def make_binary_tree():
root = TreeNode(5)
l1_1, l1_2 = TreeNode(1), TreeNode(5)
l2_1, l2_2, l2_3 = TreeNode(5), TreeNode(5), TreeNode(5)
root.left, root.right = l1_1, l1_2
l1_1.left, l1_1.right, l1_2.right = l2_1, l2_2, l2_3
return root
def make_asymmetric_tree():
root = TreeNode(1)
l2_l, l2_r = TreeNode(2), TreeNode(2)
l2_l_l3_l, l2_l_l3_r, l2_r_l3_l, l2_r_l3_r = None, TreeNode(
3), None, TreeNode(3)
root.left, root.right = l2_l, l2_r
l2_l.left, l2_l.right, l2_r.left, l2_r.right = l2_l_l3_l, l2_l_l3_r, l2_r_l3_l, l2_r_l3_r
return root
def make_binary_tree():
root = TreeNode(5)
l1_1, l1_2 = TreeNode(4), TreeNode(8)
l2_1, l2_2, l2_3 = TreeNode(11), TreeNode(13), TreeNode(4)
l3_1, l3_2, l3_3 = TreeNode(7), TreeNode(2), TreeNode(1)
root.left, root.right = l1_1, l1_2
l1_1.left, l1_2.left, l1_2.right = l2_1, l2_2, l2_3
l2_1.left, l2_1.right, l2_3.right = l3_1, l3_2, l3_3
return root
def build(stop=None):
if inorder and inorder[-1] != stop:
root = TreeNode(preorder.pop())
root.left = build(root.val)
inorder.pop()
root.right = build(stop)
return root
def build(bound=None):
if not inorder or inorder[-1] == bound:
return None
root = TreeNode(postorder.pop())
root.right = build(root.val)
inorder.pop()
root.left = build(bound)
return root
def make_binary_tree():
tn_left = TreeNode(9)
tn_right = TreeNode(20)
tn_root = TreeNode(3)
tn_root.left = tn_left
tn_root.right = tn_right
tn_root.right.left = TreeNode(15)
tn_root.right.right = TreeNode(7)
return tn_root
def helper(self, left, right):
if left > right:
return None
# always choose left middle node as a root
p = (left + right) // 2
# preorder traversal: node -> left -> right
root = TreeNode(self.nums[p])
root.left = self.helper(left, p - 1)
root.right = self.helper(p + 1, right)
return root
def helper(self, left, right):
if left > right:
return None
# always choose right middle node as a root
p = (left + right) // 2
# if left + right is odd, add 1 to p-index.
if (left + right) % 2:
p += 1
# preorder traversal: node -> left -> right
root = TreeNode(self.nums[p])
root.left = self.helper(left, p - 1)
root.right = self.helper(p + 1, right)
return root
def helper(in_left=0, in_right=len(inorder)):
# The nonlocal statement causes the listed identifiers to refer to
# previously bound variables in the nearest enclosing scope excluding globals.
nonlocal pre_idx
# if there is no elements to construct subtrees
if in_left == in_right:
return None
# pick up pre_idx element as a root
root_val = preorder[pre_idx]
root = TreeNode(root_val)
# root splits inorder list
# into left and right subtrees
index = idx_map[root_val]
# recursion
pre_idx += 1
# build left subtree
root.left = helper(in_left, index)
# build right subtree
root.right = helper(index + 1, in_right)
return root
dfs(node.left)
dfs(node.right)
if node != root:
string_builder.append(")")
string_builder = []
dfs(root)
return "".join(string_builder)
if __name__ == '__main__':
solutions = [Solution(), Solution2()]
bt1 = TreeNode(1)
bt1.left, bt1.right = TreeNode(2), TreeNode(3)
bt1.left.left = TreeNode(4)
bt2 = TreeNode(1)
bt2.left, bt2.right = TreeNode(2), TreeNode(3)
bt2.left.right = TreeNode(4)
tc = (
(bt1, "1(2(4))(3)"), # root = [1,2,3,4]
(bt2, "1(2()(4))(3)"), # root = [1,2,3,null,4]
)
for sol in solutions:
for bt_root, expected_output in tc:
actual_result = sol.tree2str(bt_root)
assert actual_result == expected_output, f"{sol.__class__.__name__}: {actual_result} != {expected_output}"
def averageOfLevels(self, root: TreeNode) -> List[float]:
if not root:
return []
level_nums = collections.defaultdict(list)
level = 0
queue = [(root, level)]
while queue:
node, level = queue.pop(0) # pop leftmost (tree node) first
level_nums[level].append(node.val)
if node.left:
queue.append((node.left, level + 1))
if node.right:
queue.append((node.right, level + 1))
return [
sum(level_nums[i]) / len(level_nums[i]) for i in range(level + 1)
]
if __name__ == '__main__':
solutions = [Solution, Solution2]
root = TreeNode(3)
root.left = TreeNode(9)
root.right = TreeNode(20)
root.right.left = TreeNode(15)
root.right.right = TreeNode(7)
expected = [3, 14.5, 11]
for sol in solutions:
res = sol().averageOfLevels(root)
assert res == expected, f"{sol.__class__.__name__}: expected {expected}, got {res}"
def make_invalid_bst():
n1 = TreeNode(1)
n0 = TreeNode(2)
n2 = TreeNode(3)
n1.left, n1.right = n0, n2
return n1