Tree Balancing

L09 Tree Balancing CX1007 Data Structures 2013/14 S2

Mark Yong

Today • Importance of balance for BSTs • Balancing operaGons in self-­‐balancing BSTs • Pseudocode + worked examples

CX1007 Data Structures 2013/14 S2

2

Recall: Why use BSTs? • BSTs are a special form of BT L • At every node, L < C ≤ R – At every node, we always know whether to conGnue searching in the leW or right subtree – If we conGnue searching in the leW subtree, all nodes in the right subtree can be ignored

H E B

A

CX1007 Data Structures 2013/14 S2

C L

F C

R

G

J I

M K

D

3

Recall: Efficient search with BSTs • Search is efficient because we traverse one external path • # operaGons is proporGonal to path length • Try to keep path length low H > D H – Ie, try to keep tree balanced

E

E > D B

A

B < D C

C < D CX1007 Data Structures 2013/14 S2

L F G

J I

M K

D 4

Recall: Efficient search with BSTs • But an imbalanced BST starts to look more like a linked list! • Path length is high A

A

E

B

B C

C E