- #ANDENGINE TOWER OF HANOI TOWERS NOT STACKING CORRECTLY HOW TO#
- #ANDENGINE TOWER OF HANOI TOWERS NOT STACKING CORRECTLY FREE#
#ANDENGINE TOWER OF HANOI TOWERS NOT STACKING CORRECTLY HOW TO#
To write a solution for the Tower of Hanoi, we need to decide how to represent the disks and the pegs in our code. Now that A is empty, the last move uses A as the placeholder. The last figure shows the move of k-1 disks from B to C. The third figure shows the move after moving the largest disk from A to C. The second figure shows the recursive step - by wishful thinking, we believe that we can solve the puzzle for k-1 disks and move k-1 disks from A to B, using C as the placeholder. The first figure shows the original configuration. The figures above illustrate the recursion steps.
#ANDENGINE TOWER OF HANOI TOWERS NOT STACKING CORRECTLY FREE#
This would free up the largest disk, which we move from A to C. First, move the top k-1 disk from A to B. How can we solve the puzzle for k disks? It turns out the solution is equally trivial. Now, let's assume that we can solve the Tower of Hanoi puzzle for k-1 disks. We will use peg B as the temporary placeholder. Let's label the pegs A, B, and C, with A being the source and C being the destination. In this version, the solution is trivial - we just move the disk from the source peg to the destination peg What is the simplest version of the Tower of Hanoi puzzle? It is the version with only a single disk. Recall the two steps in recursive problem solving: (i) reduce the problem to the simplest version where we can solve it trivially and (ii) assuming that we can solve the simpler version of the problem, we combine the solution to solve the more complex version. You can play a version online here Using Recursion Wikipedia has the following animation showing how to solve the puzzle with 4 disks in 15 steps.īy André Karwath aka Aka - Own work, CC BY-SA 2.5, Link The goal is to move all the disks onto another peg. In the beginning, we have all the disks in one peg. no disk can be placed on top of a smaller disk.we can only move the topmost disk from one peg and place the disk on another peg.There are a few rules that we have to obey:
It goes like this: There are three pegs and n disks of various size that we can slide into any of the pegs. The Tower of Hanoi problem is a famous mathematical puzzle invented by French mathematician Édouard Lucas in 1883. We will start with the Tower of Hanoi problem in this unit. In this unit and the next, we will see how we can use recursion to solve more complex problems.
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