duplicates :: [Int] -> [Int]
-- testing 6 combinations of argument values
-- pruning with 21/26 rules
-- looking through 2 candidates of size 1
-- looking through 1 candidates of size 2
-- looking through 1 candidates of size 3
-- looking through 2 candidates of size 4
-- looking through 1 candidates of size 5
-- looking through 2 candidates of size 6
-- looking through 3 candidates of size 7
-- looking through 8 candidates of size 8
-- looking through 16 candidates of size 9
-- looking through 25 candidates of size 10
-- looking through 36 candidates of size 11
-- looking through 63 candidates of size 12
-- looking through 133 candidates of size 13
-- looking through 299 candidates of size 14
-- looking through 602 candidates of size 15
-- looking through 1116 candidates of size 16
-- looking through 2031 candidates of size 17
-- tested 2451 candidates
duplicates []  =  []
duplicates (x:xs)  =  if elem x xs && not (elem x (duplicates xs))
                      then x:duplicates xs
                      else duplicates xs

duplicates :: [Int] -> [Int]
-- pruning with 21/26 rules
-- looking through 2 candidates of size 1
-- looking through 1 candidates of size 2
-- looking through 1 candidates of size 3
-- looking through 2 candidates of size 4
-- looking through 1 candidates of size 5
-- looking through 2 candidates of size 6
-- looking through 3 candidates of size 7
-- looking through 8 candidates of size 8
-- looking through 16 candidates of size 9
-- looking through 25 candidates of size 10
-- looking through 36 candidates of size 11
-- looking through 63 candidates of size 12
-- looking through 133 candidates of size 13
-- looking through 299 candidates of size 14
-- looking through 602 candidates of size 15
-- looking through 1116 candidates of size 16
-- looking through 2031 candidates of size 17
-- tested 2451 candidates
duplicates []  =  []
duplicates (x:xs)  =  if elem x xs && not (elem x (duplicates xs))
                      then x:duplicates xs
                      else duplicates xs

positionsFrom :: Int -> A -> [A] -> [Int]
-- testing 360 combinations of argument values
-- pruning with 5/10 rules
-- looking through 1 candidates of size 1
-- looking through 0 candidates of size 2
-- looking through 2 candidates of size 3
-- looking through 5 candidates of size 4
-- looking through 13 candidates of size 5
-- looking through 18 candidates of size 6
-- looking through 47 candidates of size 7
-- looking through 77 candidates of size 8
-- looking through 193 candidates of size 9
-- looking through 293 candidates of size 10
-- looking through 738 candidates of size 11
-- looking through 1173 candidates of size 12
-- looking through 2879 candidates of size 13
-- looking through 4537 candidates of size 14
-- tested 5610 candidates
positionsFrom x y []  =  []
positionsFrom x y (z:xs)  =  (if y == z then (x :) else id) (positionsFrom (x + 1) y xs)