Design a brute-force algorithm for computing the value of a polynomial (in the image below) at a given point x0 and determine its worst-case efficiency class.   Algorithm BruteForcePolynomialEvaluation(P[0..n], x)  //The algorithm computes the value of polynomial P at a given point x //by the “highest-to-lowest term” brute-force algorithm  //Input: Array P[0..n] of the coefficients of a polynomial of degree n,  // stored from the lowest to the highest and a number x  //Output: The value of the polynomial at the point x  If the algorithm you designed is in O(n^2), design a linear algorithm for this problem.  Is it possible to design an algorithm with a better than linear efficiency for this problem? Why?

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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.