Easy recursive solution Python(only 8 lines)

• ``````def maxPathSum(self, root):

def double(root): # return (max_path_from_root(root), self.maxPathSum(root))
if root is None:
return 0, float("-inf")
x, y = double(root.left)
a, b = double(root.right)

return root.val + max(x,a,0), max(y, b, (root.val + max(0, x) + max(0,a)))

m, n = double(root)
return n
``````

The function "double" returns two values 1) maximum sum of path starting from the root node and going down(max_path_from_root(root)) 2) The answer (what we want: self.maxPathSum(root)). Then these two values have recursive relations:

1. max_path_from_root(root) = root.val + max(max_path_from_root(root.left), max_path_from_root(root.right), 0)
2. self.maxPathSum(root) = max(self.maxPathSum(root.left), self.maxPathSum(root.right), root.val + max(0, max_path_from_root(root.left)) + max(0, max_path_from_root(root.right))
Note that the first two terms are the case the maximum path does not go through the root node. The last case is when it goes through the root node.

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