Hey everyone, just finished the recursion lecture and I understand the idea of recursion, but had trouble understanding old man Grimson's explanation using the Hanoi towers.
His code was:
if n == 1:
print 'move from ' + f + ' to ' + t
Can someone explain how Python interprets this code in plain english?
MIT 6.00 Intro Computer Science (OCW)
Stacey Warren - Expert brainly.com
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OK. Well I will show you what I found and how I came to understand it myself, in case it can help someone else. First, check out http://www.python-course.eu/towers_of_hanoi.php
Also, it also helps to know that the number of moves will be (2^n) - 1. So for a tower of 3, there are 7 moves. When going through the def hanoi recursion function outlined in class, you should read it as follow.
hanoi with n 3 does not meet the if statement, so it passes to the else. And will call in the following order. Look for my numbering to see where the 7 print statements come into play.
1. hanoi (1,f,t,s) -- > prints to move f to t
2. hanoi (1,f,t,s) -- > prints to move f to t
3. hanoi (1,f,t,s) -- > prints to move f to t
4. hanoi (1,f,t,s) -- > prints to move f to t
5. hanoi (1,f,t,s) -- > prints to move f to t
6. hanoi (1,f,t,s) -- > prints to move f to t
7. hanoi (1,f,t,s) -- > prints to move f to t
I hope this helps anyone who is stuck on this example and helps you all learn recursion better.
"old man Grimson"
"old man Grimson" xD!! I like him more than the others, I had a headache trying to understand that tower ... don't want to remember but try with a print in every linecode xD will help to find out what the heck that do xD
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To move a tower of just one disk is simple: you just move the disk to another pin. (that's the `if n==1:` part).
Now if you want to move a tower of let's say four disks, you can do it in three steps:
First you move the top three disks to another pin, then you move the fourth disk to the 'target' pin and finally you move the three-disk tower back on top of the fourth disk. That is exacly what's happening in the `else` part of the function:
hanoi (n-1,f,s,t) (move the top three (assuming n == 4) disks to one pin)
hanoi (1,f,t,s) (move the fourth disk to the 'target' pin)
hanoi (n-1,s,t,f) (move the top three disks back on top of the largest disk)
Now, where recursion comes into play is the question "How do I move the three disk tower?"
Again, you need three steps: First you move the top two disks to another pin, then you move the third disk to the 'target' pin and finally you move the two-disk tower back on top of the third disk. Sounds familiar?