Present an adversary argument as a lower bounds proof to show that n comparisons are necessary in the worst case when searching for an element with value X (if one exists) from among n elements....

Present an adversary argument as a lower bounds proof to show that n comparisons are necessary in the worst case when searching for an element with value X (if one exists) from among n elements.

Section 15.6 claims that by picking a pivot that always discards at least a fixed fraction c of the remaining array, the resulting algorithm will be linear. Explain why this is true. Hint: The Master Theorem (Theorem 14.1) might help you.