Let f(n) be the average number of full nodes in an n-node binary search tree.
a. determine the values of f(0) and f(1).
b. show that for n > 1
f(n)=n−2 /n +1/ n (sum n−1 i=0(f(i)+f(n−i−1)) start at i = 0 end at n-1 for the summation
c. show (by induction) that f(n)=(n−2)/3 is a solution to the equation in part (b), with the initial conditions in part (a).
d. use the results of exercise 4.6 to determine the average number of leaves in an n-node binary search tree.