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Good evening, everyone.

I know this would be pretty easy for a lot of you, but I haven't been able to find any information, how to solve things common to this one.

  • For each function f (n) (the complexity of the algorithms) and data n in the table below, determine the time t for which the algorithm will perform the calculations. We assume that the algorithms are processed on a computer capable of performing one million operations per second. You can use approximations in your answers.

I would be really greateful if anybody will explain how to solve it.

n 10 1000 1000000
lg n
n
n lg n
$$n^2$$ $$\frac{1}{10000} seconds.$$
$$2^n $$

I tried, but I'm just not sure what to do. Thank you in advance for any assistance.

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In the second column, plug in $n=10$ into the expressions in the first column to get the number of operations. Then divide by 1000000 operations/second to get the number of seconds. Repeat for the other columns for the other values of $n$.

For the provided example: plugging in $n=10$ into $n^2$ yields $10^2=100$ operations, which takes $\frac{100}{1000000} = \frac{1}{10000}$ seconds.

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