Question

If a list contains ’n’ number of elements and all the elements are by default sorted in ascending order, how many comparisons will be required during 1^st pass of bubble sort to arrange the list in ascending order?

• A. 0
• B. 1
• C. n - 1
• D. n

Answer 1

The Correct Option is C

In the Bubble Sort algorithm, during each pass, the algorithm compares adjacent elements and swaps them if they are in the wrong order. The first pass involves making comparisons across all the elements in the list except for the last one. This is because after the first pass, the largest element is guaranteed to be in its correct position at the end of the list.

Let's consider a list with 'n' elements arranged in ascending order. 

• During the 1^st pass, the algorithm will compare the 1^st element with the 2^nd, the 2^nd with the 3^rd, and so on, up to the (n-1)^th with the n^th element.
• Therefore, in the 1^st pass, there will be a total of (n-1) comparisons.

Thus, the number of comparisons required during the 1^st pass of bubble sort on a list of 'n' elements is n - 1.

Answer 2

The number of comparisons required during the first pass of bubble sort on an already sorted list is n - 1.

Additional Context:

• Bubble Sort Mechanics:
  • Always performs n-1 comparisons in first pass
  • Compares adjacent elements (i vs i+1)
  • No swaps occur in already sorted list
• Optimization Potential:
  • Can terminate early if no swaps occur
  • Still requires full first pass verification
• Example with n=4:
  • Comparisons: [0:1], [1:2], [2:3] → 3 total
  • No swaps needed for [1,2,3,4]
• Time Complexity:
  • Best case (sorted): O(n) comparisons total
  • First pass always requires n-1 comparisons

Correct Answer: (3) n - 1.