In today’s Programming Praxis exercise we have to find all the ways a given number can be written as the sum of the squares of two other numbers. Let’s get started.

All we really have to do is to convert the four cases of Dijkstra’s algorithm (listed on the second page of the exercise) from English to Haskell, which is trivial. To avoid repeating ourselves, we pattern match on the result of the comparison between x*x + y*y and n instead of recalculating it three times.

squareSum :: Integer -> [(Integer, Integer)] squareSum n = b (ceiling . sqrt $ fromIntegral n) 0 where b x y = if x < y then [] else case compare (x*x + y*y) n of LT -> b x (y + 1) EQ -> (x, y) : b (x - 1) (y + 1) GT -> b (x - 1) y

A quick test shows us that everything’s working correctly.

main :: IO () main = do print $ squareSum 50 print $ squareSum 48612265 print $ squareSum 999