Incorrectly solved Where Should Gramma's House Go

Since we didn't have any Haskell yet, I decided to commit it anyway.

Author: mcmathews

WhereShouldGrammasHouseGo/WhereShouldGrammasHouseGo.hs

@@ -0,0 +1,57 @@
+-- https://www.reddit.com/r/dailyprogrammer/comments/3l61vx/20150916_challenge_232_intermediate_where_should/
+-- This code doesn't provide optimal solution
+-- Only gives an estimate in O(nlog(n)) time
+
+import Data.List
+
+main = do
+    inputN <- getLine
+    let n = read inputN
+    coords <- readCoords n
+    let tx = maxX coords
+        bx = minX coords
+        ty = maxY coords
+        by = minY coords
+        topLeft = (bx, ty)
+        topRight = (tx, ty)
+        bottomRight = (tx, by)
+        dists = [(x, (dist topLeft x) + (dist topRight x) + (dist bottomRight x)) | x <- coords]
+    putStrLn $ show $ smallestDiff dists
+    
+    
+
+readCoords :: (Floating a, Read a) => Int -> IO [(a, a)]
+readCoords n = 
+    if n == 0
+        then return []
+        else do
+            input <- getLine
+            let coord = read input
+            rest <- readCoords (n-1)
+            return $ coord : rest
+
+dist :: Floating a => (a, a) -> (a, a) -> a
+dist (x1, y1) (x2, y2) =
+    (x1 - x2)^2 + (y1 - y2)^2
+
+maxX coords = maximum [x | (x, _) <- coords]
+maxY coords = maximum [y | (_, y) <- coords]
+minX coords = minimum [x | (x, _) <- coords]
+minY coords = minimum [y | (_, y) <- coords]
+
+smallestDiff :: (Floating a, Floating b, Ord c, Floating c) => [((a, b), c)] -> ((a, b), (a, b))
+smallestDiff dists = 
+    smallestDiff' (sortOn snd dists) ((0, 0), (0, 0)) (100000)
+
+smallestDiff' :: (Ord c, Floating c) => [((a, b), c)] -> ((a, b), (a, b)) -> c -> ((a, b), (a, b))
+smallestDiff' [_] best bestDiff = best
+smallestDiff' dists best bestDiff = 
+    let rem = tail dists
+        (coord1, dist1) = head dists
+        (coord2, dist2) = head rem
+        diff = dist2 - dist1
+        in
+            if diff < bestDiff
+                then smallestDiff' rem (coord1, coord2) diff
+                else smallestDiff' rem best bestDiff
+