Rucurrence running time

Give asymptotic upper and lower running time bounds for T(n) for each of the recurrences. Assume that T(n) is constant for n <= 2. Make bounds as tight as possible, and justify solutions. a) T(n) = 2*T(n/2) + n^3 b) T(n) = T(9n/10) + n c) T(n) = 16*T(n/4)+n^2 d) T(n) = 7*T(n/3) + n^2 e) T(n) = 7*T(n/2) + n^2

Solving a recurrence

Using the same method in attachment #1, solve the recurrence in attachment #2. I increased the bid to 6 credits, but also could you repost the Rucurrence running time problem (MasterTheorem.doc) in PDF format (as well as the solution to this problem) because the .doc says it is corrupt when I try to open it.

Design the unit testing framework for the ATM machine

Design the unit testing framework for the ATM machine in the style of JUnit Test Infected: with the following functionalities: check balance, deposit cash, and withdraw cash. The framework could be developed in pseudo-code

DATA COMMUNICATIONS QUESTION - MULTIPLEXING

Suppose I have a multiplexer that is connected to a high-speed digital transmission system that can transfer 1,536,000 information bits per second. How many standard voice channels is the high-speed transmission system capable of carrying and how do you figure this out? What is the transmission efficiency of the High-Speed Digital Transmission System if the total number of bits traveling through the system is 1,544,000 bits per second? (Note that the extra bits are used for overhead purposes such as synchronizing the multiplexer and demultiplexer). Again, how do you figure this one out?

Sum of 2 numbers problem: create a O(n log n) algorithm that determines whether or not there exist two elements in S whose sum is exactly z

I need help creating a O(n log n) algorithm that determines whether or not there exists two elements in S whose sum is exactly z. Additionally, the problem indicates that sorting is somehow related to the solution.