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Tim Sort - Technical Overview

1. Algorithm Description: Tim Sort is a hybrid sorting algorithm derived from Merge Sort and Insertion Sort. It takes advantage of naturally occurring runs (sorted sequences) in data and merges them efficiently.

2. Steps of Tim Sort:

• Break the array into small subarrays (runs) and sort each run using Insertion Sort.
• Merge the sorted runs using a merge function similar to Merge Sort.
• Repeat merging until the entire array is sorted.

3. Time Complexity: O(n log n) in the worst and average case.

4. Space Complexity: O(n) due to the auxiliary arrays used during merging.

5. Stability: Tim Sort is a stable sorting algorithm.

6. Optimizations: Tim Sort takes advantage of pre-sorted data (natural runs), making it efficient for real-world data. It also uses Insertion Sort for small arrays, which is faster for small input sizes.