Assume that we use bubble sort to sort n distinct elements in ascending order. when does the best case of bubble sort occur?

General
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assume that we use bubble sort to sort n distinct elements in ascending order. when does the best case of bubble sort occur?

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Assume that we use bubble sort to sort n distinct elements in ascending order. When does the best case of bubble sort occur?

Answer:
The best case scenario for the Bubble Sort algorithm occurs when the input list is already sorted in ascending order. In this case, Bubble Sort makes a single pass through the list to confirm that no elements need to be swapped, thus minimizing the number of operations required.

Solution By Steps:

  1. Bubble Sort Basic Principle:

    • Bubble Sort works by repeatedly stepping through the list to be sorted, comparing each pair of adjacent items and swapping them if they are in the wrong order.
    • The process continues until a pass through the list is made without any swaps, which indicates that the list is sorted.

  2. Best Case Scenario Explanation:

    • Already Sorted List: The best case for Bubble Sort occurs when the input list is already sorted in ascending order. For example, if the input list is [1, 2, 3, 4, 5], no swaps will be needed.
    • During each pass, the algorithm checks the adjacent elements, and since all elements are already in the correct order, the algorithm quickly recognizes that no further passes are necessary.

  3. Operational Analysis for Best Case:

    • In the best case scenario, Bubble Sort makes O(n) comparisons where n is the number of elements in the list.
    • Since no swaps are needed, the algorithm exits after the first pass through the list, resulting in an optimal performance.

Let’s demonstrate with a sorted list example:

Example: Sorted List [1, 2, 3, 4, 5]

  • First Pass:
    • Compare 1 and 2: No swap needed.
    • Compare 2 and 3: No swap needed.
    • Compare 3 and 4: No swap needed.
    • Compare 4 and 5: No swap needed.

After completing the first pass, the algorithm recognizes that no swaps were performed, and hence, the list is already sorted. Thus, Bubble Sort terminates.

Final Answer:
The best case of Bubble Sort occurs when the input list is already sorted in ascending order. In this scenario, the algorithm performs O(n) comparisons and 0 swaps, making it the most efficient case for Bubble Sort.