Optimize merge sort, quick sort, and knapsack algorithms

[DhruvrajSinhZala24]

Summary

This PR optimizes three algorithm implementations with bug fixes, performance improvements, and code quality enhancements.

Changes

1. sorts/merge_sort.py - Fix O(n2) merge performance

• Bug: The merge() helper used left.pop(0) and right.pop(0), which are O(n) operations on Python lists, degrading overall sort complexity from O(n log n) to O(n2 log n).
• • Fix: Replaced with index-based two-pointer traversal for O(n) merge.
• • Added type hints and comprehensive doctests (12 tests).

2. sorts/quick_sort.py - Fix input mutation & improve pivot selection

• Bug: collection.pop(pivot_index) mutated the caller's original list - a hidden side effect.
• • Fix: Eliminated pop() entirely; uses list comprehensions on unmodified input.
• • Replaced random pivot with median-of-three pivot selection with three-way partitioning.
• • Added type hints and doctests (16 tests), including a test verifying the original list is not mutated.

3. dynamic_programming/knapsack.py - Remove global state & add space-optimized variant

• Bug: mf_knapsack() relied on a global f table - fragile and not thread-safe.
• • Fix: Memoization table now passed as explicit parameter (auto-created when None).
• • Added full type hints and doctests to all functions.
• • Added new knapsack_optimized() function using O(W) space via 1-D rolling array.

Verification

• All 45 doctests pass across the 3 files.
• • ruff check - 0 issues.
• • black formatting - clean.

[algorithms-keeper]

Closing this pull request as invalid

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