[Tutor] nested "for" loops

[Peter Jakubowicz]

At 09:42 PM 5/2/2003 -0600, you wrote:
>At 07:43 PM 5/2/2003 -0700, Peter Jakubowicz wrote:
>
>>Hi,
>>
>>I've been slogging along learning Python for a while now. Nested "for" 
>>loops confuse me (I have trouble trying to run through them in my head). 
>>For example, does the following code generate (albeit redundantly) all 
>>Pythagorean triples up to 20: i.e., all integers less than or equal to 20 
>>for which i * i + j * j == k * k
>>
>>TIA,
>>Peter
>>
>>
>>
>>for i in range(1, 21):
>>     for j in range(1, 21):
>>         for k in range(1, 21):
>>             if (i * i) + (j * j) == (k * k):
>>                 print "Pythagorean triple: %d, %d, %d" % (i, j, k)
>
>Did you run the program? Did it deliver the desired results? There's your 
>answer. Is that what you wanted to know? Or are you needing a way to 
>comprehend nested loops?

Thanks. Yes, I did run the program, which is what made me wonder is the 
results were correct; I am trying to understand how nested loops work. I 
get a list of triplets, but I was wondering how I could be sure that I'd 
covered all of the possible combinations. I don't have a mental picture of 
how or if this code runs through all the combinations of integers through 
20 and outputs all possible correct answers.