# selfas

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f(n) + O(f(n)) = Θ(f(n))

## Related questions

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What is the running time of the following function (specified as a function of the input value)? void Function(int n){ int i=1; int s=1; while(s<=n){ i++; s=s+i; } } $O(n)$ $O(n^2)$ $O(1)$ $O(\sqrt n)$
The asymptotic upper bound solution of the recurrence relation given by $T(n)=2T \left ( \frac{n}{2} \right)+\frac{n}{\lg n}$ is: $O(n^{2})$ $O(n \lg n)$ $O(n \lg \lg n)$ $O(\lg \lg n)$
Among the following asymptotic expressions, which of these functions grows the slowest (as a function of $n$) asymptotically? $2^{\log n}$ $n^{10}$ $(\sqrt{\log n})^{\log ^{2} n}$ $(\log n)^{\sqrt{\log n}}$ $2^{2^{\sqrt{\log\log n}}}$
Obtain asymptotically tight bounds on $lg\ (n!)$ without using Stirling’s approximation. Instead, evaluate the summation $\sum_{k=1}^{n} lg\ k$.