Dc8c4f010f40.hanoi.towers

The Towers of Hanoi or Apocalypse When ?

A Legend ,[object Object],Stacked upon the leftmost needle were 64 golden disks, each a different size, stacked in concentric order:

A Legend ( Ct’d ) ,[object Object],But they could only move one disk at a time , and could never put a larger disk on top of a smaller one . When they completed this task, the world would end !

To Illustrate ,[object Object],Since we can only move one disk at a time, we move the top disk from A to B.

Example ,[object Object],We then move the top disk from A to C.

Example ( Ct’d ) ,[object Object],We then move the top disk from B to C.

Example ( Ct’d ) ,[object Object],We then move the top disk from A to B.

Example ( Ct’d ) ,[object Object],We then move the top disk from C to A.

Example ( Ct’d ) ,[object Object],We then move the top disk from C to B.

Example ( Ct’d ) ,[object Object],and we’re done! The problem gets more difficult as the number of disks increases...

Our Problem ,[object Object],While quite difficult to solve iteratively, this problem has a simple and elegant recursive solution.

Analysis ,[object Object],/* hanoi.cpp * ... */ void Move(int n, char src, char dest, char aux); int main() { cout << “The Hanoi Towers!” << “Enter how many disks: “; int numDisks; cin >> numDisks; Move(numDisks, ‘A’, ‘B’, ‘C’); }

Analysis (Ct’d) ,[object Object],/* hanoi.cpp * ... */ void Move(int n, char src, char dest, char aux); int main() { cout << “The Hanoi Towers!” << “Enter how many disks: “; int numDisks; cin >> numDisks; Move(numDisks, ‘A’, ‘B’, ‘C’); }

Design ,[object Object],[object Object],Since this base case could occur when the disk is on any needle, we simply output the instruction to move the top disk from src to dest .

Design ( Ct’d ) ,[object Object],[object Object],a. Recursively move n-1 disks from src to aux .

Design ( Ct’d ) ,[object Object],[object Object],b. Move the one remaining disk from src to dest .

Design ( Ct’d ) ,[object Object],[object Object],c. Recursively move n-1 disks from aux to dest ...

Design ( Ct’d ) ,[object Object],[object Object],d. We’re done!

Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Coding ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Testing ,[object Object],[object Object],[object Object]

Testing ( Ct’d ) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Testing ( Ct’d ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Testing ( Ct’d ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis ( Ct’d ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis ( Ct’d ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis ( Ct’d ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Summary ,[object Object],[object Object],[object Object]

Dc8c4f010f40.hanoi.towers

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