## Instructions

### Objective

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## Requirements and Specifications

**groupbyNTail**

Consider the groupbyN function below.It takes an input list ‘iL’ and a number ‘n’ and it groups iL’s elements into sublists of length n. The last sublist will include the leftover elements.

The given groupbyN implementation is not tail-recursive. Rewrite this function in tail-recursive form; name your function groupbyNTail.

The type of your groupbyNTail function should be same as groupbyN’s type, i.e.,

groupbyNTail :: [a] -> Int -> [[a]]

**Screenshots of output**

**Source Code**

```
module HW2
where
{- 1. groupbyNTail - 10%-}
groupbyNTail :: [a] -> Int -> [[a]]
groupbyNTail iL n = grouphelper iL n [] []
where
grouphelper [] _ buf lst = lst ++ [buf]
grouphelper (x:xs) n buf lst
| length buf >=n = grouphelper xs n [x] (lst ++ [buf])
| otherwise = grouphelper xs n (buf ++ [x]) lst
-----------------------------------------------------------
{- 2. elemAll and stopsAt - 20% -}
{- (a) elemAll - 10%-}
-- please don't include the myCatsLog list in your solution file.
elemAll :: Eq a => [a] -> [a] -> Bool
elemAll xs ys = foldr isInList True xs
where
isInList x y = (x `elem` ys) && y -- returns true if x is in ys and y is true
{- (b) stopsAt - 10%-}
stopsAt :: Eq a => [a] -> [(b,[a])] -> [b]
stopsAt stops buses = foldr selectBus [] buses
where
selectBus (name, ss) xs = -- select bus and add to list if stops in all given stops
if elemAll stops ss then name : xs -- if it has all stops, add to list
else xs -- else, don't add to list
-----------------------------------------------------------
{- 3. isBigger and applyRange - 25% -}
--define the Timestamp datatype
data Timestamp = DATE (Int,Int,Int) | DATETIME (Int,Int,Int,Int,Int)
deriving (Show, Eq)
{- (a) isBigger - 15% -}
isBigger :: Timestamp -> Timestamp -> Bool
isBigger (DATE (m1,d1,y1)) (DATE (m2,d2,y2))
| y1 > y2 = True -- year is bigger
| y1 == y2 && m1 > m2 = True -- same year but month is bigger
| y1 == y2 && m1 == m2 && d1 > d2 = True -- same year and month but day is bigger
| otherwise = False
isBigger (DATETIME (m1,d1,y1,h1,mm1)) (DATETIME (m2,d2,y2,h2,mm2))
| isBigger (DATE (m1,d1,y1)) (DATE (m2,d2,y2)) = True -- bigger date
| y1 == y2 && m1 == m2 && d1 == d2 && h1 > h2 = True -- equal date, bigger hour
| y1 == y2 && m1 == m2 && d1 == d2 && h1 == h2 && mm1 > mm2 = True -- equal date and hour, bigger minutes
| otherwise = False
isBigger (DATE (m1,d1,y1)) (DATETIME (m2,d2,y2,h2,mm2)) = isBigger (DATE (m1,d1,y1)) (DATE (m2,d2,y2)) -- compare dates
isBigger (DATETIME (m1,d1,y1,h1,mm1)) (DATE (m2,d2,y2)) = isBigger (DATE (m1,d1,y1)) (DATE (m2,d2,y2)) -- compare dates
{- (b) applyRange - 10% -}
applyRange :: (Timestamp, Timestamp) -> [Timestamp] -> [Timestamp]
applyRange (ts1, ts2) xs = foldr addInRange [] xs
where
addInRange ts ys = -- add timestamp only if in range
if isBigger ts ts1 && isBigger ts2 ts then ts : ys -- if > first and < last, add to list
else ys -- otherwise, don't add
-----------------------------------------------------------
{-4 - foldTree, createRTree, fastSearch - 35%-}
--define Tree and RTree data types
data Tree a = LEAF a | NODE a (Tree a) (Tree a)
deriving (Show, Eq, Ord)
data RTree a = RLEAF a | RNODE a (a,a) (RTree a) (RTree a)
deriving (Show, Eq, Ord)
{- (a) foldTree - 8% -}
foldTree :: (t -> t -> t) -> Tree t -> t
foldTree fun (LEAF v) = v -- don't apply function, just return the value
-- if node, apply function to folded subtrees and apply function to node value and subtree result
foldTree fun (NODE v lt rt) = fun v (fun (foldTree fun lt) (foldTree fun rt))
{- (b) createRTree - 12% -}
createRTree :: Ord t => Tree t -> RTree t
createRTree (LEAF v) = RLEAF v -- a leaf resultf in just a rleaf
-- a node creates a rnode with same value, folds to get min and max in a tuple and recurses in both l and r subtrees
createRTree (NODE v l r) =
RNODE v (foldTree min (NODE v l r), foldTree max (NODE v l r)) (createRTree l) (createRTree r)
{- (c) fastSearch - 15% -}
fastSearch :: Ord t => RTree t -> t -> [([Char], t)]
fastSearch (RLEAF v) _ = [("leaf", v)] -- if we visit a leaf, save it
fastSearch (RNODE v (a, b) l r) x =
if x >=a && x <= b then -- if searched value is inside range of tree
-- recurse search in order left and right, add searches to list
[("node", v)] ++ (fastSearch l x) ++ (fastSearch r x)
else
[("node", v)] -- not in subtree, just mark node as visited and return
-------------------------------------------------------------------
{- Tree Examples 5% -}
-- include your tree examples in the test file.
{-Testing your tree functions - 5%-}
```

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