On-Line Encyclopedia of Integer Sequences
Posted on September 14, 2005
Often in your homework you are given a sequence of numbers and asked to find a formula that produces this sequence.
For example determine the final value (an exact value as a function of n) of sum after executing the following code segment:
int sum = 0;
n = n - (n % 2);
for (int k = 1; k < n; k += 2) {
int j = 0;
while (j < k) {
++sum;
++j;
} // while
} // for
return sum;
This code produces sequence of repeated roots 0,0,1,1,4,4,9,9,16,16,25,25,36,36,49,49,64,64,81,81,100,100.
Now if you can’t find a formula, you can go to On-Line Encyclopedia of Integer Sequences and see that the formula is simply ![f(n)=[floor(n/2)]^2](http://photos1.blogger.com/blogger/3270/408/200/tmp1.gif)
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Wow! Thanks for that! Infinitely useful.
Sure, you *could* code it that way but everything just looks so much better in scheme =)
(define (testCases nbTries)
(cond
((= nbTries 0) (list (integerSequence nbTries)))
(else (append (testCases (- nbTries 1)) (list (integerSequence nbTries))))
)
)
(define (integerSequence n)
(* (/ (- n (mod2 n)) 2) (/ (-n (mod2 n)) 2))
)
(define (mod2 n)
(cond
((> n 1) (mod2 (- n 2)))
((= n 1) 1)
(else 0)
)
)
There’s probably a better way to write the mod function since this one wouldn’t scale very well but for my needs it was good enough. =)
Now when you run this:
> (testCases 21)
(list 0 0 1 1 4 4 9 9 16 16 25 25 36 36 49 49 64 64 81 81 100 100)
I was bored and needed to practice my scheme. =/
Yes scheme looks nice, challenging to read at first, but elegant.
I really wanted to take “COMP 348: Principles of Programming Languages” this semester but tutorials conflicted with my other classes. I will take it next semester for sure.
BTW smokinn can you fix your blog? I couldn’t add your RSS to bloglines, and comments don’t work.
I knew RSS didn’t work but I didn’t know about the comments… I should have some free time saturday afternoon and sunday so I’ll try to see what’s going about RSS then. I’ve already fixed the comments.