Which approach guarantees an optimal O(n) time solution without redundant height computations?
easy🔍 Pattern Recognition Q11 of Q15
Tree: Depth-First Search - Balanced Binary Tree
You need to determine if a binary tree is height-balanced, meaning the heights of the two child subtrees of any node never differ by more than one. Which approach guarantees an optimal O(n) time solution without redundant height computations?
AUse a top-down recursive approach that checks balance only at the root node.
BCompute height for each node separately and check balance at each node recursively.
CPerform a breadth-first traversal and check balance by comparing subtree sizes at each level.
DUse a postorder traversal that returns height and balance status simultaneously, stopping early if imbalance is found.
Step-by-Step Solution
Solution:
Step 1: Understand the problem constraints
The problem requires checking balance at every node efficiently without recomputing heights multiple times.
Step 2: Identify the approach that avoids redundant work
Postorder traversal that returns both height and balance status in one pass allows early exit on imbalance and avoids repeated height calculations.
Final Answer:
Option D -> Option D
Quick Check:
Postorder traversal with early exit is O(n) and avoids recomputation [OK]
Quick Trick:Postorder traversal with early exit avoids repeated height calls [OK]
Common Mistakes:
MISTAKES
Checking balance only at root misses subtree imbalances
Computing height separately for each node causes O(n²) time
Using BFS to check balance is incorrect as balance depends on subtree heights
Trap Explanation:
PITFALL
Option A looks correct but leads to O(n²) due to repeated height calls; option D misses subtree checks.
Interviewer Note:
CONTEXT
Tests if candidate knows how to combine height and balance checks efficiently.
Master "Balanced Binary Tree" in Tree: Depth-First Search
3 interactive learning modes - each teaches the same concept differently
