Data Structures: BST Analysis and Removal, Exercises of Data Structures and Algorithms

Download Data Structures: BST Analysis and Removal and more Exercises Data Structures and Algorithms in PDF only on Docsity!

CS 225

Data Structures

October 4 – BST Remove

G Carl Evans

MP Redo

• There will be two redos of MPs this semester. The redo will be done

one the code in your repo on the last day of class December 8

th

. The

redo will change you grade to the following.

Max(old_grade, .90 * new_grade)

template<typename K, typename V>

*________________________ _remove(TreeNode & root, const K & key) {

}

1 2 3 4 5 6 7 8 9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

root

remove(40);

remove(10);

remove(13);

BST Analysis

Every operation that we have studied on a BST depends on

the height of the tree: O(h).

…what is this in terms of n , the amount of data?

We need a relationship between h and n :

f(h) ≤ n ≤ g(h)

BST Analysis

Q: What is the maximum number of nodes in a tree of

height h?

A

S X

2

22

2 5

BST Analysis

Therefore, for all BST:

Lower bound:

U pper bound:

BST Analysis

The height of a BST depends on the order in which the data

is inserted into it.

ex: 1 3 2 4 5 7 6 vs. 4 2 3 6 7 1 5

Q: How many different ways are there to insert keys into a

BST?

Q: What is the average height of all the arrangements?

BST Analysis – Running Time

Operation

BST

Average case

BST

Worst case

Sorted array Sorted List

find

insert

delete

traverse

Height-Balanced Tree

What tree makes you happier?

Height balance: b = height(T

L

) - height(T

R

A tree is height balanced if:

5 9

7

7

5

9