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Algorithms | Analysis of Algorithms | Question 3

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The recurrence relation capturing the optimal time of the Tower of Hanoi problem with n discs is. (GATE CS 2012)


T(n) = 2T(n – 2) + 2


T(n) = 2T(n – 1) + n


T(n) = 2T(n/2) + 1


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 the time complexity of the above recursive solution can be written as follows. 
T(n) = 2T(n-1) + 1

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Last Updated : 06 Feb, 2013
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