Question

Assume the following are the exact number of operations performed as a function of the input size n. Suppose you have a computer that can perform 10^25 operations per second, and you need to compute a result in at most an hour of computation. For each of the following algorithms, what is the largest input size n for which you would be able to get the result within an hour? (You need to use external paper to show the calculations required. Failure to do so will be graded in half if the answer is correct. You can also achieve a partial mark if you can demonstrate the correct calculation steps) a) n^5 b) 2^2^n

          Assume the following are the exact number of operations performed as a function of the input size n. Suppose you have a computer that can perform 10^25 operations per second, and you need to compute a result in at most an hour of computation. For each of the following algorithms, what is the largest input size n for which you would be able to get the result within an hour? (You need to use external paper to show the calculations required. Failure to do so will be graded in half if the answer is correct. You can also achieve a partial mark if you can demonstrate the correct calculation steps)

a) n^5

b) 2^2^n

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Assume the following are the exact number of operations performed as a function of the input size n. Suppose you have a computer that can perform 10^25 operations per second, and you need to compute a result in at most an hour of computation. For each of the following algorithms, what is the largest input size n for which you would be able to get the result within an hour? (You need to use external paper to show the calculations required. Failure to do so will be graded in half if the answer is correct. You can also achieve a partial mark if you can demonstrate the correct calculation steps)

a) n^5

b) 2^2^n

Added by James J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Lucas Finney

05/12/2022

Step 1

The maximum number of operations we can perform in an hour is 60 * 10^25. So, we need to find the largest value of n such that n^5 is less than or equal to 60 * 10^25. Show more…

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Assume the following are the exact number of operations performed as a function of the input size n. Suppose you have a computer that can perform 10^25 operations per second, and you need to compute a result in at most an hour of computation. For each of the following algorithms, what is the largest input size n for which you would be able to get the result within an hour? (You need to use external paper to show the calculations required. Failure to do so will be graded in half if the answer is correct. You can also achieve a partial mark if you can demonstrate the correct calculation steps) a) n^5 b) 2^2^n

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Transcript

00:01 So for this problem, we're told that we have a computer that can perform 10 to the power of 25 operations per second.

00:06 And we are trying to figure out what the largest value for n is, such that we can still compute it within an hour.

00:17 So for part a, we have n to the power of five.

00:20 If we think about this, n to the power of five is n times n times n times n times n.

00:29 So we have five operations occurring.

00:34 Five operations per value of n.

00:43 So the maximum number would be equal to 10 to the power of 25 divided by 5.

00:51 And 10 to the power of 25 over 5 would give us just that is going to be equal to one moment here.

01:04 We'd get a value of 2 to the power of 24.

01:08 Then for part b, we have 2 to the power of 2 to the power of n.

01:15 So if we have 2 to the power of n, then that's going to be 2 times 2 times 2 times dot dot dot, n times.

01:24 So it takes n operations to compute 2 to the power of n once, which then means that it would take, or if we're trying to compute 2 to the power of 2, to the power of n.

01:39 It takes n operations just to compute the, just to compute the exponent here.

01:46 Then, once we've computed the exponent, we still need to evaluate this, which would be two times itself two to the power of n times.

01:55 So, this would be n times two to the power of n...

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