Saturday 12 October 2013

Towers of Hanoi Using Stack (Recursive Solution)

(The problem is moving a collection of N disks of decreasing size from one pillar to another.The movement of the disks is restricted by the following rules:
Rule1: Only 1 disk could be moved at a time.
Rule2: No larger disk could ever reside on a pillar on top of a smaller disk.
Rule3: A 3rd pillar can be used as an intermediate to store one or more disks,while the disks are moved from source to destination )

Let N represent the number of disks
Step1: If N=1,move the disk from A to C.
Step2:
  1. If N=2,move the 1st disk from A to B,
  2. Then move the 2nd disk from A to C,
  3. Then move the 1st disk in B to C.
Step3: If N=3,repeat step2,to move the first two disks from A to B using C as intermediate.
Then move 3rd disk from A to C.Then repeat the step2 to move 2disks from B to C using A as intermediate

In general,to move N disks,apply recursive technique to move (N-1) disks from A to B with C as an intermediate.Then move the Nth disk from A to C.Then again apply the recursive technique to move (N-1) from B to C using A as intermediate.

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