Fix partial heap sort

The function `partialSortByBounds` had an off-by-one error causing
all the partial heap sort functions to produce incorrect results.

The off-by-one error was fixed and the `prop_partialsort` property
test was updated to catch this error. Testing the code before the
change fails, while after the change passes.

Closes: #46

Author: erikd

src/Data/Vector/Algorithms/Heap.hs

@@ -188,8 +188,8 @@ partialSortByBounds cmp a k l u
   | len == 3   = O.sort3ByOffset cmp a l
   | len == 4   = O.sort4ByOffset cmp a l
   | u <= l + k = sortByBounds cmp a l u
-  | otherwise  = do selectByBounds cmp a k l u
-                    sortHeap cmp a l (l + 4) (l + k)
+  | otherwise  = do selectByBounds cmp a (k + 1) l u
+                    sortHeap cmp a l (l + 4) (l + k + 1)
                     O.sort4ByOffset cmp a l
  where
  len = u - l

tests/properties/Properties.hs

@@ -97,8 +97,14 @@ sanity = 100
 prop_partialsort :: (Ord e, Arbitrary e, Show e)
                  => (forall s mv. G.MVector mv e => mv s e -> Int -> ST s ())
                  -> Positive Int -> Property
-prop_partialsort = prop_sized $ \algo k ->
-  prop_sorted . V.take k . modify algo
+prop_partialsort = prop_sized $ \algo k v -> do
+  let newVec = modify algo v
+      vhead = V.take k newVec
+      vtail = V.drop k newVec
+  prop_sorted vhead
+    .&&.
+      -- Every element in the head should be < every element in the tail.
+      if V.null vtail then 1 == 1 else V.maximum vhead <= V.minimum vtail
 
 prop_sized_empty :: (Ord e) => (forall s. MV.MVector s e -> Int -> ST s ()) -> Property
 prop_sized_empty algo = prop_empty (flip algo 0) .&&. prop_empty (flip algo 10)