50 Algorithms MCQs with Answers

Last Updated : 23 Feb, 2022

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Question 1

Which of the following standard algorithms is not Dynamic Programming based.

A	Bellman–Ford Algorithm for single source shortest path
B	Floyd Warshall Algorithm for all pairs shortest paths
C	0-1 Knapsack problem
D	Prim's Minimum Spanning Tree

Dynamic Programming 50 Algorithms MCQs with Answers
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Question 1 Explanation:

Prim's Minimum Spanning Tree is a Greedy Algorithm. All other are dynamic programming based.

Question 2

Which of the following is not true about comparison based sorting algorithms?

A	The minimum possible time complexity of a comparison based sorting algorithm is O(nLogn) for a random input array
B	Any comparison based sorting algorithm can be made stable by using position as a criteria when two elements are compared
C	Counting Sort is not a comparison based sorting algorithm
D	Heap Sort is not a comparison based sorting algorithm.

Sorting Analysis of Algorithms CountingSort HeapSort 50 Algorithms MCQs with Answers
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Question 2 Explanation:

See http://www.geeksforgeeks.org/lower-bound-on-comparison-based-sorting-algorithms/ for point A. See http://www.geeksforgeeks.org/stability-in-sorting-algorithms/ for B. C is true, count sort is an Integer Sorting algorithm.

Question 3

Which of the following is not O(n^2)?

A	(15^10) * n + 12099
B	n^1.98
C	n^3 / (sqrt(n))
D	(2^20) * n

Analysis of Algorithms 50 Algorithms MCQs with Answers
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Question 3 Explanation:

The order of growth of option c is n^2.5 which is higher than n².

Question 4

Consider the following C program

int main() 
{ 
   int x, y, m, n; 
   scanf ("%d %d", &x, &y); 
   /* x > 0 and y > 0 */
   m = x; n = y; 
   while (m != n) 
   { 
      if(m>n) 
         m = m - n; 
      else
         n = n - m; 
   } 
   printf("%d", n); 
}

What does the program compute? (GATE CS 2004)

A	x + y using repeated subtraction
B	x mod y using repeated subtraction
C	the greatest common divisor of x and y
D	the least common multiple of x and y

Divide and Conquer 50 Algorithms MCQs with Answers
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Question 4 Explanation:

This is an implementation of Euclid’s algorithm to find GCD

Question 5

Which of the following is not a backtracking algorithm?

A	Knight tour problem
B	N queen problem
C	Tower of hanoi
D	M coloring problem

Backtracking 50 Algorithms MCQs with Answers
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Question 5 Explanation:

Knight tour problem, N Queen problem and M coloring problem involve backtracking. Tower of hanoi uses simple recursion.

Question 6

Suppose T(n) = 2T(n/2) + n, T(0) = T(1) = 1 Which one of the following is false. ( GATE CS 2005)
a) T(n) = O(n^2)
b) T(n) = $\theta$ (nLogn)
c) T(n) = $\Omega$ (n^2)
d) T(n) = O(nLogn)

A	A
B	B
C	C
D	D

Analysis of Algorithms (Recurrences) 50 Algorithms MCQs with Answers
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Question 6 Explanation:

See question 4 of http://www.geeksforgeeks.org/data-structures-and-algorithms-set-23/ for explanation.

Question 7

In a complete k-ary tree, every internal node has exactly k children. The number of leaves in such a tree with n internal nodes is: (GATE CS 2005)

A	nk
B	(n – 1) k+ 1
C	n( k – 1) + 1
D	n( k – 1)

Algorithm Misc 50 Algorithms MCQs with Answers
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Question 7 Explanation:

For an k-ary tree where each node has k children or no children, following relation holds L = (k-1)*n + 1 Where L is the number of leaf nodes and n is the number of internal nodes. Let us see following for example

             o
        /    |    \
      o      o      o
   / | \          / | \
  o  o  o        o  o  o
                  / | \
                 o  o  o

k = 3
Number of internal nodes n = 4
Number of leaf nodes = (k-1)*n  + 1
                     = (3-1)*4 + 1
                     = 9

Question 8

The following statement is valid. log(n!) = $\theta$ (n log n).

A	True
B	False

Analysis of Algorithms 50 Algorithms MCQs with Answers
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Question 8 Explanation:

Order of growth of $\log n!$ and $n\log n$ is same for large values of $n$ , i.e., $\theta (\log n!) = \theta (n\log n)$ . So time complexity of fun() is $\theta (n\log n)$ . The expression $\theta (\log n!) = \theta (n\log n)$ can be easily derived from following Stirling's approximation (or Stirling's formula). $\log n! = n\log n - n +O(\log(n))\$

Question 9

What is the time complexity of Floyd–Warshall algorithm to calculate all pair shortest path in a graph with n vertices?

A	O(n^2logn)
B	Theta(n^2logn)
C	Theta(n^4)
D	Theta(n^3)

Analysis of Algorithms 50 Algorithms MCQs with Answers
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Question 9 Explanation:

Floyd–Warshall algorithm uses three nested loops to calculate all pair shortest path. So, time complexity is Thete(n^3). Read here for more details.

Question 10

Assuming P != NP, which of the following is true ?
(A) NP-complete = NP

(B) NP-complete $\cap$ P = $\Phi$

(C) NP-hard = NP

(D) P = NP-complete

A	A
B	B
C	C
D	D

NP Complete 50 Algorithms MCQs with Answers
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Question 10 Explanation:

The answer is B (no NP-Complete problem can be solved in polynomial time). Because, if one NP-Complete problem can be solved in polynomial time, then all NP problems can solved in polynomial time. If that is the case, then NP and P set become same which contradicts the given condition.

There are 50 questions to complete.

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50 Algorithms MCQs with Answers

50 Algorithms MCQs with Answers

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