Question

The best-time complexity for insertion sort is _____________.

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

Answer 1

The best-time complexity for insertion sort is O(n), which occurs when the input is already sorted since each element will only compare once with the one before it without needing to move.

Step-by-step explanation:

The best-time complexity for insertion sort is O(n). Insertion sort is an algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, the algorithm provides excellent performance for small or mostly sorted datasets.

The best-case scenario for insertion sort occurs when the input list is already sorted. In this case, the time complexity is O(n), since each element will only need to be compared once with the element before it, and no actual insertions will need to take place as each element is already in its correct position. Conversely, the worst-case time complexity is O(n2) when the input list is sorted in reverse order, which would require each element to be compared with all the other elements already sorted in the list.