Programs A and B are analyzed and found to have worst-case running times no greater than 150N log2 N and N2, respectively. Answer the following questions, if possible:
a. Which program has the better guarantee on the running time, for large values of N (N > 10,000)?
b. Which program has the better guarantee on the running time, for small values of N (N < 100)?
c. Which program will run faster on average for N = 1,000?
d. Is it possible that program B will run faster than program A on all possible inputs?