CSC 345 Section 4.5

Hardware vendor XYZ Corp. claims that their latest computer will run 100 times faster than that of their competitor, Prunes, Inc. If the Prunes, Inc. computer can execute a program on input of size n in one hour, what size input can XYZ's computer execute in one hour for an algorithm whose growth rate is n^2? 100n 10 n+10 n^2​​ 10n^2 ​​ 100 n+100 n 10n 100n^2

10n

Suppose that a particular algorithm has time complexity T(n) = 8n 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? 8n 64 8n^2 ​​ 8 2^n ​​ 64n^2 ​​ 64n n^2 ​​

64n

Suppose that a particular algorithm has time complexity T(n) = n^2 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? 8n 64 8n^2 ​​ 8 2^n ​​ 64n^2 ​​ 64n n^2 ​​

8n

Suppose that a particular algorithm has time complexity T(n) = T(n)=3×2^n 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? 3n n+3 n+6 n^2 ​​ 64n 64 6 3 6n

n + 6