Question :
a) Suppose that a particular algorithm has time complexity T(n) = 3 x 2n, and that executing an implementation of it on a particular machine takes t seconds for n inputs. Now suppose that we are presented with a machine that is 64 times as fast. How many inputs could we process on the new machine in t seconds?
b) Suppose that another algorithm has time complexity T(n) = n2, and that executing an implementation of it on a particular machine takes t seconds for n inputs. Now suppose that we are presented with a machine that is 64 times as fast. How many inputs could we process on the new machine in t seconds?
c) A third algorithm has time complexity T(n) = 8n. Executing an implementation of it on a particular machine takes t seconds for n inputs. Given a new machine that is 64 times as fast, how many inputs could we process on the new machine in t seconds?