1. This problem asks you to compute worst-case run times of given algorithms (a) Consider the following algorithm r=0; for i in the range [1, n] I for j in the range i, n] for k in the range [1, j-i] r+t; print (r) Derive the run time of the above algorithm (as a function of n). You must formally derive the run-times (merely stating run times or high level explanation of run time do not suffice) (b) Consider the following algorithm. for (i = n; i >=1; i = i/2) for j in range [1, i] Constant Number of Operations Derive the run time of the above algorithm (as a function of n). You must formally derive the run-times (merely stating run times or high level explanation of run time do not suffice)