The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm.  Algorithm Euclid(a,b) Require: a, b ≥ 0 Ensure: a = GCD(a, b)     while b ̸= 0 do         t ← b         b ← a mod b         a ← t end while return a We want to estimate its worst case running time using the big-Oh notation. Assuming the Euclidian division of two integers of n bits is executed in O(n^2), give a big-Oh notation of the worst-case running time of the algorithm Euclid.

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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.