The Counting Coins problem is to count to a desired value by choosing the least possible coins and the greedy approach will force the algorithm to pick the largest possible coin. If we are provided coins of GH₵ 1, 2, 3 and 7 outline the procedure for counting the following coins based on the Greedy Algorithm. i. GH₵ 40 ii. GH₵ 27

Another recursive algorithm is applied to some data A = (a₁, ..., am) where m = 2* (i.e. 2, 4, 8,16 ...) where x is an integer ≥ 1. The running time T is characterised using the following recurrence equations: T(1) = c when the size of A is 1 T(m) = 2T (2) + c otherwise Determine the running time complexity of this algorithm.

Consider the following recursive algorithm Algorithm Q(n)// Input: a positive integer nif n == 1 return 1else return Q(n-1)+2*n-1 1) Set up a recurrence relation for this function’s value and solve it to determine what this algorithm computes. 2) Setup a recurrence relation for the number of multiplication made by this algorithm and solve it to find the total number of multiplications that are executed.

1. Determine the running time of the following algorithm. Write summations to represent loops and solve using bounding. Be sure to show work on both the upper bound and lower bound, justify the split, and check that the bounds differ by only a constant factor. Use asymptotic notation to write the answer. Func1(n) 1 2 3 4 5 6 7 8 9 10 11 S← 0; for i ←n to n² do for j← 1 to i do for k9n to 10n² do for mi to k end end end return (s); end s+s + i- j + k −m;