Consider Red lines of slope -1 passing between nodes (in following diagram). The diagonal sum in a binary tree is the sum of all nodes data lying between these lines. Given a Binary Tree of size N, print all diagonal sums.
For the following input tree, output should be 9, 19, 42.
9 is sum of 1, 3 and 5.
19 is sum of 2, 6, 4 and 7.
42 is sum of 9, 10, 11 and 12.
Example 1:
Input:
4
/ \
1 3
/
3
Output: 7 4
Example 2:
Input:
10
/ \
8 2
/ \ /
3 5 2
Output: 12 15 3
Your Task:
You don't need to take input. Just complete the function diagonalSum() that takes root node of the tree as parameter and returns an array containing the diagonal sums for every diagonal present in the tree with slope -1.
Expected Time Complexity: O(NlogN).
Expected Auxiliary Space: O(N).
Constraints:
1<=Number of nodes<=10^{5}
Note: The Input/Ouput format and Example given are used for system's internal purpose, and should be used by a user for Expected Output only. As it is a function problem, hence a user should not read any input from stdin/console. The task is to complete the function specified, and not to write the full code.

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