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AsSuule cowputer Carry Oult Ou elemeutary operation every 10-J secouds (ie: Ouc every millisecond) An algorithm has complexity function of T(n) = 0.In' 4n] 50n...

Question

AsSuule cowputer Carry Oult Ou elemeutary operation every 10-J secouds (ie: Ouc every millisecond) An algorithm has complexity function of T(n) = 0.In' 4n] 50n . How long will it take the computer T this algorithm with an input of size n = 732 Couvert your Alsweer t0 show appropriate/reasonable uits Of time for the maguitude of the Dumber.

AsSuule cowputer Carry Oult Ou elemeutary operation every 10-J secouds (ie: Ouc every millisecond) An algorithm has complexity function of T(n) = 0.In' 4n] 50n . How long will it take the computer T this algorithm with an input of size n = 732 Couvert your Alsweer t0 show appropriate/reasonable uits Of time for the maguitude of the Dumber.



Answers

How much time does an algorithm take to solve a problem of size $n$ if this algorithm uses $2 n^{2}+2^{n}$ operations, each requiring $10^{-9}$ seconds, with these values of $n ?$
$$
\begin{array}{lllll}{\text { a) } 10} & {\text { b) } 20} & {\text { c) } 50} & {\text { d) } 100}\end{array}
$$

So we have the input. He is prime our ISS primitive food Clematis All right. Of sapi A is a positive. Did Chirchir uh so I in zp So now we know that he is a discrete logarithms off a module api when r e But yeah, this equals two a with he is in the range zero close to bless that he wants to a less than in close to p minus one. Okay, so now less us vowing our power to the k mont p four k this equal to zero all the way to P minus one until we obtain our K mart p equals A. If this condition is true, we would then return the value K. We understand the basic structure of dough only gonna write down our algorithm. So we create a four loop for eyes equals zero to pain line This one then Italy of we assign a B B A b values. When are I mud? He would be It was too would be assigned to be. So we know that if a equals b, then we would return our value. I and that's our code

Okay, So for this question, we have a series of runtime orders and we want to see what happens when we increase it by just one. So, yeah, it was increasing the time. So for a we have Logan. So what we want to see it won't want to stay the difference between used in plus one subtracted by. So this is the time when we use in plus one in court. This is the time that we use one where we have an import. So just using some basic love laws. This is just log off and just want to end. It's just love off one plus one everything. Now what we know is that once the end is always going to be greater than what better than or equal to one. So then and it's always been regretting to one. So one everything is always going to lessen or what? So then this is equal to log off one by one, which is global shoot on level two, which is just less than one. So therefore it's going to be less than one millisecond being one big millisecond be we have 100. And so we do the same thing where we do 100 times I n plus one subtracted by 100 is equal to 100 I'll spot 100 minus 103 she cancels out. So you just left with 100 milliseconds. Si ence quit. We have n plus one squared Mars by in spread expanding the first time out we have ends with plus by shooting in Passport one. So track in squared, which is just shoot in last one. So it's to impress one another sentence gate and here with the same thing and plus by one here said Fact about and cute and expanding you're cuter. You have in cute plus what three ends with us by three investment. Once attractive and cute, Theseus Chantal's three ends with us about three and plus one now for E, too. And for this question, just something a bit weird, because if we do it this way, we have to end fast by one subject to, and you can't do too much with this. You can be a bit tricky and try to get some locals, but another easy way to do this is instead we compare the ratio times so we can have the ratio between two n plus one of the to end. So then this is not to be true to the end plus what one must end, which is to So what this means is that the time it takes when you jump from one, actually bubbles. In this case, the extra time is additive. But in this case, the time is actually more complicated. So if we have to in squid so for this question would do the same trick needed here. So we have to to the end plus one squared, subtract it by two and spread which is two and squared plus work two in one over to to the end square was just churches too and possible one. So the time isn't multiply by this number finally g, we have in factorial so once again we do the end plus one facto over in that soil trick Factorial Sze is by definition in 1st 1 That's what end doesn't end was my one plans by endless but to follow that will lead to one end to the in laws for one and one sensory bubble bubble which one? So this is just the definition of factory ALS these castles and cancels. So that was n plus one. So once again, the time requires multiple multiple ticketed by a factor in plus one.


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