Tower of Hanoi Problem solved through recursive algorithm

1. Tower of Hanoi

2. What????
• Three pegs, one with n disks of decreasing diameter; two other pegs
are empty

3. Objective
The Objective is to transfer the entire tower to one of the other pegs.

4. Rules
• Only one disk may be moved at a time. Specifically, only the top disk
on any disk on any peg may be moved to any other peg.
• At no time can a larger disk be placed on a smaller disk.

5. Tower of Hanoi

6. Tower of Hanoi

7. Tower of Hanoi

8. Tower of Hanoi

9. Tower of Hanoi

10. Tower of Hanoi

11. Tower of Hanoi

12. Tower of Hanoi

13. Tower of Hanoi

14. Algorithm
Let’s call the three peg BEG(Source), AUX(AUXiliary) and
st(Destination).
1) Move the top N – 1 disks from the Source to AUXiliary tower
2) Move the Nth disk from Source to Destination tower
3) Move the N – 1 disks from AUXiliary tower to Destination tower.
Transferring the top N – 1 disks from Source to AUXiliary tower can
again be thought of as a fresh problem and can be solved in the
same manner.

15. Algorithm
TOWER(N,BEG,AUX,END)
If N=1 then BEG  END RETURN
CALL(N-1,BEG,END,AUX)
BEG  END
CALL(N-1,AUX,BEG,END)
BEG  END
RETURN
*Read Notes of this page

16. Tower of Hanoi( N= 3)
1. Move from BEG to END
2. Move from BEG to AUX
3. Move from END to AUX
4. Move from BEG to END
5. Move from AUX to BEG
6. Move from AUX to END
7. Move from BEG to END

17. Tower of Hanoi( N= 4)
1. Move from BEG to AUX
2. Move from BEG to END
3. Move from AUX to END
4. Move from BEG to AUX
5. Move from END to BEG
6. Move from END to AUX
7. Move from BEG to AUX

18. Tower of Hanoi( N= 4)
8. Move from BEG to END
9. Move from AUX to END
10. Move from AUX to BEG
11. Move from END to BEG
12. Move from AUX to END
13. Move from BEG to AUX
14. Move from BEG to END
15. Move from AUX to END

19. Presented by
Akshat Saxena
Year – 2nd
Branch = CSE
College – UIT RGPV

20. Thank You