grid47 Exploring patterns and algorithms
Oct 27, 2024
4 min read
Solution to LeetCode 104: Maximum Depth of Binary Tree Problem
You are given the root of a binary tree. Your task is to return the maximum depth of the tree. The maximum depth is defined as the number of nodes along the longest path from the root node down to the farthest leaf node.
Problem
Approach
Steps
Complexity
Input: You are given the root node of a binary tree, where each node contains a value, and pointers to its left and right children.
Example: root = [5,3,8,2,4,7,9]
Constraints:
• The number of nodes in the tree is in the range [0, 10^4].
• -100 <= Node.val <= 100
Output: You should return an integer representing the maximum depth of the binary tree.
Example: Output: 3
Constraints:
• The output should be a single integer representing the depth of the tree.
Goal: The goal is to find the maximum depth of the binary tree by recursively calculating the depth of the left and right subtrees, and returning the larger of the two depths plus one.
Steps:
• Base Case: If the root is NULL, return 0.
• Recursively find the maximum depth of the left subtree.
• Recursively find the maximum depth of the right subtree.
• Return the larger of the two depths plus one to account for the current node.
Goal: The solution should be able to handle trees with up to 10,000 nodes efficiently.
Steps:
• The tree can contain up to 10,000 nodes.
Assumptions:
• The input will always represent a valid binary tree.
• Input: root = [3,9,20,null,null,15,7]
• Explanation: The binary tree has the following structure:
3
/ \
9 20
/ \
15 7
The longest path is from root (3) to leaf nodes (15 or 7), which has a depth of 3.
• Input: root = [1,null,2]
• Explanation: The binary tree consists of the root node (1) and its right child (2), forming a path of depth 2.
• Input: root = []
• Explanation: An empty tree has no nodes, so the maximum depth is 0.
Approach: The problem can be solved using a recursive approach to traverse the tree and calculate the depth of each subtree.
Observations:
• The problem can be solved using recursion by finding the depth of the left and right subtrees at each node.
• By utilizing recursion, we can efficiently calculate the maximum depth of the tree by always comparing the depths of the left and right subtrees.
Steps:
• Check if the root is null. If so, return 0.
• Recursively calculate the maximum depth of the left subtree.
• Recursively calculate the maximum depth of the right subtree.
• Return the larger of the two depths, plus one to account for the current node.
Empty Inputs:
• If the tree is empty, return 0.
Large Inputs:
• For large trees with up to 10,000 nodes, ensure the solution handles the input efficiently.
Special Values:
• If the tree is heavily unbalanced (e.g., all nodes are on one side), the depth should be calculated correctly based on the longest path.
Constraints:
• The tree can contain up to 10,000 nodes, so the algorithm should be efficient in terms of time complexity.
Recursively calculate the maximum depth of the left and right subtrees, add 1 to account for the current node, and return the result.
Best Case: O(n)
Average Case: O(n)
Worst Case: O(n)
Description: In the worst case, we need to visit each node in the tree, so the time complexity is O(n), where n is the number of nodes.
Best Case: O(1)
Worst Case: O(h)
Description: The space complexity is O(h) in the worst case, where h is the height of the tree. In the best case, the tree is perfectly balanced, and the space complexity is O(1).
