In bubble sort, how many passes are needed to guarantee the list is sorted?

Question

BlackTom AI · Accepted Answer

When analyzing how many passes bubble sort needs to guarantee the list is sorted, it's helpful to recall how bubble sort works: in each full pass, the largest unsorted element "bubbles up" to its correct position at the end of the list. After the first pass, the last element is in its final position; after the second pass, the last two elements are in place, and so on.

Option: n²
This would imply a quadratic number of passes regardless of the input, which is far from the standard behavior. Bubble sort does not require n² passes in the general case; the number of passes is tied to the length of the list, not to a quadratic factor. So this choice overstates the requirement.

Option: log n
A logarithmic number of passes would be too few to guarantee that all inversions are resolved in the worst case. Since each pass can fix at most one new position at the end, you cannot guarantee sorted order with only log n passes for arbitrary input. This undercounts the necessary passes.

Option: 2n
Doubling the length does not align with the well-known guarantee. While some algorithms have runtimes proportional to n or n log n, bubble sort’s classic worst-case guarantee is linear in the number of passes, not a multiple like 2n. This overcounts without reflecting the precise bound.

Option: n/2
Separating a fractional or sublinear number of passes from a list length does not fit the standard guarantee. With insufficient passes, some elements may remain out of order in the worst case. This choice also underestimates the needed passes for certain inputs.

Option: 1
One pass cannot guarantee a fully sorted list in general. A single pass places the largest element at the end, but many smaller elements can still be out of order relative to each other, so this underestimates the requirement for sorting the entire list.

Option: n - 1
This matches the classic guarantee for bubble sort. In the worst case, you need as many passes as the length of the list minus one to ensure every element has had the opportunity to move to its correct position, because each pass fixes at least one element at the end. Conceptually, after the first pass you settle the last position, after the second pass you settle the last two positions, and so on, culminating in n - 1 passes being sufficient to guarantee full sorting in the worst case.

In bubble sort, how many passes are needed to guarantee the list is sorted?单项选择题

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