It can be shown that the average number of comparisons
Chapter 7, Problem 7.2.50(choose chapter or problem)
It can be shown that the average number of comparisons made by the quick sort algorithm (described in preamble to Exercise 50 in Section 4.4), when sorting n elements in random order, satisfies the recurrence relation 2 n-l Cn = n + 1 + - L Ck n k = O for n = 1 , 2, ... , with initial condition Co = O. a) Show that {Cn} also satisfies the recurrence relation nCn = (n + I)Cn-1 + 2n for n = 1 , 2, .... b) Use Exercise 48 to solve the recurrence relation in part (a) to find an explicit formula for Cn.
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