Question
What is an optimal Huffman code for alphabet b of the following set of frequencies
 a: 45, b:13, c:12, d:16, e:9, f:5
Select one:
a. 111
b. 101
c. 100
d. 001

The correct answer is:101
Question
In flow networks Residual capacity Cf (u,v)=
Select one:
a. c(u,v) – f(u,v)
b. t(u,v) – s(u,v)
c. f(u, v) – c(u,v)
d. s(u,v) – t(u, v)

The correct answer is:c(u,v) – f(u,v)

Question
In Ford-Fulkerson algorithm, flow of the augmenting path is selected based on
Select one:
a. cf(p) =min{ cf (u,v):(u,v)is in f-P }
b. cf(p) =min{ cf (u,v):(u,v)is in p }
c. cf(p) =max{ cf (u,v):(u,v)is in f-P }
d. cf(p) =max{ cf (u,v):(u,v)is in p }

The correct answer is: cf(p) =min{ cf (u,v):(u,v)is in p }

Question
To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure to be used is:
Select one:
a. Queue
b. Heap
c. Stack
d. B-Tree

The correct answer is:Queue

Question
In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity by
Select one:
a. Warshall’s algorithm
b. Performing a DFS starting from S.
c. Dijkstra’s algorithm starting from S.
d. Performing a BFS starting from S

The correct answer is:Performing a BFS starting from S

Question
Consider the decision problem 2CNFSAT defined as follows:

Select one:
a. NP-hard, but not NP-complete.
b. solvable in constant time since any input instance is satisfiable.
c. NP-Complete.
d. solvable in polynomial time by reduction to directed graph reachability

The correct answer is:solvable in polynomial time by reduction to directed graph reachability

Question
Find the Running Time of the fastest algorithm to calculate the shortest path between any two vertices of a graph where all edges have equal weights.
Select one:
a. 0(V  log2V+E )
b. 0 (E+V)
c. 0(V log V2+E)
d. 0 (V+E) log2V

The correct answer is:0 (E+V)

Question
Match the following
            Group A                                                                      Group B
a) Dijkstra's single shortest path                                     p) Dynamic Programming
b) Bellmen Ford's single shortest path algorithm           q) Backtracking
c) Floyd Warshell's all pair shortest path algorithm        r) Greedy Algorithm
Select one:
a. a-p,  b-r, c-q
b. a-p,  b-p, c-p
c. a-r,  b-p, c-p
d. a-r,  b-q, c-p

The correct answer is: a-r,  b-p, c-p

Question
Match the following:

              List – I                           List – II

         1 Quick Sort              a Divide and Conquer

         2 Graph colouring     b Greedy

         3 String editing          c Dynamic Programming
                                     
         4 Prim’s Algorithm   d Back tracking
Select one:
a. 1-a, 2-c, 3-b, 4-d
b. None of these
c. 1-a, 2-d, 3-c, 4-b
d. 1-b, 2-a, 3-d, 4-c

The correct answer is: 1-a, 2-d, 3-c, 4-b

Question
Which of the following statement(s)is / are correct regarding Bellman-Ford shortest path algorithm?
P: Always finds a negative weighted cycle, if one exist s.
Q: Finds whether any negative weighted cycle is reachable
   from the source.
Select one:
a. P Only
b. Neither P nor Q
c. Both P and Q
d. Q Only

The correct answer is: Q Only

Question
The time required to find shortest path in a graph with n vertices and e edges is
Select one:
a. O (e)
b.  O (e²)         
c.  O (n)   
d.  O (n²) 

The correct answer is: O (n²)

Question
There are 5 items as follows

Select one:
a. 260 $
b. 270 $
c. 290$
d. 250$

The correct answer is:260$

Question
Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst.
If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed is
Select one:
a. 44000
b. 19000
c. 25000
d. 248000

The correct answer is:19000

Question
A simple Graph G = L U R, set of 2 non-empty vertices and each vertex from L  has an edge to atleast one vertex of R, is called as
Select one:
a.  Bifocal graph
b. Bipartite Graph
c. Complete graph
d. Flow-network graph

The correct answer is: Bipartite Graph

Question
Ram and Shyam have been asked to show that a certain problem Π is NP-complete. Ram shows a polynomial time reduction from the 3-SAT problem to Π, and Shyam shows a polynomial time reduction from Π to 3-SAT. Which of the following can be inferred from these reductions ?
Select one:
a. Π is NP-complete
b. Π is neither NP-hard, nor in NP
c. Π is NP-hard but not NP-complete
d. Π is in NP, but is not NP-complete

