50 Algorithms MCQs with Answers

  • Last Updated : 23 Feb, 2022


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: 
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 n2.5 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: 
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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