please answer all questions (problem 1 and problem 2 full) Thank You!

Sure! I'll post the other question seprately but for this post can you answer the first one? Thank you!

Problem 1. (20 points) Solve the following recurrence equations and give the solution in 0 notation; show all the steps in the derivation of the solution to get full credit. Assume T(n) is O(1) for sufficiently small n. DO NOT use the Master Theorem 5.6 of the text book. (a) T(n) = 27 (n-1) + 3n? (b) T(n) = 9T(n/2) +n assuming n is a power of 2. ) T(n) = 27(n) +logn, assuming n=22for some k > 0 Problem 2. (10 points) We are interested in measuring the time complexity of executing a sequence of n invocations of the following function with the array A initially containing all o's. Function increment(A) Input: A[0..m-1) is an array of 0-1 bits representing a binary counter Output: A after its value incremented by 1 modulo 2 while i