // Not found, exit... Delete the entry e from the node that contains e. }
- The rest of this
webpage will discuss how to:
- Delete the entry e from the node that contains e.
- The easiest delete operation is:
- Deleting an entry in a leaf node with: ≥ 2 entries
- How to delete an entry e in
this case:
- Simply remove the entry e from the (containing) node p
- Example:
- Delete key 6 from this tree:
- Simply delete the
key 6 from the node
(and reshuffle the remaining keys
within the node):
- Delete key 6 from this tree:
- I have to draw larger 2,4-trees
and there is not enough space
to display the
entire node....
- Due to space limitation,
I will use a simplified way
to represent nodes in the
(2,4)-tree:
- The delete procedure for an
entry stored in a
non-leaf node is
similar to the one
used in
Binary Search Trees:
- Delete the entry
from the non-leaf node...
- Then:
- Replace the deleted entry with its successor or predecessor entry
Note:
- The successor/predecessor
entry will
always be stored inside
a leaf node !!!)
- Therefore:
- We will always end up "deleting" an entry stored inside a leaf node
Example:
- delete entry with
key = 12:
- Delete the entry:
- Replace the
deleted entry with
its successor
(or predecessor):
- Delete the entry
from the non-leaf node...
- How to find the
successor of some
entry:
- Where is the
successor entry:
- The left most entry in the right tree of an entry
- Example:
- Procedure: (just like the one used in the
Binary Search Tree)
- Go right once
- Go left all the way down
- Where is the
successor entry:
- How to find the
predecessor of some
entry:
- Where is the
successor entry:
- The right most entry in the left tree of an entry
- Example:
- Procedure: (just like the one used in the
Binary Search Tree)
- Go left once
- Go right all the way down
- Where is the
successor entry:
- Repeated example of deletion now with
successor location algorithm:
- Delete key 12 from this tree:
- First,
delete the
key 12 from the node
(do not
reshuffle the remaining keys
within the node):
Find the successor entry....
- Then,
replace the
deleted entry with
its
successor entry
(or its predecessor)
- Delete key 12 from this tree:
- Important fact:
- The deletion an
entry from an node with
internal children node
(i.e, from a
non-leaf node)
will eventually result
in:
- "moving" (deleting) an entry from a node with only external children nodes (= a leaf node) the lowest level
(This is exactly like a delete operation in a binary search tree)
- The deletion an
entry from an node with
internal children node
(i.e, from a
non-leaf node)
will eventually result
in:
- Note:
- The remainder of this webpage will assume that we are "deleting (or moving)" an entry from a node with only external children nodes