## April 30, 2020

### #LeetCode: Binary Tree Maximum Path Sum

Given a non-empty binary tree, find the maximum path sum.

For this problem, a path is defined as any sequence of nodes from some starting node to any node in the tree along the parent-child connections. The path must contain at least one node and does not need to go through the root.

Example 1:
Input: [1,2,3]

1
/ \
2   3

Output: 6

Example 2:
Input: [-10,9,20,null,null,15,7]

-10
/ \
9  20
/  \
15   7

Output: 42

Algorithm:
For any node, there can be 4 ways from which the max path goes through:
1. From the node only.
2. Max path through the left child and node
3. Max path through the right child and node
4. Max path through the left child, node and then max path through the right node.

We are going to trace all these above mentioned path and find the max one. We will be calling a recursive function, in which we consider each node as a root with a subtree. This function will return the maximum path sum 'maxNodeLeftRight' such that at most one child of root is involved. This maxNodeLeftRight will used in previous function call to calculate the maximum path.

Java Solution:

ALSO CHECK: Other LeetCode Solutions in Java

-K Himaanshu Shuklaa..