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# Max Path Sum From Leaf To Root

Given a binary tree in which each node contains an integer number. Find the maximum possible path sum from a leaf to root.

Assumptions

The root of given binary tree is not null.

Examples

         10

       /      \\

    -2        7

  /     \\

8      -4

The maximum path sum is 10 + 7 = 17.

**Solution:** Recursive bottom up

Base Case: root == null, return 0

From Children: get two max value paths

At current level: 

To parent: pick higher value path between left and right and return to parent