Consider the following Algorithm: ALGORITHM P(n) //Input a positive integer n i←1 j←0 for k← 1 to n do j←i+ji←j-i return j 1. a) What does this algorithm return when n=1, n=2, n=5? 2. b) What is its basic operation? 3. c) How many times the basic operation executed? 4. d) What is the space cost of the algorithm expressed in big-Theta? 5. e) What is the efficiency class of the algorithm? Show any assumptions you made to arrive at your answer. Indicate whether the efficiency class is constant, linear, quadratic, exponential, etc. in the input size.

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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.