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.

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If an appliance consumes 500 w of power and is left on for 5 hours, how much energy is used over this time period? a. 2.5 kwh b. 25 kwh c. 250 kwh d. 2500 kwh