Sum of the greatest possible path between any pair of leaves in a binary tree

In the realm of Data Structures and Algorithms (DSA), a solution has been devised for an intriguing problem: finding the maximum sum from one leaf node to another in a binary tree. This problem, often encountered in companies like Microsoft, Amazon, Facebook, Directi, Accolite, FactSet, and OYO, is addressed within the 'Tree' class.

The approach involves maintaining two values in recursive calls for each visited node. For every node x, the maximum root to leaf sum is found in the left and right subtrees of x. To solve the problem, we traverse each node and recursively calculate the maximum sum from leaf to root in the left and right subtrees of each node.

The time complexity of this solution is O(n), as it requires visiting each node only once. The maximum sum can be found using a single traversal of the binary tree. Interestingly, the solution does not go through the root node explicitly but considers it as part of the sum calculation.

An example of the maximum sum path is 27 (3 + 6 + 9 + 0 - 1 + 10), demonstrating the effectiveness of this method. However, it's worth noting that the binary tree may or may not include the root in the maximum sum path.

The auxiliary space complexity is O(h), where h is the height of the tree. This means the space requirement increases as the tree becomes deeper.

While the implementation of this approach is provided, there is no information available about the name of the developer who created the method for finding the maximum value in a given tree with numbers at each node. Nonetheless, this solution serves as a valuable tool for solving problems related to binary trees in the DSA domain.