Binary search Tree(BST) Practice question
Duration: 7 min
This video lesson is available to enrolled students.
AI Summary
An AI-generated summary of this video lecture.
This educational video provides a detailed walkthrough of a recursive C function designed to calculate the maximum depth or height of a binary tree. The instructor begins by presenting the code structure, highlighting the base case where a NULL node returns 0. He then uses a hand-drawn diagram of a binary tree to trace the execution flow, demonstrating how the function recursively calls itself for left and right subtrees. The core of the lesson focuses on determining the correct return values for the recursive step, specifically explaining why the depth of a node is calculated as one plus the maximum depth of its children. The instructor systematically eliminates incorrect options to arrive at the correct implementation.
Chapters
0:00 – 2:00 00:00-02:00
The instructor introduces the problem of finding the maximum depth of a binary tree, where the root is at level 1. He displays the C code for the function `maxDepth(struct node* node)` and points out the base case condition `if (node==NULL) return 0;`. To visualize the recursion, he draws a simple binary tree structure on the screen with a root node labeled 'A' and two children labeled 'B' and 'C'. He explains that the function needs to compute the depth of each subtree recursively.
2:00 – 5:00 02:00-05:00
The instructor expands the tree diagram by adding a node 'D' as a child of 'B' to create a deeper structure. He traces the execution of `maxDepth(A)`, which calls `maxDepth(B)` and `maxDepth(C)`. He explains that `lDepth` stores the result of the left subtree call and `rDepth` stores the result of the right subtree call. He specifically traces the call for node 'D', noting that since its children are NULL, the function returns 0 for those calls. He then calculates the depth for node 'D' itself as 1, and subsequently for node 'B', showing how the values propagate back up the call stack.
5:00 – 6:55 05:00-06:55
Focusing on the final logic, the instructor analyzes the lines `if (lDepth > rDepth) return X; else return Y;`. He deduces that to correctly calculate the height, the function must return the depth of the current node, which is 1 plus the depth of the deeper subtree. Therefore, he concludes that X must be `lDepth + 1` and Y must be `rDepth + 1`. He identifies option (B) as the correct answer, explaining that simply returning `lDepth` or `rDepth` without adding 1 would fail to account for the current node's level in the tree.
The video effectively demonstrates the recursive logic required for tree traversal problems. By breaking down the problem into a base case and a recursive step, and using a visual diagram to trace the execution, the instructor clarifies how the height is accumulated. The key takeaway is that the height of a node is defined as one plus the maximum height of its children, a fundamental concept in tree algorithms.