Binary Tree Maximum path sum@leetcode

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Given a binary tree, find the maximum path sum.

The path may start and end at any node in the tree.

For example:
Given the below binary tree,

       1
      / \
     2   3

Return 6.

» Solve this problem

We need to pay attention on 3 points in this problem:
1. Binary tree
2. It can start and end in any place.
3. The node value can be positive, 0 and negative.

I referred to the solution from Peking2 at MITBBS. The main idea is recursion and DFS.

Analyse the problem, when we are in a root node, how we decided to include the subtree in the maximum path sum? So we need to calculate the max path sum in both subtree. In the meantime, we need to set a variable "max" to store the max path sum we found during the recursion. Pay attention to one thing is, when a root's value is negative, we need to decide include it or discard it.