# Binary Tree Maximum Path Sum

Binary Tree Maximum Path Sum tree

Given a 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.

``````For example:
Given the below binary tree,

1
/ \
2   3

Return 6.
``````

Binary Tree Maximum Path Sum Solution

``````/**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/
public class BinaryTreeMaximumPathSum {
int max = Integer.MIN_VALUE;

public int maxPathSum(TreeNode root) {
maxPathSumRecursive(root);
return max;
}

private int maxPathSumRecursive(TreeNode root) {
if(root == null) {
return 0;
}

int left = Math.max(maxPathSumRecursive(root.left), 0);
int right = Math.max(maxPathSumRecursive(root.right), 0);

max = Math.max(max, root.val + left + right);

return root.val + Math.max(left, right);
}
}``````