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## Randomized Binary Search Tree MCQs

**1. What is the expected depth of a node in a randomized binary search tree?**

a) log n

b) n!

c) n2

d) 2 log n + O(1)

**Answer: **d

**2. What is the expected number of leaves in a randomized binary search tree?**

a) n + 1

b) (n + 1)/3

c) (n + 1)/2

d) n + 3

**Answer: **b

**3. Which of the following is not a random tree?**

a) Treap

b) Random Binary Tree

c) Uniform Spanning Tree

d) AVL Tree

**Answer: **d

**4. Which process forms the randomized binary search tree?**

a) Stochastic Process

b) Branching Process

c) Diffusion Process

d) Aggregation Process

**Answer: **a

**5. How many randomized binary search trees can be formed by the numbers (1, 3, 2)?**

a) 2

b) 3

c) 6

d) 5

**Answer: **d

**6. Is Treap a randomized tree.**

a) True

b) False

**Answer: **a

**7. What is the probability of selecting a tree uniformly at random?**

a) Equal to Catalan Number

b) Less Than Catalan Number

c) Greater than Catalan Number

d) Reciprocal of Catalan Number

**Answer: **d

**8. Is mathematical randomized tree can be generated using beta distribution.**

a) True

b) False

**Answer: **a

**9. What is the longest length path for a node x in random binary search tree for the insertion process?**

a) log x

b) x2

c) x!

d) 4.311 log x

**Answer: **d

**10. What is the range of β in finding the length of the longest path in a randomized binary search tree?**

a) (-1, 0)

b) (1, 0)

c) (0, 5)

d) (0, 1)

**Answer: **d