1. (20 points) SELECT-7. Consider the deterministic selection algorithm SELECT that we saw in case where we divided the n elements into groups of 5, determined the pivot then recursively called SELECT on the appropriate sub-array. Suppose that we modified SELECT of that instead of dividing the n elements into groups of 5, we divided the elements into groups of 7. The rest of the procedure remains the same. Let us call this new algorithm SELECT-7 (a) (1 point) How many groups (in terms of n) will we have when divide the n elements into groups of 7? (b) 1 point) In each group, how many elements are greater than the group median? (c) (1 point) In each group, how many elements are less than the group median? (d)1 point) How many elements (at least) are less than the pivot? (e) (1 point) How many elements (at least) are greater than the pivot? (f) (15 points) Write down and solve the recurrence of SELECT-7 using any method you prefer. Is the running time asymptotically better than the original SELECT algorithm? Explain your