Algorithms | Analysis of Algorithms | Question 3
The recurrence relation capturing the optimal time of the Tower of Hanoi problem with n discs is. (GATE CS 2012)
(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
Explanation: 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