Skip to content
Related Articles

Related Articles

Data Structures and Algorithms | Set 29

View Discussion
Improve Article
Save Article
  • Difficulty Level : Easy
  • Last Updated : 13 Dec, 2021
View Discussion
Improve Article
Save Article

Following questions have been asked in GATE 2012 exam. 

1) The recurrence relation capturing the optimal time of the Tower of Hanoi problem with n discs is 
(A) T(n) = 2T(n – 2) + 2 
(B) T(n) = 2T(n – 1) + n 
(C) T(n) = 2T(n/2) + 1 
(D) T(n) = 2T(n – 1) + 1 

Answer (D) 

Following are the steps to follow to solve Tower of Hanoi problem recursively. 
 

Let the three pegs be A, B and C. The goal is to move n pegs from A to C.
To move n discs from peg A to peg C:
    move n-1 discs from A to B. This leaves disc n alone on peg A
    move disc n from A to C
    move n?1 discs from B to C so they sit on disc n

The recurrence function T(n) for time complexity of the above recursive solution can be written as following. 

T(n) = 2T(n-1) + 1 

2) Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices S and T. Which one will be reported by Dijkstra?s shortest path algorithm? Assume that, in any iteration, the shortest path to a vertex v is updated only when a strictly shorter path to v is discovered. 

 

(A) SDT 
(B) SBDT 
(C) SACDT 
(D) SACET 

Answer (D) 

3) Suppose a circular queue of capacity (n – 1) elements is implemented with an array of n elements. Assume that the insertion and deletion operation are carried out using REAR and FRONT as array index variables, respectively. Initially, REAR = FRONT = 0. The conditions to detect queue full and queue empty are 
(A) Full: (REAR+1) mod n == FRONT, empty: REAR == FRONT 
(B) Full: (REAR+1) mod n == FRONT, empty: (FRONT+1) mod n == REAR 
(C) Full: REAR == FRONT, empty: (REAR+1) mod n == FRONT 
(D) Full: (FRONT+1) mod n == REAR, empty: REAR == FRONT 

Answer (A) 
See this for details. 

Please see GATE Corner for all previous year paper/solutions/explanations, syllabus, important dates, notes, etc. 

Please write comments if you find any of the answers/explanations incorrect, or you want to share more information about the topics discussed above.
 

My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!