  VIl. (10 points) The recurrence equation )2 )I B) (assuming n is a power of 2), yields, by the substitution method, that πη) . (a) nign (b) n Ign+n (c) Ign (d) Ign+1 (e) None of the above Applying the Master Theorem to VIIl. (10 points) Applying the Master Theorem to the recurrence equation the recurrence equation Yields the result that TIn) is in Yields the result that T(n) is in (a) e(n) (b) e(log n) (c) e(nlogn) (d) e(n2) (e) None of the above (b) Θ(log n) (c) e(nlogn) (e) None of the above IX. (15 points) T/F (a) Both the worst-case and the average-case complexity functions for Binary Search are in (log n). T/F (b) For Sequential Search the best-case complexity function B(n) 0. T/F (c) For Merge Sort the best-case, worst-case, and average-case complexity functions are in e(nlog n). T/F (d) In Merge Sort the maximum number of comparisons required to merge two arrays of size n/2 into an array of size n is (n – 1). T/F (e) A complexity function for an algorithm maps the number of basic operations required for an input of size n into n. Show transcribed image text VIl. (10 points) The recurrence equation )2 )I B) (assuming n is a power of 2), yields, by the substitution method, that πη) . (a) nign (b) n Ign+n (c) Ign (d) Ign+1 (e) None of the above Applying the Master Theorem to VIIl. (10 points) Applying the Master Theorem to the recurrence equation the recurrence equation Yields the result that TIn) is in Yields the result that T(n) is in (a) e(n) (b) e(log n) (c) e(nlogn) (d) e(n2) (e) None of the above (b) Θ(log n) (c) e(nlogn) (e) None of the above IX. (15 points) T/F (a) Both the worst-case and the average-case complexity functions for Binary Search are in (log n). T/F (b) For Sequential Search the best-case complexity function B(n) 0. T/F (c) For Merge Sort the best-case, worst-case, and average-case complexity functions are in e(nlog n). T/F (d) In Merge Sort the maximum number of comparisons required to merge two arrays of size n/2 into an array of size n is (n – 1). T/F (e) A complexity function for an algorithm maps the number of basic operations required for an input of size n into n.