The correct answer is:Π is NP-complete

Question
A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. We are given two sequences X[m] and Y[n] of lengths m and n respectively, with indexes of X and Y starting from 0.
We wish to find the length of the longest common sub-sequence(LCS) of X[m] and Y[n] as l(m,n), where an incomplete recursive definition for the function l(i,j) to compute the length of The LCS of X[m] and Y[n] is given below:
l(i,j) = 0, if either i=0 or j=0
       = expr1, if i,j > 0 and X[i-1] = Y[j-1]
       = expr2, if i,j > 0 and X[i-1] != Y[j-1]
Select one:
a. expr2 ≡ max(l(i-1,j-1),l(i,j))
b. expr2 ≡ max(l(i-1, j), l(i, j-1))
c. expr1 ≡ l(i-1, j) + 1
d. expr1 ≡ l(i, j-1)

The correct answer is: expr2 ≡ max(l(i-1, j), l(i, j-1))

Question
If all c(i, j )’s and r(i, j)’s are calculated, then OBST algorithm in worst case takes one of the following time.
Select one:
a. O(log n)
b. O(n³)    
c. O(n log n)   
d. O(n²)

The correct answer is: O(n³)

Question
Kruskal’s algorithm uses-------- and prim’s algorithm uses------ in determining the MST
Select one:
a. edges,edges
b. vertex,vertex
c. edges,vertex
d. vertex,edges

The correct answer is: edges,vertex

Question
For 0/1 KNAPSACK problem, the algorithm takes ________ amount of time for memory table, and ______time to determine the optimal load, for N objects and W as the capacity of KNAPSACK.
Select one:
a. O(NW), O(N)
b. O(NW), O(N+W)
c. O(N), O(NW)
d.   O(N+W), O(NW)

The correct answer is:O(NW), O(N+W)

Question
Consider the following two problems of graph.
1) Given a graph, find if the graph has a cycle that visits every vertex exactly once except the first visited vertex which must be visited again to complete the cycle.
2) Given a graph, find if the graph has a cycle that visits every edge exactly once. Which of the following is true about above two problems
Select one:
a. Both problems belong to P set
b. Problem 1 belongs to P set and 2 belongs to NP Complete set
c. Problem 1 belongs NP Complete set and 2 belongs to P
d. Both problems belong to NP complete set

The correct answer is: Problem 1 belongs NP Complete set and 2 belongs to P

Question 1A)
The time factor when determining the efficiency of algorithm is measured by
a) Counting microseconds
b) Counting the number of key operations
c) Counting the number of statements
d) Counting the kilobytes of algorithm

Answer: b
Justification: It is hardware and language independent , rest are dependent on hardware or on software

1B) The concept of order Big O is important because
a) It can be used to decide the best algorithm that solves a given problem
b) It determines the maximum size of a problem that can be solved in a given  amount of time
c) It is the lower bound of the growth rate of algorithm
d) Both A and B

Answer: a
Justification: We know that Big Oh notation is used in time complexity . the reason why we called Big Oh because it says "at any condition this is worst time that an algorithm could take " where as Big Omega says its is "best time that you can get , You cant get better than this.

1C) In worst case Quick Sort has order
A) O (n log n)            B. O (n² /2)                C. O (log n)                         D. O (n² /4)

Answer: A
Justification: In the worst case of quick sort has order O(n2). Quick sort is the quickest comparison-based sorting algorithm. It is very fast and requires less additional space, only O(n log n) space is required.

1D) Consider the following program segment. What is the Space complexity?
Begin
i=0;
S=0;
S=s+1;
Return s;
End

Answer: [If i,S considered as integers] => Space Complexity = 4 +(4*2)  = 12 bytes, where additional 4 bytes is for return value

To calculate the Space complexity of an algorithm, we need to follow the below instruction first:

Space Complexity = Auxiliary Space + Input space

Calculating the Space Complexity:

Type	Size
bool, char, unsigned char, signed char	1 byte
short, unsigned short,	2 bytes
float, int, unsigned int, long, unsigned long	4 bytes
double, long double, long long	8 bytes

1E)  What is the time complexity of optimal binary search
(1) a)O(n) b) O(1) c)O(2^n/2)  d) O(n²)

Answer: d
Justification:
An optimal binary search tree is a binary search tree for which the nodes are arranged on levels such that the tree cost is minimum.

For Reference:
The complexity of linear search algorithm is
a) O(n)
b) O(log n)
c) O(n²)
d) O(n log n)

Answer: a
Justification: It refers to n values complexity in the algorithm which can be reduced by choosing the other algorithms.

The complexity of Bubble sort algorithm is
a) O(n)
b) O(log n)
c) O(n²)
d) O(n log n)

Answer: c
Justification: Bubble sort, is a simple sorting algorithm that works by repeatedly stepping through the list to be sorted, comparing each pair of adjacent items and swapping them if they are in the wrong order.

Question
Randomised algorithms are also called as __________________ and whose behavior is dependent  on  _______________ in decision making as part of its logic

Question:
Assume that there are two algorithms A and B for a given problem P. The time complexity functions of algorithms A and B are 5n and log2n    respectively. Which algorithm should be selected assuming that all other conditions remain the same for both the algorithms?

Solution:
Assuming that all conditions remain the same for both algorithms, the best algorithm takes less time when the input is changed to a larger value. Results obtained employing different values of n are shown below: