[Solved] You are given a binary tree where each node contains an integer value (which can be negative).... Which approach guarantees an optimal solution for this problem? | Tree: Depth-First Search

Tree: Depth-First Search - Binary Tree Maximum Path Sum

You are given a binary tree where each node contains an integer value (which can be negative). The task is to find the maximum sum of values along any path in the tree, where a path can start and end at any node and must be connected through parent-child links. Which approach guarantees an optimal solution for this problem?

APerform a postorder traversal with recursion, tracking the maximum gain from each subtree and updating a global maximum path sum.

BEnumerate all possible paths in the tree and compute their sums to find the maximum.

CUse a greedy traversal that picks the maximum child at each node and sums values along that path.

DUse a breadth-first search (BFS) to find the longest path and sum its node values.

Step-by-Step Solution

Solution:

Step 1: Understand the problem constraints
The path can start and end at any node, not necessarily the root or leaf, and node values can be negative.
Step 2: Identify the approach that handles all cases optimally
Postorder recursion allows computing maximum gains from left and right subtrees, considering negative values by ignoring negative gains, and updating a global max path sum that includes both children and the current node.
Final Answer:
Option A -> Option A
Quick Check:
Postorder recursion with global max handles negative values and arbitrary paths [OK]

Quick Trick: Postorder recursion tracks max gains and global max [OK]

Common Mistakes:

MISTAKES

Greedy approach fails on negative values and non-root paths
Enumerating all paths is inefficient and impractical
BFS does not capture arbitrary path sums

Trap Explanation:

PITFALL

Greedy and BFS seem simpler but fail to consider negative values and arbitrary path start/end nodes, making them suboptimal.

Interviewer Note:

CONTEXT

Tests if candidate recognizes the need for subtree gain tracking and global max update.

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Which approach guarantees an optimal solution for this problem?

Step 1: Understand the problem constraints

Step 2: Identify the approach that handles all cases optimally

Final Answer:

Quick Check:

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