This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Randomized Binary Search Tree”.

**1. 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)**

Explanation: In a randomised binary search tree, the longest path is around 4.311 log x for node x, but it has been discovered that the longest range is around 4.311 log x for node x. This is also the same as 1/log x when x is in the set (0, 1).

**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

Explanation: Using chance, the predicted value of the number of leaves in a randomised binary search tree is found to be exactly (n + 1)/3 in a random mathematical model.

**3. Is Treap a randomized tree.****A) True**

B) False

Explanation: Treap is a data structure that is a hybrid of a binary tree and a heap. A randomised binary search tree is an example. It keeps track of meaning in pairs.

**4. 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**

Explanation: A Catalan number is a natural number series that is used to solve counting problems. As a result, it is discovered that picking a tree uniformly at random is reciprocal of Basque number.

**5. Is mathematical randomized tree can be generated using beta distribution.****A) True**

B) False

Explanation: A randomised binary search tree can be created using the beta distribution and a different shape to create a botanical tree, which is a unique form of tree.

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

A) Treap

B) Random Binary Tree

C) Uniform Spanning Tree**D) AVL Tree**

Explanation: Treap is a random tree that is also known as random binary search tree, Random binary tree, and Uniform spanning tree. A random tree is one that is generated by a random process of node addition and deletion. The AVL tree is a binary search tree that is self-balanced.

**7. Which process forms the randomized binary search tree?****A) Stochastic Process**

B) Branching Process

C) Diffusion Process

D) Aggregation Process

Explanation: The stochastic method creates the randomised binary search tree. A stochastic process, also known as a random process, is a mathematical tool or entity that incorporates random variables.

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

A) 2

B) 3

C) 6**D) 5**

Explanation: There are a total of six combinations that can be made with three numbers (1, 3, 2), but since (2, 1, 3) and (2, 3, 1) are the same, there are only five randomised binary search trees that can be formed.

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

A) log n

B) n!

C) n^{2}**D) 2 log n + O(1)**

Explanation: The expected depth of a node is found to be at most 2 log n + O for node a, and the expected length of path from root to node an is found to be at most 2 log n + O. (1).

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

A) log x

B) x^{2}

C) x!**D) 4.311 log x**

Explanation: While finding the length of the longest path in a randomised binary search tree is difficult, the longest length has been discovered to be about 4.311 log x.

A random binary tree is a binary tree chosen at random from a binary tree probability distribution. Binary trees created by adding nodes one at a time according to a random permutation and binary trees chosen from a uniform discrete distribution in which all distinct trees are equally likely are the two most common distributions. Other distributions can also be created, for example, by repeatedly splitting.