AI Model Key Matrix to Tree Transformation
Given a matrix representing usage statistics of keys managed in various AI models over time, transform this matrix data into a tree structure. Each cell in the matrix is labeled with m[i][j] where i corresponds to a specific AI model and j to a time unit. Each cell contains a count of key usages. Your task is to construct a binary search tree (BST) where each node represents a unique key usage count that occurs in the matrix. The BST should be constructed by inserting matrix elements row-wise.
[ [ 1, 2, 3 ], [ 2, 3, 4 ] ]
Explanation. The tree starts with 1, then 2 is added as the right child of 1 because 2 > 1, and 3 follows in the right subtree, etc.
[ [ 5, 3, 9 ], [ 1, 2, 2 ] ]
Explanation. Starting with 5 as the root, with 3 and 9 as children sorted as per BST rules, followed by 1 under 3, and multiple 2s showing handling of duplicates.
Follow-up: Could you optimize the insertion process if the matrix elements are partially pre-sorted? What would be the implications of having duplicate key usage counts in terms of the tree structure and how might you handle them?
1. Each row in the matrix will have the same number of columns.\n2. All integers in the matrix will be non-negative.\n3. The resulting tree must adhere to the properties of a binary search tree.
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