Finding if two numbers have the same digit and then remove them from in the original number in Haskell

Question

Hi I am doing project euler question 33 and have divised a refactor to solve it but I can't think of how to remove the digit if it is the same across both x and y. I got this far:

import Ratio
import List
p33 =  [ (x%y) | y <- [10..99] , x <- [10..y], (x `rem` 10) /= 0 , (y `rem` 10) /= 0 , x /= y , (length $ nub $ concat $ map decToList [x,y]) == 3 , [numerator(x%y),denominator(x%y)] == WHAT GOES HERE? ]

The cancelling of 0's is not allowed. What it should do is:

49/98 {cancel the 9's}

to get:

4/8 as the result. But I can't think of how to remove the common digits from each number.

Answer 1

Let x and y be the two numbers. Then one can remove the digits in x which it has in common with y like this:

Prelude> import Data.List
Prelude Data.List> let x = 68
Prelude Data.List> let y = 76
Prelude Data.List> read (show x \\ show y) :: Int
8

Flip x and y to remove digits from y. This uses xs Data.List.(\\) ys, which removes the first occurrence of each element in ys from xs.

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Edit: you may have solved problem 33 by now. If not, let me give you some more hints:

The code which I gave above, i.e. read (show x \\ show y) is not really suitable for this problem. What happens if x equals ab and y equals ba, for some digits a and b?

The solution to this problem can be written as a single list comprehension. You may want to use Data.List.intersect and Data.List.nub to create the following term in your list comprehension:

s <- nub $ intersect (show x) (show y)

Now s ranges over the digits that x and y have in common. You can remove these from x and y using

map (read . delete s . show) [x, y]

I cannot be more explicit without solving the exercise for you, but I'll leave you with two more hints:

• In your code you write y <- [10..99], x <- [10..y], x /= y. Observe that this can be written more succinctly as y <- [10..99], x <- [10..y-1].
• Have a look at Data.Ratio, which provides an easy way to test the equality of rational numbers and automatically calculates the numerator and denominator of a fraction in its reduced form.