A simple purely functional circular list, or ring, data type.
Lets describe what we mean by
ring. A ring is a circular data structure
such that if you continue rotating the ring, you'll eventually return to
the element you first observed.
All of our analogies involve sitting at a table who's top surface rotates about its center axis (think of those convenient rotating platforms one often finds in an (Americanized) Chinese Restaurant).
Only the closest item on the table is avialable to us. In order to reach other elements on the table, we need to rotate the table to the left or the right.
Our convention for this problem says that rotations to the right are a forward motion while rotations to the left are backward motions.
We'll use the following circular list for our examples:
8 7 6 9 5 A 4 B 3 C 2 D 0 1 ^
The pointer at the bottom represents our position at the table. The element
currently in front of is is referred to as the
focus. So, in this case,
our focus is 0.
If we were to rotate the table to the right using the
rotR operation, we'd
have the following table.
9 8 7 A 6 B 5 C 4 D 3 0 1 2 ^
This yeilds 1 as our new focus. Rotating this table left would return 0 to the focus position.
- data CList a
- empty :: CList a
- fromList :: [a] -> CList a
- singleton :: a -> CList a
- update :: a -> CList a -> CList a
- leftElements :: CList a -> [a]
- rightElements :: CList a -> [a]
- toList :: CList a -> [a]
- toInfList :: CList a -> [a]
- focus :: CList a -> Maybe a
- insertL :: a -> CList a -> CList a
- insertR :: a -> CList a -> CList a
- removeL :: CList a -> CList a
- removeR :: CList a -> CList a
- rotR :: CList a -> CList a
- rotL :: CList a -> CList a
- balance :: CList a -> CList a
- packL :: CList a -> CList a
- packR :: CList a -> CList a
- isEmpty :: CList a -> Bool
- size :: CList a -> Int
A functional ring type.
|Eq a => Eq (CList a)|
|Show a => Show (CList a)|
The show instance prints a tuple of the balanced CList where the left list's right-most element is the first element to the left. The left most-most element of the right list is the next element to the right.
|Arbitrary a => Arbitrary (CList a)|
Creation of CLists
Update of CList
Converting CLists to Lists
Starting with the focus, go left and accumulate all elements of the CList in a list.
Starting with the focus, go right and accumulate all elements of the CList in a list.
Extraction and Accumulation
Insert an element into the CList as the new focus. The old focus is now the next element to the left.
Insert an element into the CList as the new focus. The old focus is now the next element to the right.
Remove the focus from the CList. The new focus is the next element to the left.