# Programming Praxis: The Sum of Two Integers

Published: Wed 05 October 2011

In blog.

A couple of months ago the Programming Praxis website put up a challenge to find a sum inside an array of integers (the direct wording of the challenge can be found here) and since I’ve come up with my own solution, this little challenge has provided me with a lot of feedback.

Just to get some of the geeky stuff out of the way, here is the code I wrote for the problem:

 ```1 2 3 4 5 6 7 8 9``` ```import Data.List import Data.Maybe sumCheck :: Int -> [Int] -> [Int] -> Maybe (Int, Int) sumCheck _ [] _ = Nothing sumCheck total (x:xs) ys = if total' == Nothing then sumCheck total xs ys else return (x, (ys !! ( fromJust total'))) where total' = (total - x) `elemIndex` ys ```

In thinking about the problem a little bit I came up with this subtraction approach. My first approach was to use addition and add every item in the array against all the other items. But this method didn’t sit well with me. After a little bike ride I came up with the code you see above.

After I wrote it, I submitted my code to the Haskell-beginners email list asking for critiques and possible enhancements. Arlen Cuss contributed a slight improvement of my code:

 ```1 2 3 4 5``` ```sumCheck total (x:xs) ys = let diff = total - x in if diff `elem` ys then Just (x, diff) else sumCheck total xs ys ```

And Adityz Siram contributed his version. Which is basically the first algorithm that I came up with and wanted to improve upon. His code is here:

 `1` ```sums i as bs = [(x,y) | x <- as, y <- bs, x + y == i] ```

Finally, Gary Klindt took all of our code snippets, used some performance analysis tools inside GHC and came up with some run times that are (hopefully) more accurate than running time on an application. Here are those stats:

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```print \$ sumCheck 500 [1..1000] [1..1000] sumCheck1: 58,648 sumCheck2: 58,484 sumCheck3: 70,016 print \$ sumCheck 5000 [1..10000] [1..10000] sumCheck1: 238,668 sumCheck2: 238,504 sumCheck3: 358,016 ```

(unit: byte)

Out of the three code snippets, my function was in the middle, speed-wise. But I think that it’s also really nice to see how much better it is than the regular addition method. It’s also nice to see how the little change made to my code can improve the overall speed of the function.

At the end of the day I take a little bit of pride in myself for coming up with an improved algorithm for this task on my own. I know that on a hardware level, subtraction takes more time than addition. But I get the improvements I get because I reduce the number of additions and comparisons I have to make in order for the function to be complete. I also estimate the worst case speed for my algorithm to be O(n), which isn’t too shabby.

When I started learning Haskell, one of the things I read on the internet was how the people who programmed it were helpful to one another. I was skeptical when I first read that, but I have to say that all of my doubt has been removed. And it is interactions like this that make me glad to participate in a community as helpful as this one.