unit-4 test-2

Suppose a binary search tree with 1000 distinct elements is also a complete binary tree. The tree is stored using the array representation of binary heap trees. Assuming that the array indices start with 0, the 3^rd largest element of the tree is stored at index ___________.

• 509

• 409

• 510

• 408

The preorder traversal of a binary search tree is 15, 10, 12, 11, 20, 18, 16, 19. Which one of the following is the postorder traversal of the tree?

• 20, 19, 18, 16, 15, 12, 11, 10

• 10, 11, 12, 15, 16, 18, 19, 20

• 11, 12, 10, 16, 19, 18, 20, 15

• 19, 16, 18, 20, 11, 12, 10, 15

The postorder traversal of a binary tree is 8,9,6,7,4,5,2,3,1. The inorder traversal of the same tree is 8,6,9,4,7,2,5,1,3. The height of a tree is the length of the longest path from the root to any leaf. The height of the binary tree above is ______.

• 3

• 4

• 5

• 2

The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are

• 63,6

• 64,5

• 32,6

• 31,5

Which of the following is/are correct inorder traversal sequence(s) of binary search tree(s)?

I. 3, 5, 7, 8, 15, 19, 25
II. 5, 8, 9, 12, 10, 15, 25
III. 2, 7, 10, 8, 14, 16, 20
IV. 4, 6, 7, 9 18, 20, 25

• I. IV.

• II. III.

• II. IV.

• II.

What are the worst-case complexities of insertion and deletion of a key in a binary search tree?

• log(n), log(n)

• n,n

• n, log(n)

• log(n),n

A binary tree T has 20 leaves. The number of nodes in T having two children is _______________.

• 20

• 19

• 18

• 22

Consider a binary tree T that has 200 leaf nodes. Then, the number of nodes in T that have exactly two children are ________.

• 200

• 202

• 199

• 201

While inserting the elements 71,65,84,69,67,83 in an empty binary search tree in the sequence shown, the element in the lowest level is

• 65

• 67

• 83

• 69

Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly 4 nodes O(n^a Log^bn ).

Then the value of a + 10b is _________

• 4

• 3

• 2

• 1