Maximum Depth of a Tree

#52 · Trees · Beginner · 45 XP · about 8 min

The depth of a binary tree is the number of nodes on the longest path from the root down to a leaf, a node with no children. Write max_depth(root) that returns the depth of the tree that starts at root. An empty tree (root is None) has depth 0.

Each node is a Node with a value val and two children, left and right, which are None when missing. The provided build makes a tree from a list of values in level order, where None marks a missing child.

Examples

max_depth(build([4, 1, 7, None, None, 5, 9]))  # returns 3
max_depth(build([6, None, 9]))  # returns 2
max_depth(build([]))  # returns 0

The drawing shows the first tree. Its longest paths, 4, 7, 5 and 4, 7, 9, each have three nodes.

Note

A tree with only a root has depth 1.

# Provided: do not change

from collections import deque

class Node:

def __init__(self, val, left=None, right=None):

self.val = val

self.left = left

self.right = right

def build(values):

"""Build a tree from a level-order list; None marks a missing child."""

if not values or values[0] is None:

return None

root = Node(values[0])

queue = deque([root])

i = 1

while queue and i < len(values):

node = queue.popleft()

if values[i] is not None:

node.left = Node(values[i])

queue.append(node.left)

i += 1

if i < len(values) and values[i] is not None:

node.right = Node(values[i])

queue.append(node.right)

i += 1

return root

def max_depth(root):

# Your code here

pass

print(max_depth(build([4, 1, 7, None, None, 5, 9])))

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