# tower of hanoi problem and problem solving

• September 21st, 2013, 09:07 PM
wholegrain
tower of hanoi problem and problem solving
So i am able to code it, but only because i saw some sample code. the thing with this problem is that you don't expect that you would only need 2 recursive statements to solve it.

http://www.sparknotes.com/cs/recursi...section6.rhtml

Use the one disc solution to move the top disc to the intermediate pole.
Use the one disc solution to move the bottom disc to the final pole.
Use the one disc solution to move the top disc to the final pole.

Use the two disc solution to move the top discs to the intermediate pole.
Use the one disc solution to move the bottom disc to the final pole.
Use the two disc solution to move the top discs to the final pole.

Use the N - 1 disc solution to move the top discs to the intermediate pole.
Use the one disc solution to move the bottom disc to the final pole.
Use the N - 1 disc solution to move the top discs to the final pole

However, I think I could have done it if I read these 9 sentences without looking at the code, but only after a few tries. It's very difficult to simulate the whole thing in your head and even now I just have the gist of it and not the whole process in every minute detail. I can parse it, but I feel quite down, because I don't think I could have figured it on my own.

So I would like to know if most people are like me, or I am just really dumb. This problem is different from a simple for loop, which is easy to simulate in your head, so that was the big wall for me, so to speak. I can program it, but I feel like it's only because I remember the code and not because I fully understood it. I am wondering at what level most programmers understand the algorithm.
• September 21st, 2013, 09:28 PM
wholegrain
Re: tower of hanoi problem and problem solving
move(3,1,3)^ move flow #4 >>final #1 -
|move(2,1,2)^ move flow #2 s>i >>temp - 2 fin
||move(1,1,3)^ move flow #1 s>i >>outoftheway out2 - 1 int
|||move(0,1,2)
|||move(0,2,3)
||move(1,3,2)^ move flow #3 i>e >>outoftheway in3 - 3 fin (3; 1,2; 0)
|||move(0,3,1)
|||move(0,1,2)
MID POINT
|move(2,2,3)^ move flow #6 i>e >>final #2 -2 fin
||move(1,2,1)^ move flow #5 s>i >>outoftheway out2 -1 int
|||move(0,2,3)
|||move(0,3,1)
||move(1,1,3) ^ move flow #7 i>e >>final #3 -3 fin (0; 0; 1,2,3)
|||move(0,1,2)
|||move(0,2,3)

i>e final or ootw in

s>i temp or ootw out

1 Use the two disc solution to move the top discs to the intermediate pole.
2 Use the one disc solution to move the bottom disc to the final pole.
3 Use the two disc solution to move the top discs to the final pole.

move(3,1,3) START 1 INT 2 END 3
|move(2,1,2) START 1 INT 3 END 2
||move(1,1,3) START 1 INT 2 END 3
|||move(0,1,2)
|||move(0,2,3)
||move(1,3,2) START 3 INT 1 END 3
|||move(0,3,1)
|||move(0,1,2)
MID POINT
|move(2,2,3) START 2 INT 1 END 3
||move(1,2,1) START 1 INT 2 END 3
|||move(0,2,3)
|||move(0,3,1)
||move(1,1,3) START 1 INT 2 END 3
|||move(0,1,2)
|||move(0,2,3)

some of the parsing I did, didn't really help at all. I just understand the gist of it.
• September 21st, 2013, 09:29 PM
wholegrain
Re: tower of hanoi problem and problem solving
Also... umm like with the for loop you can know exactly what will happen say at n = 2,

but for the hanoi tower algorithm, you can't simply know what will happen at say... n = 4 after the 4th recursive call of the first recursive statement.
• September 22nd, 2013, 02:50 AM
dazzle
Re: tower of hanoi problem and problem solving
Quote:

Originally Posted by wholegrain
So I would like to know if most people are like me, or I am just really dumb.

I also find Towers of Hanoi difficult. I've read different explanations in several textbooks and watched lectures on Youtube but I'm still not convinced the inductive proof is correct. In fact I'm pretty sure it isn't! :)

Normally I have no problems with recursive algorithms & data structures. I find them quite easy actually. But Towers of Hanoi eludes me and always has. If this means I'm dumb so be it. I've come to accept my shortcoming and it has never stood in my way. I suggest you just drop it and move on.
• September 22nd, 2013, 08:46 AM
2kaud
Re: tower of hanoi problem and problem solving