Aspire Faculty ID #18935 · Topic: UGC NET Computer Science Nov 2020 (Paper II) · Just now
UGC NET Computer Science Nov 2020 (Paper II)

If algorithm A and another algorithm B take $\log_2(n)$ and $\sqrt n$ microseconds, respectively, to solve a problem, then the largest size n of a problem these algorithms can solve, respectively, in one second are ____ and _____.

Solution

One second $=10^6$ microseconds.

For algorithm A:

$\log_2 n \le 10^6$

$n \le 2^{10^6}$

For algorithm B:

$\sqrt n \le 10^6$

$n \le (10^6)^2=10^{12}$

So, the largest sizes are $2^{10^6}$ and $10^{12}$.

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