Programming Interview Question: How to print all diagonal's sums for a given binary tree?

'N' lines drawn at slope -1 and cutting through a left branches of a binary tree divide the binary tree into 'N+1' partitions called diagonals.

How can you print sum of nodes in a partition for all partitions?

For example, If a tree has '1' as its root '2' as its left child and '3' as its right child then there are two diagonals in it. #1 diagonal consisting of nodes '1' and '3' and #2 diagonal consisting a node '2'. Output should be - sum for diagonal 0 : 4 and sum for diagonal 1 : 2

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