(i) The worst-case computing time of Heapsort is O (
).
a) n
b) nlog2n
c) log2n
d) n2
(ii) The
solves the single-source shortest path problem for a
non- negative weighted graph.
a) Binary Search
b) Breadth First Search
c) Depth first search
d) Dijikstra’s Algorithm
(iii) In a diagraph, vertex w is said to be
to vertex v if there is a directed arcs from v to w.
a) Stack
b) Queue
c) Adjacent
d) Percolate down
(iv) A collision strategy in which the hash table is an array or vector of linked lists that
store the items is known as .
a) Linear Probing
b) Separate Chaining
c) Quadratic Probing
d) Double Hashing
(v) Which of the following is nonlinear data structure ?
a) Stack
b) Queue
c) Array
d) Graph
1
(vi) A node that have no children is called
.
a) Siblings
b) Leaf
c) an Edge
d) a Cycle
(vii) Height of the given tree is
.
a) 1
b) 2
c) 3
d) 4
(viii) In a Binary Tree, any node can have maximum of
children.
a) 0
b) 1
c) 2
d) 3
(ix) An array or vector can be used to store a heap efficiently because a heap is a
a) Complete
b) Red Black
c) B+
d) B
(x) Secondary clustering happens due to
.
a) Linear Probing
b) Quadratic Probing
c) Double Hashing
d) Separate Chaining
2
tree.
(i) The worst-case computing time of binary search is O___________________.
a) n
b) nlog2n
c) log2n
d) n2
(ii) The ___________________ solves the single-source shortest path problem for a nonnegative weighted graph.
a) Graph theory
b) Breadth First Search
c) Depth first search
d) Dijikstra’s Algorithm
(iii) The process of swapping an element with its parent, in order to restore the heap order
property is called:
a) Enqueue
b) Queue
c) Percolate up
d) Percolate down
(iv) In Depth First Search graph traversal algorithm, which of the following data structure is used?
a) Stack
b) Queue
c) Linked List
d) Integer
(v) The case of two items needing to be placed at the same location in hash table is called ______.
a) Hashing
b) Collision
c) Overlapping
d) Clustering
(vi) Two Nodes that have the same parent is called _____.
a) Leaf
b) Siblings
c) an Edge
d) a Cycle
3
(vii) To represent hierarchical relationship between elements, which data structure is suitable?
a) Graph
b) Priority Queue
c) Tree
d) Stack
(viii) A Binary tree, in which each any node can have maximum ________ children.
a) 0
b) 1
c) 2
d) 3
(ix) An array or vector can be used to store a heap efficiently because a heap is a _____ tree.
a) Complete
b) Red Black
c) B+
d) B
(x) Best case complexity of Linear Search is O _____
a) n
b) n+1
c) 1
d) log2n
1. The case of two items needing to be placed at the same location in hash table is called
_ Collision___.
2. An Algorithm’s efficiency is express in terms of
3. Another name for an AVL tree is
4.
time
and
space .
Height balanced tree.
Priority Queue is a collection of data elements (all of the same type) in which a certain
priority is associated with each data item.
5. The worst-case computing time of Linear Search is O (__n__).
6. Primary clustering happens due to___Linear Probing_____.
7. Linear probing is a method for dealing with ____Collisions____.
8. Considering the Addition rule of Big O notation, O (100n5+ 2000n4 + 30000n3) = ___n___
4
Short Questions
2. Write an algorithm for Binary Search. Also find the Worst Case Complexity for Binary
Search.
Ans: Page no 556 and Worse Case is O (log n to base 2) page no 557
3. Write an algorithm for Heapsort.
Ans: Page no 744 and worse case is O (nlog n to base 2)
4. Define Binary Search Tree with suitable example.
Ans: page no 667 and best examples page number 667
5. Write the Depth First Search algorithm in detail. Also find the Breadth First Traversal for the
following Graph (starting with node 4.
Ans: page no 896 and BFS: 4 1 3 0 2
DFS: 4 1 0 2 3
6. Draw the binary tree that represents the following expression and then use traversal to find the
equivalent prefix and postfix expression.
A / (B – (C – (D – (E – F))))
Ans: page no 666 problem number 12
7. Explain AVL tree with suitable example.
Ans: page number 841
5
8. What two criteria are usually used to measure an algorithm’s efficiency? From the following given
algorithm, find the Computing time for the algorithm.
/* Algorithm to find the mean of x[0],.. . x[n+1] */
1. Initialize sum = 0.
2. Initialize index variable i = 0.
3. while i < n+2do the following:
4. a. Add x[i] to sum.
