1. For sorting problem, there are two categories of algorithms: one sorts by reducing the problem size by one at each step, and the other category of algorithms divides the problem into two smaller problems, solves each smaller problem recursively, and combines the two sorted lists. The first category of algorithms are not optimal and time complexity of these algorithms are O(n^2). Whereas, some of the algorithms in the second category have optimal time complexity. But optimal algorithms are not always fastest. In many cases, if input size is greater than a constant then only algorithm is faster. In this homework problem you have to find the constant. Suppose your are comparing implementations of bubble sort and merge sort algorithms on the same machine. For input size n, bubble sort runs in 10n^2 steps, while the heap sort runs in 640nlog2n (log base 2 NOT 2n) steps. (a) For which values of n bubble sort beats the heap sort? Note that n 1. (b) Explain how you found your answer and show your work