a. For the quicksort implementation in this chapter, what is the running time when all keys are equal?
b. Suppose we change the partitioning strategy so that neither i nor j stops when an element with the same key as the pivot is found. What ?xes need to be made in the code to guarantee that quicksort works, and what is the running time when all keys are equal?
c. Suppose we change the partitioning strategy so that i stops at an element with the same key as the pivot, but j does not stop in a similar case. What ?xes need to be made in the code to guarantee that quicksort works, and when all keys are equal, what is the running time of quicksort?