Question

I’m Haskell newbie and I have the little problem.
I’m trying to write a function that recognizes if list is arithmetic sequence or not.

I have this not working code:

isArithmSeq :: [Int] -> Bool
isArithmSeq [] = False;
isArithmSeq [x] = False;
isArithmSeq [x,y] = True;
isArithmSeq (x:y:xs) = (sum (x:y:xs)) == (sum [x,y..(last xs)])

I have no idea how to make it work. Can anyone help me correct this?

Thx.

Answer 1

Try this:

isArithmSeq :: [Int] -> Bool
isArithmSeq [] = False
isArithmSeq [x] = False
isArithmSeq [x,y] = True
isArithmSeq (x:y:z:xs) = (x - y) == (y - z) && isArithmSeq (y:z:xs)

You’ve defined a nice base case for a recursive definition. Now, you just need to check that the difference between successive elements is always the same. The reason that

isArithmSeq (x:y:xs) = (sum (x:y:xs)) == (sum [x,y..(last xs)])

didn’t work is because the sum is not the only requirement for an arithmetic sequence:

(sum [2,3,4,0,11,7]) == (sum [2,3,4,5,6,7])