Part A: 1) Implement both the Brute Force and Improved versions of the MCS algorithms. 2) Check the correctness of the algorithms for the following sequences: a. -1, -2, -3, -4,-5, -6 MCS: See notes b. -1, 1,-1, 1,-1, 1 MCS: See notes c. -1, 2, 3, -3,2 MCS: See notes d. 1,-5, 2,-1,3 MCS: 2, -1, 3 e. -2, 2, -2, -2, 3,2 MCS: 3,2 3) Modify both algorithms to record the number of iterations used. Test your modified algorithms on the above examples. 4) Generate 10 random sequences of length 5, 10, 15, ..., 50 each (100 sequences in totals). Record the number of iterations for each sequence. Plot the results (x=length = n, y=iterations) to compare the algorithm's time complexity. Also compare the Brute Force algorithm's iterations with n(n+1)/2 and the Improved algorithm's iterations with n. [Produce 3 plots: Brute vs. Improved, Brute vs. n(n+1)/2 and Improved vs.n]. Part A: 1) Implement both the Brute Force and Improved versions of the MCS algorithms. 2) Check the correctness of the algorithms for the following sequences: a. -1, -2, -3, -4,-5, -6 MCS: See notes b. -1, 1,-1, 1,-1, 1 MCS: See notes c. -1, 2, 3, -3,2 MCS: See notes d. 1,-5, 2,-1,3 MCS: 2, -1, 3 e. -2, 2, -2, -2, 3,2 MCS: 3,2 3) Modify both algorithms to record the number of iterations used. Test your modified algorithms on the above examples. 4) Generate 10 random sequences of length 5, 10, 15, ..., 50 each (100 sequences in totals). Record the number of iterations for each sequence. Plot the results (x=length = n, y=iterations) to compare the algorithm's time complexity. Also compare the Brute Force algorithm's iterations with n(n+1)/2 and the Improved algorithm's iterations with n. [Produce 3 plots: Brute vs. Improved, Brute vs. n(n+1)/2 and Improved vs.n]