Which approach guarantees an optimal solution to this problem?
easy🔍 Pattern Recognition Q11 of Q15
Tree: Depth-First Search - Diameter of Binary Tree
Given a binary tree, you need to find the length of the longest path between any two nodes in the tree. This path may or may not pass through the root. Which approach guarantees an optimal solution to this problem?
APerform a postorder traversal computing heights and update the diameter at each node using recursion with a global variable.
BApply dynamic programming with memoization on node pairs to find longest paths.
CUse a greedy traversal that always chooses the deeper subtree at each node.
DCalculate the height of the tree and multiply by two to estimate the diameter.
Step-by-Step Solution
Solution:
Step 1: Understand the problem requires the longest path between any two nodes, not necessarily passing through root.
The diameter can be found by checking the sum of left and right subtree heights at every node.
Step 2: Recognize that a postorder traversal with recursion and a global variable to track diameter updates at each node ensures all paths are considered.
This approach visits each node once, updating the diameter with left_height + right_height.
Final Answer:
Option A -> Option A
Quick Check:
Postorder traversal with global diameter update covers all nodes [OK]
Quick Trick:Diameter updates at every node, not just root [OK]
Common Mistakes:
MISTAKES
Thinking diameter must pass through root
Using greedy to pick deeper subtree only
Confusing diameter with twice height
Trap Explanation:
PITFALL
Greedy or root-only approaches seem simpler but miss longest paths elsewhere.
Interviewer Note:
CONTEXT
Tests if candidate knows diameter requires global updates, not just root-based or greedy.
Master "Diameter of Binary Tree" in Tree: Depth-First Search
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