Sorting Algorithms with Minimum Swap Operations

When the swap operation is very costly, we need to choose a sorting algorithm that minimizes the number of swap operations. Among the given options, the preferred sorting algorithm is Selection Sort. Let’s see why.

Selection Sort

Selection Sort is a simple sorting algorithm that works by repeatedly finding the minimum element from the unsorted part of the array and putting it at the beginning. It has the following steps:

- Find the minimum element in the unsorted part of the array.
- Swap it with the first element of the unsorted part.
- Move the boundary of the sorted part one element to the right.

Advantages of Selection Sort

- Selection Sort performs the minimum number of swap operations among all the comparison-based sorting algorithms.
- It has a time complexity of O(n^2) which is better than some other sorting algorithms like Bubble Sort.

Disadvantages of Selection Sort

- Selection Sort has a time complexity of O(n^2) which is not efficient for large arrays.
- It does not perform well if the array has many duplicate elements.

Comparison with Other Sorting Algorithms

Heap Sort: Heap Sort is a comparison-based sorting algorithm that uses a heap data structure to sort an array. It has a time complexity of O(n log n) which is better than Selection Sort. However, Heap Sort performs more swap operations than Selection Sort, which makes it less suitable when swap operations are very costly.

Insertion Sort: Insertion Sort is a simple sorting algorithm that works by repeatedly inserting an element from the unsorted part into its correct position in the sorted part. It has a time complexity of O(n^2) which is the same as Selection Sort. However, Insertion Sort performs more swap operations than Selection Sort, which makes it less suitable when swap operations are very costly.

Merge Sort: Merge Sort is a comparison-based sorting algorithm that uses a divide-and-conquer strategy to sort an array. It has a time complexity of O(n log n) which is better than Selection Sort. However, Merge Sort performs more swap operations than Selection Sort, which makes it less suitable when swap operations are very costly.

Conclusion

When swap operation is very costly, the preferred sorting algorithm is Selection Sort because it performs the minimum number of swap operations among all the comparison-based sorting algorithms. However, if the array is very large or has many duplicate elements, other sorting algorithms like Heap Sort or Merge Sort may be more suitable despite performing more swap operations.