Problem 3.(20 points) Multiple Choice. Must fll the final answers in the table below Give the big-0 notation for the running time T/N), for each divide and conque equation described below. For example: T(N) 2T(N/2)+NTIN Eacts: 22 4, 2-8, 3229, 3,#27, log 8-3, logr4.2, log 2.1. lega.2.lag,3,1 s O(NlogN) 2. T(N)-27T(N/3) +2.(N^ 2)T(N)e- A. 8 (NIgN) B. 0 (N2) Select Algorithm. There are two algorithms called Alg1 and Alg2 for a problem of size n. Alg1 runs in n microseconds and Alg2 runs in 1On-logion microseconds. Alg1 can be implemented using 10 hours of programmer time. On the other hand, Alg2 requires 40 hours of programmer time. It programmers are paid $50 per hour and CPU time costs $0.002 (2'103) dollar per second Facts: 1 microsecond 10 second, logio(104)4 A problem instance of size 104 will be solved 5000 times using a program algorithm should be chosen for this program based on cost efficiency? Which 4. B. Alg2 C. They are the same .Algi When perform Mergesort to sort the following list: 15, 13,2,7,18, 4,3,6, the last merge operation to produce the final result is to merge A. 15, 13, 2, 7 and 18, 4, 3,6 B. 13, 15, 2, 7 and 4, 18, 3,6 C. 2,7, 13, 15 and 3, 4, 6, 18 D. 2,3,4, 6 and 7, 13, 15, 18 5. 6. What is the time complexity T(n) of the nested loops below? For simplicity, you may 2 for some positive integer k assume that n is a power of 2. That is, n