Question

Which of the following sorting algorithms are best to sort n integers that range in {0, 1, ..., 232-1}?

Select all that are best. You may assume that n <<232.
a) Merge sort
b) Heap sort
c) Quick sort
d) Radix sort
e)Counting sort

Answer 1

The best sorting algorithms to sort n integers that range from 0 to 2^32-1 are Radix sort, Counting sort, and Quick sort. Option c, d, e.

Step-by-step explanation:

The best sorting algorithms to sort n integers that range from 0 to 232-1 are Radix sort, Counting sort, and Quick sort.

Radix sort and Counting sort are both linear-time sorting algorithms, meaning that they have a time complexity of O(n). They are especially efficient when the range of the input values is known and small, in this case, the range is 232-1.

Radix sort has a complexity of O(kn), where k is the number of digits in the largest number. Counting sort has a complexity of O(n+k), where k is the range of the input values. Quick sort has an average-case time complexity of O(n log n) and is efficient for sorting large datasets, despite having a worst-case time complexity of O(n2).

Merge sort and Heap sort are also efficient sorting algorithms, but they have a time complexity of O(n log n), which is not as optimal as the previously mentioned algorithms for the given problem. Option c, d, e.