Merge Sort

Merge Sort is a highly efficient, stable sorting algorithm that uses a divide-and-conquer strategy to sort an array or list. It works by repeatedly dividing the array into smaller subarrays until each subarray contains a single element, then merging these subarrays back together in sorted order.

1. Basic Concept:
   • Divide the array into two halves recursively
   • Sort each half independently
   • Merge the sorted halves back together
2. Key Features:
   • Stable sorting algorithm
   • Predictable performance
   • Works well for linked lists
   • Parallelizable
   • External sorting
3. Key Advantages:
   • Guaranteed O(n log n) time complexity
   • Stable sorting (maintains relative order of equal elements)
   • Efficient for large datasets

Complexity Analysis of Merge Sort

Merge Sort provides consistent performance across all cases:

• Time Complexity: O(n log n) for all cases
  • Best Case: O(n log n)
  • Average Case: O(n log n)
  • Worst Case: O(n log n)
• Space Complexity: O(n)
  • Requires additional space proportional to input size
  • Not in-place sorting algorithm

When to Use Merge Sort:

• When stable sorting is required
• When dealing with linked lists
• When predictable performance is needed
• When external sorting is required
• When parallel processing can be utilized

Implementation Tips:

• Ensure sufficient memory is available
• Consider using insertion sort for small subarrays
• Can be optimized for specific data types
• Useful for sorting linked lists with O(1) extra space
• Maximum recommended array size: Any (scales well with size)