Question

I want to find the difference between two numbers in a range, but I need to be able to wrap around to the beginning of the range, like a circular list.

The range is 9.

So if the number is 6 and the guess is 5 the answer should be 1, but if the number is 8 and the guess is 2, then the answer should be 3.

My first thought was to bump the number by 10 like this:

n is the correct number, g is the guess, r is the result. 

( let
   [ r (min (- (+ n 10) g) (- g n)) ]

   (if (> 0 r) ( * -1 r ) r) ) 
)

… and that worked for wrapping around, but then the problem is that the existence of the number 10 increases the result by 1 if it wraps. Just subtracting 1 from the result or the number doesn’t work either in all cases.

Depending on the numbers in question, the result is negative, so the if statement is to swap it around to positive.

This isn’t a clojure problem exactly, it’s really a math issue and I’d have this problem in any language, but it so happens that’s what I’m writing it in. I’ve only just started using clojure (or any functional language), so it’s entirely possibly I’m doing things wrong or wildly unidiomatic.

thanks for any help

Answer 1

If you include zero in your loop the question becomes smaller of A – B mod R or B – A mod R

R = 9
8 - 3 mod 9 = 5
3 - 8 mod 9 = 4
min(5 3) = 3

You can get the effect of not allowing guesses of zero by decrementing the numbers you read and incramenting the numbers you print though your game will be mathematically easier if you allow them to guess the number zero.

(defn mod- [x y r] 
  (let [res (rem (- x y) r)]
  (if (neg? res)
    (+ res r)
    res)))

(min (mod- A B r) (mod- B A r))