def construct_bst_helper(left_bound: int,
right_bound: int) -> Optional[TreeNode]:
if left_bound > right_bound:
return None
mid_point = (left_bound + right_bound) // 2
root_node = TreeNode(values[mid_point])
root_node.left = construct_bst_helper(left_bound, mid_point - 1)
root_node.right = construct_bst_helper(mid_point + 1, right_bound)
return root_node
def reversed_pre_order_traversal(current_node: TreeNode) -> None:
"""
:param current_node: flattening sub tree beneath current_node; current_node is not None
"""
nonlocal previous_node
if current_node.right:
reversed_pre_order_traversal(current_node.right)
if current_node.left:
reversed_pre_order_traversal(current_node.left)
current_node.right = previous_node
current_node.left = None
previous_node = current_node
def _trim_boundary_helper(current_node: TreeNode) -> TreeNode:
if not current_node:
return current_node
if current_node.val < low_val:
# root and its left tree will be dropped
return _trim_boundary_helper(current_node.right)
elif current_node.val > high_val:
# root and its right tree will be dropped
return _trim_boundary_helper(current_node.left)
current_node.left = _trim_boundary_helper(current_node.left)
current_node.right = _trim_boundary_helper(current_node.right)
return current_node
def mark_parent(current_node: TreeNode,
parent_node: TreeNode = None) -> None:
current_node.parent = parent_node
if current_node.left:
mark_parent(current_node.left, current_node)
if current_node.right:
mark_parent(current_node.right, current_node)
def convert_bst_helper(current_node: TreeNode) -> None:
nonlocal accumulator
if current_node is not None:
convert_bst_helper(current_node.right)
accumulator += current_node.val
current_node.val = accumulator
convert_bst_helper(current_node.left)
def build_bst(i: int, j: int) -> TreeNode:
"""
:return: build binary search tree for in_order_list[i: j]
"""
mid = (i + j) // 2
return TreeNode(in_order_list[mid],
left=(build_bst(i, mid) if mid > i else None),
right=(build_bst(mid + 1, j) if mid + 1 < j else None))
def construct_bst_helper(
list_start: Optional[ListNode]) -> Optional[TreeNode]:
if list_start is None:
return None
slow_ptr = list_start
slow_before = None
fast_ptr = list_start
while fast_ptr.next and fast_ptr.next.next:
slow_before = slow_ptr
slow_ptr = slow_ptr.next
fast_ptr = fast_ptr.next.next
root_node = TreeNode(slow_ptr.val)
if slow_before:
slow_before.next = None
root_node.left = construct_bst_helper(list_start)
if slow_ptr.next:
root_node.right = construct_bst_helper(slow_ptr.next)
return root_node
def add_merkle_hash_to(current_node: TreeNode) -> str:
"""
:param current_node: add Merkle hash code to represent the sub tree beneath current_node
:return: Merkle hash code of the sub tree beneath current_node
"""
current_node.hash_code = get_sh256_hash((add_merkle_hash_to(current_node.left) if current_node.left else '#') +
str(current_node.val) +
(add_merkle_hash_to(current_node.right) if current_node.right else '#'))
return current_node.hash_code
def test_build_tree(node_list: List[Optional[int]]) -> BinaryTree:
if not node_list or node_list[0] is None:
return BinaryTree(None)
return_tree = BinaryTree(TreeNode(node_list[0]))
node_queue = deque([return_tree.root])
node_child_counter = 0
current_node = None
for i in range(1, len(node_list)):
if node_child_counter == 0:
current_node = node_queue.popleft()
if node_list[i] is not None:
if node_child_counter:
current_node.right = TreeNode(node_list[i])
node_queue.append(current_node.right)
else:
current_node.left = TreeNode(node_list[i])
node_queue.append(current_node.left)
node_child_counter = (node_child_counter + 1) % 2
return return_tree
def invert_tree(root: TreeNode) -> Optional[TreeNode]:
"""
:param root: root of a binary tree
:return: root of the inverted binary tree, after flipping left and right child of each node
"""
if root is None:
return None
right = invert_tree(root.right) if root.right else None
left = invert_tree(root.left) if root.left else None
root.left, root.right = right, left
return root
def prune_tree_helper(current_root: TreeNode) -> bool:
"""
Prune the subtree of current_root
:param current_root: root node of current sub tree; guaranteed not equals to None
:return: whether subtree of current_root contains 1
"""
subtree_contains_1 = False
if current_root.left:
if prune_tree_helper(current_root.left):
subtree_contains_1 = True
else:
current_root.left = None
if current_root.right:
if prune_tree_helper(current_root.right):
subtree_contains_1 = True
else:
current_root.right = None
return current_root.val == 1 or subtree_contains_1
def trim_BST(root: TreeNode, low_val: int, high_val: int) -> TreeNode:
"""
Recursively remove all nodes whose values that are out of [low_val, high_val]
:param root: root node of the original Binary Search Tree
