How many swaps does Selection Sort perform in the worst case?O(n)O(n log n)O(n^2)O(log n)

To determine how many swaps Selection Sort performs in the worst case, we can follow these steps:

1. Break Down the Problem

Selection Sort works by repeatedly selecting the smallest (or largest) element from the unsorted portion of the array and moving it to the sorted portion. In the worst case, we need to consider how many total swaps occur during this process.

2. Relevant Concepts

In Selection Sort:

• For each of the n elements, we need to find the minimum from the unsorted portion.
• After finding the minimum, a swap is made with the first unsorted element.

3. Analysis and Detail

• The Selection Sort algorithm makes exactly one swap for each pass through the array, regardless of the initial order of elements:
  • The first pass involves n comparisons and one swap.
  • The second pass involves n-1 comparisons and one swap.
  • This pattern continues until the second last element, resulting in n-1 passes.

Thus, the total number of swaps made during the sorting process will be:

$\text{Total Swaps} = 1 + 1 + 1 + \ldots + 1 \quad (\text{for each of the } n-1 \text{ passes}) = n-1$

4. Verify and Summarize

The total number of swaps in the worst case for Selection Sort is constant, equal to n-1 swaps for an array with n elements. This does not grow with the complexity of the input array, thus it exhibits a complexity of O(n) in terms of swaps.

Final Answer

The number of swaps Selection Sort performs in the worst case is O(n).