AI Model Key Matrix to Tree Transformation

MatrixSimulationTree

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.

Example 1

Input

Output

Root: 1, Left Child: null, Right Child: 2 (as per BST rules), Right Child of 2: 3, and so forth

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.

Example 2

Input

Output

Root: 5, Left Child of 5: 3, Right Child of 5: 9, Left Child of 3: 1, Right Child of 1: 2, Right Child of 2: another 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?

Constraints:

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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