:param low_val: remove all nodes that are strictly less than low_val
:param high_val: remove all nodes that are strictly greater than low_val
:return: root of the updated Binary Search Tree
"""
if not root:
return root
if root.val < low_val:
# root and its left tree will be dropped
return trim_BST(root.right, low_val, high_val)
elif root.val > high_val:
# root and its right tree will be dropped
return trim_BST(root.left, low_val, high_val)
root.left = trim_BST(root.left, low_val, high_val)
root.right = trim_BST(root.right, low_val, high_val)
return root
def insert(self, v: TREE_NODE_TYPE) -> TREE_NODE_TYPE:
"""
:param v: insert a TreeNode into the tree with value node.val = v so that the tree remains complete
:return: the value of the parent of the inserted TreeNode;
"""
parent_node = self.node_not_full[0]
self.node_not_full.append(TreeNode(v))
if not parent_node.left:
parent_node.left = self.node_not_full[-1]
else:
parent_node.right = self.node_not_full[-1]
self.node_not_full.pop(0)
return parent_node.val
def insert(self, value: TREE_NODE_TYPE) -> None:
"""
:return: insert a new node of value into the BST
"""
if self.root is None:
self.root = TreeNode(value)
else:
current_node = self.root
inserted = False
while not inserted:
if value < current_node.val:
if not current_node.left:
current_node.left = TreeNode(value)
inserted = True
else:
current_node = current_node.left
else:
if not current_node.right:
current_node.right = TreeNode(value)
inserted = True
else:
current_node = current_node.right
def merge_trees(root1: Optional[TreeNode], root2: Optional[TreeNode]) -> Optional[TreeNode]:
"""
:param root1: root of binary tree 1
:param root2: root of binary tree 2
:return: root of merged tree; returned tree may point to TreeNodes in root1 or root2
"""
if root1 is None and root2 is None:
return None
if root1 is not None and root2 is not None:
return TreeNode(root1.val + root2.val,
left=merge_trees(root1.left, root2.left) if root1.left or root2.left else None,
right=merge_trees(root1.right, root2.right) if root1.right or root2.right else None)
else:
return root1 if root1 else root2
def add_one_row(root: TreeNode, value: int, depth: int) -> TreeNode:
"""
:param root: root of a proper binary tree
:param value: add a new row at level depth with all nodes set to value
:param depth: add a new row at level depth with all nodes set to value
:return: root of the new binary tree
"""
if depth == 1:
return TreeNode(value, left=root)
current_level = [root]
current_depth = 1
while current_depth < depth - 1:
next_level = [node.left for node in current_level if node.left is not None]
next_level.extend([node.right for node in current_level if node.right is not None])
current_depth += 1
current_level = next_level
for node in current_level:
node.left = TreeNode(value, left=node.left)
node.right = TreeNode(value, right=node.right)
return root
def invert_tree(root: TreeNode) -> Optional[TreeNode]:
"""
:param root: root of a binary tree
:return: root of the inverted binary tree, after flipping left and right child of each node
"""
if root is None:
return None
right = invert_tree(root.right) if root.right else None
left = invert_tree(root.left) if root.left else None
root.left, root.right = right, left
return root
node = TreeNode(4)
node.left = TreeNode(2)
node.left.left = TreeNode(1)
node.left.right = TreeNode(3)
node.right = TreeNode(7)
node.right.left = TreeNode(6)
node.right.right = TreeNode(9)
tree = BinaryTree(node)
assert tree.preorder_traversal() == [4, 2, 1, 3, 7, 6, 9]
assert tree.inorder_traversal() == [1, 2, 3, 4, 6, 7, 9]
assert tree.postorder_traversal() == [1, 3, 2, 6, 9, 7, 4]
assert tree.layer_traversal_by_layer() == [[4], [2, 7], [1, 3, 6, 9]]
assert tree.leetcode_traversal() == [
4, 2, 7, 1, 3, 6, 9, None, None, None, None, None, None, None, None
]
# print('Deleted: %d, Remaining: %s' % (values[i], str(deletion_tree.traversal())))
assert deletion_tree.traversal() == values[:i] + values[i + 1:]
expected_values = [6, 7, 8, 9, 10, 11, 12, 13]
assert new_bst.traverse_range(6, 13) == expected_values
assert new_bst.traverse_range(6, 14) == expected_values
assert new_bst.traverse_range(5.5, 13) == expected_values
sorted_list = list(range(1, 11))
head = LinkedList.create_linked_list(sorted_list)
new_bst = BST(head)
assert new_bst.traversal() == sorted_list
assert new_bst.is_balanced()
new_bst = BST([-1])
new_bst.root.right = TreeNode(1)
new_bst.root.right.left = TreeNode(-1)
assert new_bst.is_valid()
new_bst = BST([1])
new_bst.root.left = TreeNode(-1)
new_bst.root.left.right = TreeNode(1)
assert not new_bst.is_valid()
new_bst = BST([1, 3, 4])
new_bst.root.left.right = TreeNode(2)
for i in range(1, 5):
assert new_bst.kth_smallest_element(
i) == i, "Expecting %d got %d" % (i, new_bst.kth_smallest_element(i))
assert new_bst.kth_smallest_element(5) is None