5. b. sum=sum + i
6. c. Increment i by 1.
End while.
7. Calculate and return mean = sum / ( n+2).
Answer







Initialize sum = 0.
Initialize index variable i= 0.
while i< n+2do the following:
a. Add x[i] to sum.
b. sum=sum+i
c. Increment i by 1.
o End while.
Calculate and return mean = sum / (n+2).
1
1
n+3
n+2
n+2
n+2
1
Answer: T(n) = 1+1 +n +3 +n +2+n+2+n +2+1
T(n) = 4n + 12
T(n) is O(n)
Page no 552
6
9. Question a-e refer to the following binary tree:
a. List all the leaves
b. Is the binary tree complete?
c. Find the height of the tree.
d. Is this binary tree balanced? If not, explain why it isn’t.
e. Show the array used to represent the binary tree
10. Define Binary Search Tree with suitable example.
Answer: Page No 667
11.
Write the Breadth First Search algorithm in detail. Also, find the Breadth First Traversal for the
following Graph (starting with node 2).
Ans: 2 4 5 3 6 7
7
12. Write the preorder traversal algorithm for a binary tree. Perform an inorder and preorder traversal
for the following binary tree.
Answer :
Pre – Order: NLR
FBADCEGIH
In – Order: L N R
ABCDEFGHI
13. Construct a binary search tree with the key elements 55 , 33 , 77, 22, 11 , 44 , 88 , 66 , 99 in the
given order. Show the tree and balance factor for each node before and after each rebalancing.
Answer: AVL Trees Refer to Exercise Solutions in Text Book
8
Long Questions
1. Construct a binary search tree with the key elements 55, 33 , 77, 22, 11 , 44 , 88 , 66 , 99 in the
given order. Show the tree and balance factor for each node before and after each rebalancing.
Ans[1]
9
2. Explain Adjacency Matrix representation. Find the adjacency matrix representation and
adjacency list representation for the following directed graph.
Ans [2]
Adjacency-Matrix Representation
There are several common ways of implementing a directed graph using data structures
already known to us. One of these is the adjacency matrix of the digraph. To
construct it, we first number the vertices of the digraph 1, 2, . . ., n; the adjacency
matrix is the n x n matrix adj, in which the entry in row i and column j is 1 (or true)
if vertex j is adjacent to vertex i (that is, if there is a directed arc from vertex i to verEptex j), and is 0 (or false) otherwise. (Note: In mathematics, the rows and columns are
usually numbered beginning with 1.) For example, the adjacency matrix for the
digraph.
Adj A
1
2
3
4
5
6
1
0
1
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
1
1
1
4
0
0
0
0
0
1
5
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
3. Explain Linear Probing. Using Hash Table with Eleven locations and the hashing function
h(i)=i%11, show the hash table that result when the following integers are inserted in the
order given : 42, 41, 95, 64, 67, 20, 18, 27, 28 , 80 , 31. Assume that collision are resolved
using Linear Probing.
Answer [3]
Linear Probing
One simple strategy for handling collisions is known as linear probing. In this scheme, a
linear search of the table begins at the location where a collision occurs and continues
until an empty slot is found in which the item can be stored.
0
1
2
3
4
5
6
7
8
9
10
20
67
18
80
31
27
28
95
41
42
64
h(42) = i%11 = 42%11 = 9
h(41) = 41%11 = 41%11= 8
h(95)=95%11 = 7
h(64)= 64%11 = 9 collision = 9+1 = 10
h(67) = 67%11 = 1
h(20) = 20%11 = 9 collision = 9 + 1 = 10 collision = 9 + 2 = 11%11= 0
h(18)= 18%11 = 7 collision = 7 + 1 = (8,9,10,0,1 )collision
h(18)= (18+6)%11 = 2
h(27) = 27%11 = 5
h(28) =28%11 = 6
h(80) = 80%11 = 3
h(31) = 31%11 = 9 + 1= (10,0,1,2,3) collision
= (31+6) % 11 = 4
1
4. Write the algorithm for Heapsort.Sort the following list using Heapsort
35,15,77,60,22,41.
Answer [4]
Heap Sort Chapter
5. Explain Adjacency Matrix representation.Find the adjacency matrix representation and
adjacency list representation for the following directed graph.
10. Explain Quadratic Probing. Using Hash Table with Fourteen locations and the hashing
function h(i)=i%14, show the hash table that result when the following integers are
inserted in the order given : 42, 41, 45, 64, 67, 20, 18, 26, 28 ,70, 31, 16. Assume that
collision are resolved using Quadratic Probing
1