Maximum Depth of Tree: Finding the Longest Path from Root to Leaf

Introduction

In this blog post, we will discuss how to find the maximum depth of a binary tree. The maximum depth of a binary tree refers to the number of nodes along the longest path from the root node down to the farthest leaf node.

Problem Statement

Given the root of a binary tree, our task is to calculate its maximum depth.

Data Structure Used

We will be using the concept of binary trees to solve this problem. Each node in the binary tree contains a value and references to its left and right child nodes (if they exist).

Algorithmic Approach

To find the maximum depth of a binary tree, we will use a recursive approach. We will define a function maxDepth() that takes the root of the tree as its parameter. The function will perform a depth-first search (DFS) on the tree and return the maximum depth encountered.

Here is the code implementation:

int maxDepth(TreeNode *root)
{
    if (root == NULL)
    {
        return 0;
    }
    return maxDepthChecker(root, 0);
}

int maxDepthChecker(TreeNode *node, int depth)
{
    if (node == NULL)
    {
        return depth;
    }
    int leftDepth = maxDepthChecker(node->left, depth + 1);
    int rightDepth = maxDepthChecker(node->right, depth + 1);
    return max(leftDepth, rightDepth);
}

The maxDepth() function checks if the root is NULL. If so, it returns 0 as the depth. Otherwise, it calls the helper function maxDepthChecker(), passing the root and an initial depth of 0.

The maxDepthChecker() function recursively calculates the depth of the left and right subtrees. It returns the maximum depth between the left and right subtrees plus 1, representing the depth of the current node.

Time Complexity

The time complexity of this approach is O(n), where n is the number of nodes in the binary tree. In the worst-case scenario, we need to visit each node once to calculate the maximum depth.

Space Complexity

The space complexity of this approach is O(h), where h is the height of the binary tree. In the worst-case scenario, the height of the binary tree can be equal to the number of nodes, resulting in O(n) space complexity.

Conclusion

Finding the maximum depth of a binary tree can be efficiently solved using a recursive approach. By performing a depth-first search, we can calculate the maximum depth encountered during the traversal. The provided code demonstrates a simple and effective solution to solve this problem.

Feel free to use the provided code as a reference or implement it in your own projects. Understanding the maximum depth of a binary tree is essential for various tree-related problems and can greatly enhance your algorithmic skills.

Maximum Depth of Binary Tree