# Questions tagged [asymptotics]

Questions about asymptotic notations and analysis

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### Solving or approximating recurrence relations for sequences of numbers

In computer science, we have often have to solve recurrence relations, that is find a closed form for a recursively defined sequence of numbers. When considering runtimes, we are often interested ...
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### The order of growth analysis for simple loop

What would the order of growth for this loop be: int sum = 0; for (int n = N; n > 0; n /= 2) for(int i = 0; i < n; i++) sum++; The first loop ...
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### Compare asymptotic WC runtime with measured AC runtime

I have an algorithm and I determined the asymptotic worst-case runtime, represented by Landau notation. Let's say $T(n) = O(n^2)$; this is measured in number of operations. But this is the worst case,...
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### Solving recurrence relation with square root

I am trying to solve the following recurrence relation :- $T(n) = T(\sqrt{n}) + n$ using masters theorem. We can substitute $n = 2 ^ m$ $T(2^m) = T(2 ^ {\frac{m}{2}}) + 2^m$ Now we can rewrite it ...
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### Exact meaning of $2^{\mathcal{O}(f(n))}$

In Sipser's Introduction to the Theory of Computation he uses the notation $2^{\mathcal{O}(f(n))}$ to denote some asymptotic running time. For example he says that the running time of a single-tape ...
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### Merge sort worst case running time for lexicographical sorting?

A list of n strings each of length n is being sorted in lexicographical order using the merge sort algorithm. Since we have to take care of comparison of each character in the strings so the merge ...
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### how to understand time complexity from a plot?

This is my first question here. I'm not a CS at all, so it might be quite trivial. I have written a program in C where I allocate memory to store a matrix of dimensions n-by-n and then feed a linear ...
### Is $\log(n!)$ in $\Theta(n \log(n))$?
I had two questions on my automated test which I don't understand the answer for. $\log(n!) = \log(n\cdot (n-1)\cdot \cdots \cdot 2\cdot 1) = \log(n)+\log(n-1)+....+\log(1)$. So it is in \$O(n\log(...