1. Goals Design decisions Design Insertion
2-3 Trees
Goals
Design decisions
Design
Insertion
5/22/2019
CS 303 – 2-3 Trees
Lecture 10

2. 2-3 Trees: Goals Goal – Almost Balanced Tree with leaves sorted Why?
Balanced -> O(log n) speed
Sorted
speeds INSERT/DELETE
often required by the application, anyway
5/22/2019
CS 303 – 2-3 Trees
Lecture 10

3. 2-3 Trees: Design Values stored at leaves (not at internal nodes!)
Interior nodes have either 2 or 3 children (never only 1)
Restructure as needed to keep all paths from root to leaf the same length (or nearly so)
5/22/2019
CS 303 – 2-3 Trees
Lecture 10

4. 2-3 Tree: Definition a b < a a > a, < b b >b 5/22/2019
CS 303 – 2-3 Trees
Lecture 10

5. 2-3 Trees: Insertion To insert x Search for x
At lowest interior level, there are two cases:
1) the easy case x b b
a b
a x b
plus two other cases, x < a < b, and a < b < x
5/22/2019
CS 303 – 2-3 Trees
Lecture 10

6. 2-3 Trees: Insertion... 2) the hard case
And now, we need to insert the new node into the Parent, where there are 2 cases...
2) the hard case
Parent x c b c
a b c
a x
b c
plus three other cases:
x < a < b < c, a < b < x < c, and a < b < c < x
Do an example, e.g.
insert 5,2,7,0,3,4,6,1,8,9...
5/22/2019
CS 303 – 2-3 Trees
Lecture 10