# Questions tagged [notation]

Use this tag whenever you have a question about what some particular symbol/notation means.

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### O(·) is not a function, so how can a function be equal to it?

I totally understand what big $O$ notation means. My issue is when we say $T(n)=O(f(n))$ , where $T(n)$ is running time of an algorithm on input of size $n$. I understand semantics of it. But $T(n)$ ...
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### Order of growth definition from Reynolds & Tymann

I am reading a book called Principles of Computer Science (2008), by Carl Reynolds and Paul Tymann (published by Schaum's Outlines). The second chapter introduces algorithms with an example of a ...
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### What is the name the class of functions described by O(n log n)?

In "Big O", common notations have common names (instead of saying, "Oh of some constant factor"): O(1) is "Constant" O(log n) is "Logarithmic" O(n) is "Linear" O(n^2) is "Quadratic" O(n * log n) ...
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### Is there any reason why the modulo operator is denoted as %?

I would like to know if there is any reason why many programming languages use the notation % for the modulo operator? It is used in the most "famous" ...
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### What is the purpose of using NIL for representing null nodes?

In my Algorithms and Data Structures course, professors, slides and the book (Introduction to Algorithms, 3rd edition) have been using the word NIL to denote for ...
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### Can a Big-Oh time complexity contain more than one variable?

Let us say for instance I am doing string processing that requires some analysis of two strings. I have no given information about what their lengths might end up being, so they come from two distinct ...
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### What is this fraction-like "discrete mathematics"–style notation used for formal rules?

In the paper "A Conflict-Free Replicated JSON Datatype", I encountered this notation for formally defining "rules": What is this notation called? How do I read it? For example: the ...
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### What is the origin of λ for empty string?

I usually use the symbol $\varepsilon$ for empty string (empty word or null string). But I know some people use $\lambda$ instead of $\varepsilon$. I think $\varepsilon$ is derived from the word "...
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### What does up arrow ($\uparrow$) mean in pseudocode?

I'm learning vantage point trees, and I met this while reading the paper Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces by Peter Yianilos (Proceedings of SODA 1993,...
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### Programming Symbols : Instance/Instantiation

Is there a generally accepted symbol for indicating instantiation. That is indicating an object is an instance of a class. My first guess is to use a left arrow with a double or triple line but this ...
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### Weight functions in graph algorithms

In text books, for instance in the 3rd edition of Introduction to Algorithms, Cormen, on page 625, the weights of the edge set $E$ is defined with a weight function $w:E\rightarrow \mathbb{R}$. Why ...
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### What type of formal notation is being used here to represent functional algorithms?

Interested in learning more about algorithm design in functional programming, I picked up Andrew Bird's Pearls of Functional Algorithm Design. I have experience with a number of programming languages,...
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### What's the difference between the concatenation and union of symbols within a language

I feel like I'm confusing myself perhaps but I'm having a bit of trouble figuring out how exactly this language works. I'm given the following regular expression (a + b)* (abba* + (ab)*ba) Can ...
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### What does > mean in this TAOCP solution?

For our assignment we have to implement a solution given to one of the problems in The Art of Computer Programming by D.E. Knuth (Ex24; Chapter 5: Sorting; TAOCP, Vol3, 2nd). However, I fail to ...
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### Expressing that a function converges to 1 with linear rate using Landau notation

I am working on an algorithm which approximates a certain optimal quantity. The approximation becomes better when the size of the problem ($n$) becomes larger: the difference from the optimum is ...
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### graph theory single bar vs double bar size notation

A follow-up on https://stackoverflow.com/questions/15037679/what-do-the-absolute-value-bars-mean-in-graph-theory What is the difference between single bar $|G|$ and double bar $||G||$ notation (both ...
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### Parentheses after Typing Environment

I've been reading about System F Omega lately, and I keep stumbling across a construct in typing rules that I cannot find an explanation of: Γ(x) = k. For example, ...
### Why is subarray $A[p..k-1]$ empty when $k=p$?
I'm working through a proof of correctness for merge sort. I'm given a loop invariant for a for loop, which makes reference to a subarray $A[p..k-1]$. During the initialization step of the ...