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Can you find the sum of values and the number of nodes for every sub-tree ?
Can you find the sum of values and the number of nodes for a sub-tree given the sum of values and the number of nodes of it's left and right sub-trees ?
Use depth first search to recursively find the solution for the children of a node then use their solutions to compute the current node's solution.
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Yes, tree-based DFS problems like Maximum Average Subtree are common in technical interviews at major tech companies. They test understanding of tree traversal, recursion, and aggregating information across subtrees.
A binary tree combined with recursion (DFS) is the most suitable structure for this problem. The recursion stack helps aggregate subtree sums and node counts while traversing the tree in postorder.
The optimal approach uses a DFS postorder traversal to compute the sum and size of every subtree. With these values, the average can be calculated at each node and compared with a global maximum. This ensures each node is processed once, making the algorithm efficient.
Postorder traversal processes the left and right children before the parent node. This allows the algorithm to know the total sum and size of both subtrees before computing the average for the current node.