Open Language TYS

[wtd]

Write a function which sums an inclusive range of numbers. Bonus points for efficiency.

[Cervantes]

Maybe I don't understand the question, because here's my solution:

scheme:

(define (sum low high)     (/ (- (* high (sub1 high)) (* (sub1 low) (- low 2))) 2))

Are we supposed to take into account negative numbers too, I suppose?

[Clayton]

In my eyes, it shouldn't make a difference. Adding 1 + 2 is the same as adding 2 + 1 right? so you just get the range and add all numbers together to find the total, so I'm not sure why you're multiplying there Cervantes

[Hikaru79]

Freakman @ Thu Feb 15, 2007 1:16 pm wrote:

In my eyes, it shouldn't make a difference. Adding 1 + 2 is the same as adding 2 + 1 right? so you just get the range and add all numbers together to find the total, so I'm not sure why you're multiplying there Cervantes

He's using the identity that the sum of the first n consecutive numbers is n(n+1)/2. This gives us an almost constant-time solution to wtd's TYS, which also leads me to think he meant something else. Cervantes' solution is also what I would have done; it's just too easy

[wtd]

No no... you got the right answer.

[Clayton]

Shows how little I know, and how much I need to learn

[Cervantes]

This reminds me of a problem I liked, stolen from Project Euler:

Quote:

The palindromic number 595 is interesting because it can be written as the sum of consecutive squares: 6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2 + 12^2.

There are exactly eleven palindromes below one-thousand that can be written as consecutive square sums, and the sum of these palindromes is 4164. Note that 1 = 0^2 + 1^2 has not been included as this problem is concerned with the squares of positive integers.

Find the sum of all the numbers less than 10^8 that are both palindromic and can be written as the sum of consecutive squares.