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|
functor Tree (Key: sig
type key
val compare: key * key -> order
end) :> sig
type key = Key.key
type 'datum tree
val size: 'datum tree -> int
val empty: 'datum tree
val single: key * 'datum -> 'datum tree
val add: 'datum tree * key * 'datum -> 'datum tree
val find: 'datum tree * key -> 'datum option
val exists: 'datum tree * key -> bool
val up: 'datum tree -> (key * 'datum) Stream.stream
val down: 'datum tree -> (key * 'datum) Stream.stream
val upFrom: 'datum tree * key -> (key * 'datum) Stream.stream
val downFrom: 'datum tree * key -> (key * 'datum) Stream.stream
val fromList: (key * 'datum) list -> 'datum tree
val fromStream: (key * 'datum) Stream.stream -> 'datum tree
(*
val remove: 'datum tree * key -> 'datum tree
*)
end = struct
type key = Key.key
structure Height = Int8
datatype 'datum tree =
Leaf
| Branch of {
height: Height.int
, less: 'datum tree
, key: key
, datum: 'datum
, greater: 'datum tree
}
fun size tree = case tree of
Leaf => 0
| Branch {less, greater, ...} =>
1 + size less + size greater
val empty = Leaf
fun single (key, datum) = Branch {
height = 1
, less = Leaf
, key = key
, datum = datum
, greater = Leaf
}
fun height tree = case tree of
Leaf => 0
| Branch {height, ...} => height
fun calculateHeight {key, datum, less, greater} = Branch {
key = key
, datum = datum
, less = less
, greater = greater
, height = 1 + Height.max (height less, height greater)
}
fun rotateLess branch = case branch of
(*
b d
a d => b e
c e a c
*)
{
less = a
, key = bKey
, datum = bDatum
, greater = Branch {
less = c
, key = dKey
, datum = dDatum
, greater = e
, height = _
}
} => calculateHeight {
less = calculateHeight {
less = a
, key = bKey
, datum = bDatum
, greater = c
}, key = dKey
, datum = dDatum
, greater = e
} | _ => raise Fail "rotateLess"
fun rotateGreater branch = case branch of
(*
d b
b e => a d
a c c e
*)
{
less = Branch {
less = a
, key = bKey
, datum = bDatum
, greater = c
, height = _
}, key = dKey
, datum = dDatum
, greater = e
} => calculateHeight {
less = a
, key = bKey
, datum = bDatum
, greater = calculateHeight {
less = c
, key = dKey
, datum = dDatum
, greater = e
}
} | _ => raise Fail "rotateGreater"
fun balance (branch as {key, datum, less, greater}) =
let
val heightLess = height less
val heightGreater = height greater
in
if heightLess < heightGreater - 2 then
rotateLess branch
else if heightLess > heightGreater + 2 then
rotateGreater branch
else calculateHeight branch
end
fun add (tree, newKey, newDatum) = case tree of
Leaf => single (newKey, newDatum)
| Branch {height, less, key, datum, greater} =>
case Key.compare (newKey, key) of
EQUAL => Branch {
height = height
, less = less
, key = newKey
, datum = newDatum
, greater = greater
} | LESS => balance {
less = add (less, newKey, newDatum)
, key = key
, datum = datum
, greater = greater
} | GREATER => balance {
less = less
, key = key
, datum = datum
, greater = add (greater, newKey, newDatum)
}
fun find (tree, desiredKey) = case tree of
Leaf => NONE
| Branch {less, key, datum, greater, ...} =>
case Key.compare (desiredKey, key) of
EQUAL => SOME datum
| LESS => find (less, desiredKey)
| GREATER => find (greater, desiredKey)
fun exists (tree, desiredKey) = case find (tree, desiredKey) of
NONE => false
| SOME _ => true
fun up tree = Stream.create (fn () =>
case tree of
Leaf => NONE
| Branch {less, key, datum, greater, ...} =>
Stream.getItem (
Stream.append (
up less
, Stream.cons (
(key, datum)
, up greater
)
)
)
)
fun down tree = Stream.create (fn () =>
case tree of
Leaf => NONE
| Branch {greater, key, datum, less, ...} =>
Stream.getItem (
Stream.append (
down greater
, Stream.cons (
(key, datum)
, down less
)
)
)
)
fun upFrom (tree, firstKey) = Stream.create (fn () =>
case tree of
Leaf => NONE
| Branch {less, key, datum, greater, ...} =>
case Key.compare (firstKey, key) of
LESS => Stream.getItem (
Stream.append (
upFrom (less, firstKey)
, Stream.cons (
(key, datum)
, up greater
)
)
) | EQUAL => SOME (
(key, datum)
, up greater
) | GREATER => Stream.getItem (
upFrom (greater, firstKey)
)
)
fun downFrom (tree, firstKey) = Stream.create (fn () =>
case tree of
Leaf => NONE
| Branch {greater, key, datum, less, ...} =>
case Key.compare (firstKey, key) of
LESS => Stream.getItem (
downFrom (less, firstKey)
) | EQUAL => SOME (
(key, datum)
, down less
) | GREATER => Stream.getItem (
Stream.append (
downFrom (greater, firstKey)
, Stream.cons (
(key, datum)
, down less
)
)
)
)
fun fromStream stream =
Stream.fold (fn ((key, datum), tree) =>
add (tree, key, datum)
) empty stream
fun fromList list = fromStream (Stream.fromList list)
end
|
