1.Write a Θ(n) algorithm that sorts n distinct integers, ranging in size between 1 and kn inclusive, where k is a constant positive integer. (Hint: Use a knelement array.) 2.Algorithm A performs 10n 2...

1.Write a Θ(n) algorithm that sorts n distinct integers, ranging in size between 1 and kn inclusive, where k is a constant positive integer. (Hint: Use a knelement array.)

2.Algorithm A performs 10n 2 basic operations, and algorithm B performs 300 ln n basic operations. For what value of n does algorithm B start to show its better performance?

3. There are two algorithms called Alg1 and Alg2 for a problem of size n. Alg1 runs in n 2 microseconds and Alg2 runs in 100n log n microseconds. Alg1 can be implemented using 4 hours of programmer time and needs 2 minutes of CPU time. On the other hand, Alg2 requires 15 hours of programmer time and 6 minutes of CPU time. If programmers are paid 20 dollars per hour and CPU time costs 50 dollars per minute, how many times must a problem instance of size 500 be solved using Alg2 in order to justify its development