Why can't I download some test cases? when I try I am presented with:

{"error":"Sorry! testcases are not available for download"}

This is indeed a subproblem of the Convex Hall Problem. Most of the Convex Hall Algorithm uses a function to determine whether consecutive 3 points are counter-clockwise or not. This problem can be solved by using this counter-clockwise function after sorting points (for example, by polar angle)

Test case 2 has self intersecting polygon.

5

0 0

2 0

0 2

2 2

1 0

Expected result is 'No'. really?

cool, got to re-use code for the convex hull problem:

insert :: [Point] -> Point -> [Point]
insert vs v = case vs of
  (x:y:z:ws) -> case orientation v x y of
    Up -> insert (tail vs) v
    _ -> v : vs
  _ -> v : vs

convexHull :: [Point] -> [Point]
convexHull = foldl' insert []

convex :: [Point] -> Bool
convex xs = length xs == length (convexHull xs)

concave = not . convex

solve :: [Point] -> String
solve xs
  | concave xs = "YES"
  | otherwise  = "NO"

FYI, test #1 seems to have Windows new lines (i.e. \r) which causes ocaml's read_int () to freak out. It would be nice if this could be fixed.