Question

The worst-time complexity for bubble sort is _____________.

A. O(1)
B. O(logn)
C. O(n)
D. O(nlogn)
E. O(n*n)

Answer 1

The worst-case time complexity for bubble sort is O(n*n), which happens when the array to be sorted is in reverse order, requiring the maximum number of comparisons and swaps.

Step-by-step explanation:

The worst-case time complexity for bubble sort is O(n*n). This scenario occurs when the array is in reverse order, and each element needs to be compared and swapped with every other element in the list. In each pass through the array, bubble sort compares adjacent pairs of elements and swaps them if they are in the wrong order. The process repeats until no swaps are needed, which means the list is sorted.

Let's consider an array of n elements. In the first pass, bubble sort makes n-1 comparisons, in the second pass n-2, and so on, until only one comparison is made in the final pass (n-(n-1)). Therefore, the total number of comparisons is (n-1) + (n-2) + ... + 1, which is the sum of the first n-1 integers. This sum can be expressed as n*(n-1)/2, which simplifies to O(n*n) when we drop constants and lower-order terms.