Which statement about sorting algorithms is true?

Which statement about sorting algorithms is true?

• A. Bubble sort runs in O(n log n); Merge sort runs in O(n^2).
• B. Bubble sort runs in O(n^2) time; Merge sort runs in O(n log n) time.
• C. Bubble sort is O(n); Merge sort is O(n).
• D. Bubble sort is O(n log n); Merge sort is O(n log n).

Answer: (B)

Understanding how time grows with input size is key here. Bubble sort compares adjacent pairs and swaps them as needed, which on average involves many passes through the list. This leads to roughly proportional to n^2 operations, so its time complexity is O(n^2). Merge sort, on the other hand, splits the list in half repeatedly and then merges sorted halves. The divide-and-conquer approach produces about log2(n) levels of work, and each level processes all n elements, giving O(n log n) time overall. So the statement that bubble sort is O(n^2) and merge sort is O(n log n) matches how these algorithms behave. The other options mix up the growth rates, as they assign O(n) or swap the complexities between the two algorithms.

Understanding how time grows with input size is key here. Bubble sort compares adjacent pairs and swaps them as needed, which on average involves many passes through the list. This leads to roughly proportional to n^2 operations, so its time complexity is O(n^2). Merge sort, on the other hand, splits the list in half repeatedly and then merges sorted halves. The divide-and-conquer approach produces about log2(n) levels of work, and each level processes all n elements, giving O(n log n) time overall. So the statement that bubble sort is O(n^2) and merge sort is O(n log n) matches how these algorithms behave. The other options mix up the growth rates, as they assign O(n) or swap the complexities between the two algorithms.