B) (10 pts) Suppose you have an algorithm that performs T(n)...

b) (10 pts) Suppose you have an algorithm that performs $T(n) = 10n^2$ arithmetic operations on input of size $n$. This algorithm runs on two different servers with the following capabilities: Server 1 performs 1000 arithmetic operations per second, while Server 2 is a thousand times faster. What is the largest value of $n$ that can be handled by each server in 1 hour?

Transcript

00:01 Okay, so what is the largest end for which one can solve within a minute using an algorithm which each operation carries out in 10 to the minus 12 seconds? so what this means is that one operation, one operation is carried out in 10 to the minus 12 seconds.

00:19 So we first want to calculate, well first let's just change to seconds.

00:25 So it's a change to seconds, we're just times 10 to the 12 on both sides.

00:28 So 10 to the 12 operators in one seconds and we want it in minutes so it times each side by 60.

00:37 So this is 60 times by 10 to the 12 or six times by 10 to the 13 operations in 60 minutes, which is just one.

00:48 Oh so 60 seconds, which is just one minute.

00:54 So we have this many operations and the first part all we really need to to do is we just need to solve log of log n is equal to six times by 10 to the 13.

01:11 So to solve this, we just have to use our basic log laws and we get log.

01:16 This is based two.

01:18 So log base two of n is equal to two to the six times by 10 to the 13.

01:23 And we use the log laws again.

01:25 Just give you two to the two to the six to the ten times by 13.

01:33 Now for b, we have log n is equal to 6 times by 10 to the 13.

01:40 I write 60 times of 10 to the 12 because that's what the answers use.

01:45 So once again, we just use our basic log laws.

01:47 This just gives you 2 to the 60 or n is equal to times by 10 to 12.

01:53 C, log n squared is equal to 60 times like 10 to the 12.

02:00 We take square root, so log of n is equal to 6 times by 10 to the 12.

02:03 Is equal to square root of 60 times by 10 to the 12...

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