Consider the following binary tree made up of both positive and negative integers. 5 -15) -8 1 4 10 Our problem is to find the maximum possible sum from one leaf to another in a binary tree. In the example above, the maximum sum is 27 which starts at leaf node 3 and ends at leaf node 10, that is, 3+6+9+0-1 + 10 = 27. a) (6 marks) Outline an algorithm that finds the maximum sum between two leaf nodes using a single traversal of the binary tree. b) Implement (10 marks) and test (4 marks) your algorithm in part a). You may wish to store additional information in each node. c) (4 marks) Augment your code in part b) to return the actual values along the maximum-sum path between the two leaf nodes.

Consider the following binary tree made up of both positive and negative integers. 5 -15) -8 1 4 10 Our problem is to find the maximum possible sum from one leaf to another in a binary tree. In the example above, the maximum sum is 27 which starts at leaf node 3 and ends at leaf node 10, that is, 3+6+9+0-1 + 10 = 27. a) (6 marks) Outline an algorithm that finds the maximum sum between two leaf nodes using a single traversal of the binary tree. b) Implement (10 marks) and test (4 marks) your algorithm in part a). You may wish to store additional information in each node. c) (4 marks) Augment your code in part b) to return the actual values along the maximum-sum path between the two leaf nodes.