Add Median of Two Sorted Arrays Algorithm to Divide and Conquer Section

[balaraj74]

📝 Summary

This pull request implements the Median of Two Sorted Arrays algorithm using an efficient divide-and-conquer approach, addressing issue TheAlgorithms#13717.

🎯 What does this PR do?

Adds a new algorithm that finds the median of two sorted arrays in logarithmic time complexity. This is a classic computer science problem that demonstrates the power of the divide-and-conquer paradigm.

📂 Files Added

• divide_and_conquer/median_of_two_sorted_arrays.py - Main implementation with comprehensive documentation

✨ Implementation Highlights

Algorithm Features:

• Time Complexity: O(log(min(m, n))) - Very efficient using binary search partitioning
• Space Complexity: O(1) - Constant extra space
• Type Support: Works with both integers and floating-point numbers
• Edge Cases Handled:
  • One or both arrays can be empty (with appropriate error handling)
  • Arrays of different lengths
  • Negative numbers
  • Duplicate values
  • Odd and even total element counts

How It Works:

The algorithm uses a partition-based approach:

1. Always binary search on the smaller array for efficiency
2. Find the correct partition point where elements on the left are ≤ elements on the right
3. Calculate median based on whether total elements are odd or even

✅ Testing

The implementation includes 10 comprehensive doctests covering:

• ✓ Basic cases (odd/even total lengths)
• ✓ Empty array handling (one empty)
• ✓ Both arrays empty (raises ValueError)
• ✓ Floating-point numbers
• ✓ Negative numbers
• ✓ Duplicate values
• ✓ Significantly different array sizes

All tests pass successfully! ✨

python3 -m doctest divide_and_conquer/median_of_two_sorted_arrays.py -v
# Result: 10 passed and 0 failed

🔗 Related Issue

Closes TheAlgorithms#13717

📚 Code Quality

• ✓ Type hints for all parameters and return values
• ✓ Comprehensive docstring with examples
• ✓ Clear variable names following Python conventions
• ✓ Detailed inline comments explaining the algorithm
• ✓ Follows repository coding standards
• ✓ Snake_case naming convention

🚀 Why This Matters

This algorithm is:

• A fundamental problem in computer science interviews
• Demonstrates efficient divide-and-conquer thinking
• Much more efficient than the naive O(m+n) merge approach
• A great learning resource for the community

🙏 Acknowledgments

Thanks to @devdandekar24 for opening this issue and to the maintainers of TheAlgorithms/Python for maintaining this excellent learning resource!

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Ready for review! Happy to make any adjustments based on feedback. 😊