  • Uses a queue: enqueue root, then repeatedly dequeue a node and enqueue its children.



  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                                                                 
                                                                                                   


  Planning Shell command

  I need to run a command using the Shell tool, but I have to remember the guidelines that say 
  no
  long-lived commands are allowed. Using sleep 10 is okay, so that gives


  ⬢ Thinking...  40 tokens
 ┌────────────────────────────────────────────────────────────────────────────────────────────────┐
 │ → Add a follow-up                                                               ctrl+c to stop │
 └────────────────────────────────────────────────────────────────────────────────────────────────┘

  Auto · 4.7%
  / commands · @ files · ! shell

