Suppose that the splits at every level of quick sort are in the proportion 1 - to , where 0 < 1/2 is a constant.

Suppose that the splits at every level of quick sort are in the proportion 1 - α to α, where 0 < α ≤ 1/2 is a constant. Show that the minimum depth of a leaf in the recursion tree is approximately - lg n/ lg α and the maximum depth is approximately -lg n/ lg(1 - α). (Don't worry about integer round-off.)