Big O Notation with Absolute Value?

Question

I\'m going through some programming interview question books, and I\'ve seen reference to \"O(|A|)\" time complexity. I\'ve never seen this notation with the a

Answer 1

You will see this notation always when A is not a number.

A could be many things, so |A| depends on the context. E.g.

• A is a vector of a lattice, so |A| is the length of the vector.
• A is an (maybe unknown) algorithm (e.g. an attacker to an encryption), then |A| could be the complexity of this algorithm or the length of the random bit vector this algorithm uses.
• A is a set, then is |A| the number of elements in the set, as Kostub Deshmukh mentioned.

There can be many more cases.

Answer 2

In set theory notation |A| is the cardinality of set A, in other words the number of elements contained in set A.

For Reference: http://www.mathsisfun.com/sets/symbols.html