

  Shape and performance

  • If the tree is balanced (roughly the same number of nodes on left and right subtrees), the
    height is about \(\log_2 n\), so:
    • Search, insert, delete: \(O(\log n)\) on average.
  • If the tree becomes skewed (like a linked list), height becomes \(O(n)\) and operations
    degrade to \(O(n)\).

  Self-balancing trees (like AVL trees, Red‑Black trees) automatically rearrange themselves on
  insert/delete to keep height near \(\log n\).

  ────────────────────────────────────────

  If you tell me your preferred language (e.g., Python, Java, C++), I can show you a minimal
  binary tree / BST implementation and walk through the code.

                                                                                                   
  Run this shell command: sleep 10                                                                 
                                                                                                   

  I'll run sleep 10 in your repo directory and wait for it to complete.

  The sleep 10 command has completed after pausing for 10 seconds.


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