Question

Describe a recursive algorithm for solving the Towers of Hanoi puzzle for an arbitrary n (see Creativity Exercise C-5.16 for more details).

C-5.16 In the Towers of Hanoi puzzle, we are given a platform with three pegs, a, b, and c, sticking out of it. On peg a is a stack of n disks, each larger than the next, so that the smallest is on the top and the largest is on the bottom. The puzzle is to move all the disks from peg a to peg c, moving one disk at a time, so that we never place a larger disk on top of a smaller one. See Figure 5.15 for an example of the case n 4. Describe a recursive algorithm for solving the Towers of Hanoi puzzle for arbitrary n. (Hint: Consider first the subproblem of moving all but the nth disk from peg a to another peg using the third as "temporary storage.") Figure 5.15: An illustration of the Towers of Hanoi puzzle.

Answer 1

Algorithm for solving Towers of Hanoi puzzle:

Step 1: START

Step 2: FUNCTION TowerOfHanoi(nofdisks,source,destination,temp):

IF nofdisks = = 1, THEN

move the disk from source peg to destination peg

ELSE

TowerOfHonai(disk - 1, source, temp , destination)

TowerOfHonai(disk - 1, temp, destination,source)

END IF

STEP 3: STOP

So to move the n disks from peg a to peg c, follow the steps below:

• At first ,move n-1 disks from peg a to peg b, this results in leaving nth disk alone on peg a
• Then move nth disk from peg a to peg c
• move disk n -1 disks from peg b to peg c, so that these n-1 disks will be placed on nth disk