# Questions tagged [big-o-notation]

Big O Notation is an informal name of the "O(x)" notation used to describe asymptotic behaviour of functions. It is a special case of Landau notation, where the O is the Greek letter capital omicron. Please consider using the [landau-notation] tag instead if your question is related to small omicron, omega, or theta in Landau notation.

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### Why is $\sum_{i=1}^n O(i)$ not the same as $O(1)+O(2)+\dots+O(n)$?

The well-known textbook Introduction to Algorithms ("CLRS", 3rd edition, chapter 3.1) claims the following: $$\sum_{i=1}^n O(i)$$ is not the same as (I'm not using DNE because the book explicitly ...
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### Algorithms: Determining Asymptotic Notation from a given execution time

I'm studying for an Algorithms and Data Structure test. There is a type of question that is usually always asked by my professor but I don't know how to answer/solve it. Question 1: An Algorithm with ...
• 13
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### Summation of asymptotic notation

How can we solve summation of asymptotic notations like given below: $$\sum_{k=1}^{n-1} O(n).$$
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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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### Time complexity $O(m+n)$ Vs $O(n)$

Consider this algorithm iterating over $2$ arrays $(A$ and $B)$ size of $A = n$ size of $B = m$ Please note that $m \leq n$ The algorithm is as follows ...
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