def floor(self, key: Key):
r = self.rank(key)
if r >= len(self._items):
return self.max()
if r == 0 and not eq(self._items[r].key, key):
return None
return self._items[r].key if eq(self._items[r].key,
key) else self._items[r - 1].key
def delete(self, key):
# no node with the given key exists in the tree
if self.get(key) is None:
return
parent = None
is_node_left_child = False
node = self._root
while node is not None:
if eq(key, node.key):
break
parent = node
# this is why we want to make sure that the key must exist in the tree.
parent.node_count = parent.node_count - 1
if lt(key, node.key):
node = node.left
is_node_left_child = True
else:
node = node.right
is_node_left_child = False
successor, parent_of_successor = self._find_successor_and_parent(node)
if successor is None: # the deleted node has no right subtree
if parent is None: # the deleted node is the current root
self._root = node.left
elif is_node_left_child:
parent.left = node.left
else:
parent.right = node.left
else:
# replace successor by its right child
# Note: Because the successor is the left-most node, it can either have no child or only one right child,
# and it must be its parent's left child.
if parent_of_successor is not None:
parent_of_successor.left = successor.right
# replace the deleted node by its successor
if parent is None: # the deleted node is the current root
self._root = successor
elif is_node_left_child:
parent.left = successor
else:
parent.right = successor
successor.left = node.left
# the successor is the node's right child if it is the only node in the node's right subtree,
# and we want to avoid cycle here.
if not eq(successor, node.right):
successor.right = node.right
if successor is not None:
successor.node_count = node.node_count - 1
if parent_of_successor is not None:
parent_of_successor.node_count = parent_of_successor.node_count - 1
def ceiling(self, key: Key):
r = self.rank(key)
if r >= len(self._items):
return None
if r == 0 and not eq(self._items[r].key, key):
return self.min()
return self._items[r].key
def _rank(self, key, node):
if node is None:
return 0
left_child_count = node.left.node_count if node.left is not None else 0
if eq(key, node.key):
return left_child_count
if gt(key, node.key):
return 1 + left_child_count + self._rank(key, node.right)
return self._rank(key, node.left)
def put(self, key: Key, value):
r = self.rank(key)
if r >= len(self._items):
self._items.append(KeyValue(key, value))
elif eq(self._items[r].key, key):
self._items[r].value = value
else:
shift_right(self._items, r)
self._items[r] = KeyValue(key, value)
def get(self, key) -> Optional[Node]:
if self.is_empty():
return None
current = self._root
while current is not None:
if eq(current.key, key):
return current
current = current.left if lt(key, current.key) else current.right
return None
def _ceiling(self, key, node):
if node is None:
return None
if eq(key, node.key):
return node
if gt(key, node.key):
return self._ceiling(key, node.right)
left_subtree_ceiling = self._ceiling(key, node.left)
return left_subtree_ceiling if left_subtree_ceiling is not None else node
def _floor(self, key, node):
if node is None:
return None
if eq(key, node.key):
return node
if lt(key, node.key):
return self._floor(key, node.left)
right_subtree_floor = self._floor(key, node.right)
return right_subtree_floor if right_subtree_floor is not None else node
def binary_search(items, item):
low = 0
high = len(items) - 1
while high >= low:
mid = int(floor((high + low) / 2))
if eq(items[mid], item):
return mid
if gt(item, items[mid]):
low = mid + 1
else:
high = mid - 1
return None
def range(self, low: Key = None, high: Key = None):
rank_of_low = self.rank(low) if low is not None else 0
rank_of_high = self.rank(high) if high is not None else len(
self._items) - 1
if rank_of_low > rank_of_high:
return []
result = []
for i in range(rank_of_low, rank_of_high):
result.append(self._items[i].key)
if high is None or (0 <= rank_of_high < len(self._items)
and eq(self._items[rank_of_high].key, high)):
result.append(self._items[rank_of_high].key)
return result
def _put(self, new_node: Node, position: Node):
if position is None:
return new_node
if eq(new_node.key, position.key):
position.value = new_node.value
return position
if lt(new_node.key, position.key):
position.left = self._put(new_node, position.left)
else:
position.right = self._put(new_node, position.right)
position.node_count = (position.left.node_count if position.left is not None else 0) \
+ (position.right.node_count if position.right is not None else 0) \
+ 1
return position
def has_same_items(l1, l2):
"""
This implementation takes O(n*log(n)) time mainly for sorting the two lists before comparing their items.
Another implementation would be to loop over the first list, build a hash table from that list, and then
loop over the second list to check if any item not in the hash table. Note that we also need to keep track of
the item count to handle duplicated items. This implementation takes O(n) time.
"""
if len(l1) != len(l2):
return False
sorted_l1 = quick_sort(l1)
sorted_l2 = quick_sort(l2)
for i in range(len(sorted_l1)):
if not eq(sorted_l1[i], sorted_l2[i]):
return False
return True
def rank(self, key: Key):
low = 0
high = len(self._items) - 1
while high >= low:
mid = int(floor(high + low) / 2)
if eq(key, self._items[mid].key):
return mid
if mid + 1 < len(self._items) and gt(
key, self._items[mid].key) and lt(
key, self._items[mid + 1].key):
return mid + 1
if gt(key, self._items[mid].key):
low = mid + 1
else:
high = mid - 1
if low >= len(self._items):
return len(self._items)
if high < 0:
return 0
def _index_of_key(self, key):
r = self.rank(key)
return r if r < len(self._items) and eq(self._items[r].key,
key) else None
def equals(self, other):
return eq(self.value, other.value)
def equals(self, other):
return eq(self.key, other.key)
def test_check_equals(self):
assert eq(None, None)
assert not eq(1, 2)
assert eq(2, 2)
assert not eq(2, 1)
assert not eq(1.1, 1.2)
assert not eq(2.1, 1.9)
assert eq(2.1, 2.1)
assert not eq(KeyValue(1), KeyValue(2))
assert eq(KeyValue(2), KeyValue(2))
assert not eq(KeyValue(2), KeyValue(1))
assert not eq(KeyValue(Key(1)), KeyValue(Key(2)))
assert eq(KeyValue(Key(2)), KeyValue(Key(2)))
assert not eq(KeyValue(Key(2)), KeyValue(Key(1)))