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  ┃  # Merge sort explained with complexity analysis                            9,989  2% ($0.00) 
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     - Merge sort is stable (equal elements keep relative order) if merge is implemented 
     carefully (choose left element first on equality).
     - This makes it great when sorting by multiple keys (e.g., sort by last name then by first 
     name).

     Why people use merge sort
     - Guaranteed O(n log n) performance.
     - Stable sort.
     - Works very well for:
       - Linked lists (can be done with little extra memory),
       - External sorting (data too big for RAM; merge chunks from disk).

     Trade-offs
     - Extra memory usage (O(n)) for arrays.
     - Often slower constant factors than quicksort for in-memory arrays in practice (though 
     language/runtime-specific).

     Bottom-up (iterative) variant
     - Instead of recursion, merge subarrays of size 1, then 2, then 4, then 8, etc.
     - Same asymptotic complexity: O(n log n) time, O(n) extra space.
     - Avoids recursion overhead.

     If you want, I can also show:
     1) clean pseudocode, or  
     2) a step-by-step visual trace of the merge pointers on one merge pass.

     ▣  Build · gpt-5.3-codex · 16.3s

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  ┃  Build  GPT-5.3 Codex OpenAI                                                                  
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