def make_set(self, id: SetID) -> None:
if id in self._sets:
raise DuplicateIDException()
n = Node(
parent=None,
id=id,
rank=0,
size=1,
)
n.parent = n
self._sets[id] = n
self._size += 1
def UNION_RANK(root_a: Node, root_b: Node) -> None:
if root_a.rank < root_b.rank:
root_a, root_b = root_b, root_a
elif root_a.rank == root_b.rank:
root_a.rank += 1
root_b.parent = root_a
def FIND_PATH_SPLITTING(node: Node) -> Node:
while node.parent is not node:
next = node.parent
node.parent = next.parent
node = next
return node
def FIND_PATH_COMPRESSION(node: Node) -> Node:
root = node
while root.parent is not root:
root = root.parent
while node.parent is not root:
parent = node.parent
node.parent = root
node = parent
return root
def UNION_SIZE(root_a: Node, root_b: Node) -> None:
if root_a.rank < root_b.rank:
root_a, root_b = root_b, root_a
root_b.parent = root_a
root_a.size = root_b.size + root_a.size
def UNION_NAIVE(a: Node, b: Node) -> None:
a.parent = b
def FIND_PATH_HALVING(node: Node) -> Node:
while node.parent is not node:
node.parent = node.parent.parent
node = node.parent
return node