

  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.

  $ sleep 10 Waiting for approval... in current dir


 ┌────────────────────────────────────────────────────────────────────────────────────────────────┐
 │ $  sleep 10 in .                                                                               │
 └────────────────────────────────────────────────────────────────────────────────────────────────┘
 ┌────────────────────────────────────────────────────────────────────────────────────────────────┐
 │ Run this command?                                                                              │
 │ Not in allowlist: sleep 10                                                                     │
 │  → Run (once) (y)                                                                              │
 │    Add Shell(sleep) to allowlist? (tab)                                                        │
 │    Run Everything (shift+tab)                                                                  │
 │    Skip (esc or n)                                                                             │
 └────────────────────────────────────────────────────────────────────────────────────────────────┘


