1. Write a program in C++ which implements the two algorithms prefixAverages1, and prefixAverages2 from Section 1.4 in the textbook (and also provided at the end of this document). 2. Perform careful experimental analysis of their running times by doing the following: a. For each algorithm, choose at least 5 appropriate values for n, where n is the input array size, and determine how long it takes to run in microseconds. Please note the following: . One good strategy is to grow the input size by repeated doubling (e.g 200000,400000,800000, etc). If your timings are erratic (e.g. Os or there is no clear increase in time with respect to input size), try choosing larger values for n. You are not required to use the same values of n for both algorithms. . b. Plot the running times obtained in part (a) as a function of n as scatter plots on a linear scale for each algorithm. Algorithm prefixAveragesi (x): Input: An n-element array X of numbers. Output: An n-element array A of numbers such that A[i] is the average of elements X(O).....X[i]. Let A be an array of numbers. for i = 0 to 1-1 do 40 for jo to i do a +a+X[j] A[i] -- a/(1+1) return array A Algorithm 1.14: Algorithm prefixAverages1. Algorithm prefixAverages2(x): Input: An n-clement array X of numbers. Output: An n-element array A of numbers such that A[ij is the average of elements XO),..., X[1. Let A be an array of n numbers. S+0 for i 0 to 1-1 do 5+5+X[] Ai -- 5/(i+1) return array A Algorithm 1.15: Algorithm prefixAverages2