# Tower of Hanoi Problem (TOH) – Data Structure

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TOH ( Tower of Hanoi) is a mathematical game or puzzle. It consist of 3 pegs A, B and C. N Disks of different diameters are placed on peg A so that a larger disk is always below a smaller disk.

The aim is to move the N disks to peg C using peg B as auxiliary. Only  the top disk on any peg may be moved to any other peg and a larger disk may never rest on a smaller one.

for example,

## Recursive algorithm for TOH,

To move n disks from peg A to peg C, using peg B as auxiliary.
• If n==1, move the single disk from A to C
Stop.
• Move the top n-1 disk from A to B, using C as auxiliary.
• Move the remaining disk from A to C.
• Move the n-1 disks from B to C, using A as auxiliary.

## Tower of Hanoi

transfer(n, from, aux)
{
if(n==1)
{
move disk n 'from ' to 'to'
}

transfer(n-1, from, aux, to)
move disk n 'from' to 'to'
transfer (n-1, aux, to, from)
}

To calculate the steps for tower of hanoi tracing follow below step,

If N = 2, steps 2^2-1 = 3

If N = 5, steps 2^5-1 = 31

N = 1,

transfer (1, from, to, aux {

/* from "A", to "C", aux "B" */

n==1 (true)
move disk 1 'from' to 'to'

/* from "A", to "C" */
}