Final answer:
To sort an array of binary digits 0 and 1, one can use common sorting algorithms such as Bubble sort, Selection sort, Insertion sort, or Merge sort. However, a linear time counting sort approach is more efficient for binary arrays. It involves counting the frequency of 0s and 1s and then overwriting the original array with sorted 0s and 1s.
Step-by-step explanation:
A student has asked how to sort an array of binary digits 0 and 1 using various sorting algorithms. Sorting an array of binary digits can be efficiently performed by any comparison-based sorting algorithm, such as Bubble sort, Selection sort, Insertion sort, or Merge sort. However, because the array only contains two distinct elements, there are more optimal specialized algorithms that can sort the array in linear time.
To sort the binary array, one could also use a counting sort approach, where we simply count the number of 0s and 1s and then overwrite the original array with the sorted sequence of 0s followed by 1s. This approach is more efficient for binary arrays because it sorts in linear time, i.e., O(n), where n is the length of the array.
Here are the steps for a simple linear time sorting:
Initialize two variables, say zeroCount and oneCount, to 0.
Traverse the array and increment zeroCount when a 0 is encountered and oneCount when a 1 is encountered.
After counting, overwrite the first zeroCount elements with 0s and the remaining oneCount elements with 1s.
Nevertheless, if one is required to use a traditional sorting algorithm, all of the aforementioned algorithms (Bubble sort, Selection sort, Insertion sort, Merge sort) can be used to sort a binary array, but their performance will be less optimal in comparison to counting sort.