Consider the following array:{16, 4, 9, 3, 18, 14, 15}For the array, if A is the number of comparisons in bubble sort and B is the number of comparisons in selection sort, thena)A = Bb)A Bc)A

Question

Consider the following array:{16, 4, 9, 3, 18, 14, 15}For the array, if A is the number of comparisons in bubble sort and B is the number of comparisons in selection sort, thena)A = Bb)A > Bc)A < Bd)A and B are incomparableCorrect answer is option 'C'. Can you explain this answer?

Answer

Understanding Bubble Sort and Selection Sort Comparisons
To determine the relationship between the number of comparisons made by Bubble Sort (A) and Selection Sort (B), we need to analyze how each algorithm operates.
Bubble Sort Comparisons (A)
- In Bubble Sort, adjacent elements are compared and swapped if they are in the wrong order.
- The algorithm makes multiple passes through the array until no swaps are needed.
- For an array of size n, the worst-case scenario involves n-1 comparisons for the first pass, n-2 for the second, and so on, leading to a total of (n-1) + (n-2) + ... + 1 comparisons.
- This results in A = n(n-1)/2 comparisons in the worst case.
Selection Sort Comparisons (B)
- In Selection Sort, the algorithm divides the array into a sorted and an unsorted region.
- It repeatedly selects the minimum element from the unsorted region and moves it to the sorted region.
- The number of comparisons for each pass remains constant at n-1 for the first pass, n-2 for the second, etc., leading to B = n(n-1)/2 comparisons as well.
- However, Selection Sort makes exactly the same number of comparisons regardless of the array's order, which is n(n-1)/2.
Comparison of A and B
- For the given array {16, 4, 9, 3, 18, 14, 15}, both algorithms will have the same number of comparisons in the worst case.
- Thus, A = B.
Conclusion
- The correct answer is option 'C': A < b='' is='' incorrect='' as='' they='' yield='' the='' same='' number='' of='' />
- Therefore, both A and B are equal, leading to a conclusion that they are comparable, but A does not strictly exceed or fall short of B.

Answer

If there are n elements in the list, then (n - 1) passes are required to compare the elements in the first pass.

Thus, total number of comparisons (A) in bubble sort for a list of N elements = n - 1 = 7 - 1 = 6

In selection sort, selecting the lowest element requires n - 1 + n - 2 + n - 3 + ... comparisons for n elements.
B =

= 21
Hence, A < B

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