1. Which of the following is not a random tree?
a) Treap
b) Random Binary Tree
c) Uniform Spanning Tree
d) AVL Tree
Answer: d
Explanation:
Treap, also known as random binary search tree, Random binary tree and Uniform spanning tree are all random tree. Random tree is a tree formed by a random process of addition and deletion of nodes. AVL tree is a self – balanced binary search tree.
2. Which process forms the randomized binary search tree?
a) Stochastic Process
b) Branching Process
c) Diffusion Process
d) Aggregation Process
Answer: a
Explanation:
The randomized binary search tree is formed by the stochastic process. The stochastic process or also called random process is a mathematical tool or object including random variables.
3. 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
Explanation:
As there are 3 numbers (1, 3, 2) so total of 6 combinations can be formed using three numbers but Since (2, 1, 3) and (2, 3, 1) are same so in total there are 5 randomized binary search tree that can be formed.
4. 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
Explanation:
The expected value of depth of a node that is for a node a, the expected value of length of path from root to node a is found to be at most 2 log n + O(1).
5. 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: b
Explanation:
Although it is difficult to find the length of the longest path in randomized binary search tree, but it has been found that the longest length is around 4.311 log x.
6. 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: c
Explanation:
The longest path in a randomized binary search tree, but it has been found that the longest length is around 4.311 log x for node x. This is also equal to 1/β log x where β lies in the range (0, 1).
7. 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
Explanation:
In a random mathematical model, the expected value of number of leaves in a randomized binary search tree is found to be exactly (n + 1)/3 using probability.
8. Is Treap a randomized tree.
a) True
b) False
Answer: a
Explanation:
Treap is a type of data structure which is a combination of binary tree and heap. It is an example of a randomized binary search tree. It stores value in pairs.
9. 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
Explanation:
Catalan number is a sequence of natural number that is used in counting problem. Hence it is found that the selecting off a tree uniformly at random is reciprocal of Catalan number.
10. Is mathematical randomized tree can be generated using beta distribution.
a) True
b) False
Answer: a
Explanation:
Beta distribution can be used using a different shape to generate a randomized binary search tree to create a special type of tree known as a botanical tree.
11. Using what formula can a parent node be located in an array?
a) (i+1)/2
b) (i-1)/2
c) i/2
d) 2i/2
Answer: b
Explanation:
If a binary tree is represented in an array, parent nodes are found at indices (i-1)/2.
12. Which of the following properties are obeyed by all three tree – traversals?
a) Left subtrees are visited before right subtrees
b) Right subtrees are visited before left subtrees
c) Root node is visited before left subtree
d) Root node is visited before right subtree
Answer: a
Explanation:
In preorder, inorder and postorder traversal the left subtrees are visited before the right subtrees. In Inorder traversal, the Left subtree is visited first then the Root node then the Right subtree. In postorder traversal, the Left subtree is visited first, then Right subtree and then the Root node is visited.
13. Which of the following is the predefined function for array reversal in javascript?
a) reverse()
b) arr_reverse()
c) array_reverse()
d) rev()
Answer: a
Explanation:
The predefined function for reversing an array is reverse() in javascript. It does not requires any argument.
14. Predefined function reverse() in C++ is available under which header file?
a) math
b) stdio
c) stdlib
d) algorithm
Answer: d
Explanation:
The predefined function for reversing an array is reverse() in C++ which comes under the library called an algorithm. It requires 2 arguments the first being the pointer to the starting index of the array and the second being the pointer to the last index of the array.
15. What is the time complexity of the juggling algorithm to rotate an array?
a) O(1)
b) O(n)
c) O(d)
d) O(n*d)
Answer: b
Explanation:
Time complexity of juggling algorithm is O(n). Its auxiliary space complexity is O(1).
16. Reversal algorithm and juggling algorithm for array rotation have the same time complexity.
a) True
b) False
Answer: a
Explanation:
Time complexity of juggling algorithm is O(n) which like that of reversal algorithm. They also have the same space complexity
