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Big O describes the concepts of time complexity and space complexity, but is there a more general higher-level category which describes the domain of the complexity described by Big O notation?

For example, if someone brought up the topic of complexity in an application, I might ask "do you mean cyclomatic complexity or Big O complexity?". However, Big O is a notation for describing complexity, not an actual type of complexity.

Are the concepts of time complexity and space complexity distinct to the point where they are not grouped into a more formal general category? If these concepts are commonly grouped into a more general category then what is the name of that category?

mort
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Jim Thompson
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  • I'm not sure what you mean, but the complexity (space or time) is independent from the big O notation. The big O notation is just a mathematical tool that is also used to make complexities more simple. So if you want to ask, which complexity someone is talking about, you have to use the terms "time or space complexity". – AbcAeffchen Jun 01 '16 at 02:22
  • Thanks abc - is Big O notation used to represent any other types of complexity besides time complexity and space complexity? – Jim Thompson Jun 01 '16 at 02:30
  • no, as far as I know. But it is used in math for all kind of things. – AbcAeffchen Jun 01 '16 at 02:33

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One important property of statements that involve Big-O notation is that they apply only to asymptotic complexity. In that it is different from cyclomatic complexity or other software metrics.

Other aspects that could differentiate it from software metrics are that it applies to algorithms, therefore you could refer to it as algoritmic complexity or theoretical complexity (of an algorithm).

Dima Chubarov
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