What is the optimal time complexity of solving Binary Tree Maximum Path Sum?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Binary Tree Maximum Path Sum?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Binary Tree Maximum Path Sum?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Binary Tree Maximum Path Sum?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Binary Tree Maximum Path Sum

Learn how to solve the 'Binary Tree Maximum Path Sum' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Hard

A path in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence at most once. Note that the path does not need to pass through the root.

The path sum of a path is the sum of the node's values in the path.

Given the root of a binary tree, return the maximum path sum of any non-empty path.

The tree is represented as a level-order list. Implement a function maxPathSum(root: list) -> int.

Constraints

•The number of nodes in the tree is in the range [1, 30000]
•-1000 <= Node.val <= 1000

Examples

Example 1

Input

[1,2,3]

Output

Explanation

The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6.

Example 2

Input

[-10,9,20,None,None,15,7]

Output

Explanation

The optimal path is 15 -> 20 -> 7 with a path sum of 15 + 20 + 7 = 42.

Example 3

Input

[-3]

Output

-3

Explanation

The only path is the single node -3.

Need a Hint?

Perform a recursive tree traversal (DFS) or level-order traversal (BFS) using a queue/stack.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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