[Solved] You are given a binary tree and need to find the longest path from the root node down to the farthest... Which algorithmic approach guarantees an optimal solution to determine this maximum depth? | Tree: Depth-First Search

Tree: Depth-First Search - Maximum Depth of Binary Tree

You are given a binary tree and need to find the longest path from the root node down to the farthest leaf node. Which algorithmic approach guarantees an optimal solution to determine this maximum depth?

ADynamic Programming with memoization on node values

BGreedy traversal picking the first child node at each step

CDepth-First Search (DFS) or Breadth-First Search (BFS) to explore all nodes

DSorting nodes by value and selecting the deepest node

Step-by-Step Solution

Solution:

Step 1: Understand the problem requires exploring all paths from root to leaves
Finding maximum depth means checking every path from root to leaves, so partial or greedy approaches won't guarantee correctness.
Step 2: Identify algorithms that explore all nodes
DFS or BFS traverse all nodes systematically, ensuring the maximum depth is found. Greedy or sorting approaches do not consider all paths.
Final Answer:
Option C -> Option C
Quick Check:
DFS and BFS both visit all nodes to find max depth [OK]

Quick Trick: Max depth requires full traversal, not greedy or sorting [OK]

Common Mistakes:

MISTAKES

Assuming greedy traversal finds max depth
Confusing max depth with max node value
Thinking sorting nodes helps depth calculation

Trap Explanation:

PITFALL

Greedy or sorting seem simpler but miss exploring all paths, leading to incorrect max depth.

Interviewer Note:

CONTEXT

Tests if candidate can recognize traversal patterns for tree depth problems.

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Which algorithmic approach guarantees an optimal solution to determine this maximum depth?

Step 1: Understand the problem requires exploring all paths from root to leaves

Step 2: Identify algorithms that explore all nodes

Final Answer:

Quick Check:

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