Answer :
In computer science, a sorting algorithm is an algorithm that sorts the elements of a list. The most commonly used orders are numeric and lexicographic, ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms that require the input data to be sorted lists, such as search and merge algorithms.
Using Counting Sort takes O(n^2) time because the size of the given range is n^2. Using comparison-based sorts such as merge sort, heapsort, etc. takes O(n Logn) time.
Now the question is how to do it with 0(n)? First, is it possible? Are you sure you want to use the given data? n numbers in the range 0 to n2 – 1?
The idea is to use radix sort. A standard radix sorting algorithm follows.
Suppose the input integer has d digits. A radix sort takes O(d*(n+b)) time. where b is the radix that represents the number. For example, b is 10 in decimal. n2-1 is the maximum possible value, so the value of d is O(logb(n)). So the overall time complexity is O((n+b)*O(logb (n)) , which looks larger than the time complexity of large k comparison-based sorting algorithms. The idea is to change base b. If we set b as n, the value of O(log b(n)) is O(1) and the total time complexity is O(n).
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