Question

1. Suppose you are given a balanced binary search tree with 15 nodes in it, containing the even numbers from 2 to 30 inclusive.

   1. (a) (5 points) Draw this tree.

   2. (b) (3 points) Explain how you would check if the number 18 is in this

      tree, and state the number of operations this would take.

   3. (c) (2 points) Explain how you would insert the number 27 into this tree,

      and state the number of operations this should take.

Answer 1

a). Tiee'! 2g

b).1st operation :- 18 will be compared with root.if it is equal it return yes.but 18 is not equal to 16 so,2nd operation is performed.

2nd operation:- If 18 is not equal to root(which is the case here) then it checks whether 18 is greater or smaller than root.clearly,it is greater than 16 so,it moves to right child of root.

3rd operation:- it is same as 1st operation except for the fact that the root is now right child i.e 24.

4th operation:-Same as 2nd operation but here 18 is smaller than 24 so,it moves to the left child of current root i.e 24.

5th operation:-same as 1st operation except here root is 20.

6th operation:- same as 2nd operation but here 18 is smaller than 20,so,search proceeds on left child of 20.

7th operation:-same as 1st operation but here 18 is actually equal to 18 so it return yes.

c).To insert any data into Balanced BST follow this procedure:-

i).First find the correct place for the node in balanced BST.this step takes O(logn) time.

ii).now,attach the node to its correct place.

iii).Check if the tree is balanced or not?if it not then perform appropriate rotations.

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