The maximum number of swaps that can be performed in the selection sort algorithm is n - 1 , where n is the number of elements in the array. This is because selection sort performs exactly one swap per pass to place the minimum element in its correct position, and there are n - 1 passes in total.
- In the best case , when the array is already sorted, the number of swaps can be zero if the implementation avoids swapping an element with itself. The algorithm still performs all comparisons but no swaps are needed since elements are already in place.
- In the worst case , selection sort performs one swap in each of the n - 1 passes, resulting in n - 1 swaps. This worst-case scenario does not necessarily occur with a fully reversed array but rather with inputs that cause the minimum element to always be found at the last unsorted position, such as a "sine wave" pattern of alternating increases and decreases.
- The average case number of swaps is roughly (n−1)/2(n-1)/2(n−1)/2, as the minimum element tends to be found somewhere in the middle of the unsorted portion on average.
Selection sort is known for minimizing the number of swaps compared to other simple sorting algorithms like bubble sort, which can perform O(n2)O(n^2)O(n2) swaps. Selection sort always does at most n - 1 swaps, even though it performs O(n2)O(n^2)O(n2) comparisons in all cases (best, average, and worst)
. In summary:
Case| Number of Swaps
---|---
Best case| 0 (if no unnecessary swaps)
Average case| Approximately (n−1)/2(n-1)/2(n−1)/2
Worst case| n−1n-1n−1
This behavior makes selection sort useful in scenarios where the cost of swapping is high, as it guarantees a minimal number of swaps regardless of input order
