At each node of the recursion tree, we return the maximum path sum of the "single" path to the parent node, i.e., max(root.val, root.val + left, root.val + right). In the meantime, update the global maximum.
public int maxPathSum(TreeNode root) {
int[] max = new int[] { Integer.MIN_VALUE };
helper(root, max);
return max[0];
}
private int helper(TreeNode root, int[] max) {
if (root == null) return 0;
int left = helper(root.left, max);
int right = helper(root.right, max);
left = left < 0 ? 0 : left;
right = right < 0 ? 0 : right;
max[0] = Math.max(max[0], root.val + left + right);
return root.val + Math.max(left, right);
}
