Suppose you have an unsorted array A of n elements and we want to know if A contains any duplicate elements. These elements are integers from the range 1, … , 2n. Tell the asymptotic order T(n) of the worst-case running time for this solution. Try to find the efficient algorithm.

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Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.