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Merge Sort and Complexity

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Your question is Merge Sort and Complexity. Start with the requirements on the right.

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Problem

DMI services may need predictable ordering when sorting records displayed in a digital service workflow. Implement a stable merge sort that orders records by a specified field without using Python's built-in sorting functions.

Formal Specification

Implement sort_records(records, field), where records is a list of dictionaries and field is a string containing a key present in every record. Return a new list sorted in ascending order by record[field].

The algorithm must be stable: if two records have equal field values, they must remain in their original relative order. Do not mutate records, call sorted, or call .sort().

Use either recursive divide-and-conquer or an iterative bottom-up design. Explain why merge sort has O(n log n) time complexity and O(n) auxiliary space complexity.

Constraints

  • 0 <= len(records) <= 10^5
  • Every record contains field
  • Field values are mutually comparable using <=
  • Record dictionaries may contain additional fields
  • Do not use sorted or list.sort

Function Signature

def sort_records(records, field):
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