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I'm having a hard time conceptualizing c++ sets, actually sets in general.
What are they? How are they useful?
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Sets in C++ Sets are associative containers that store unique elements. A stored element must be unique because it is identified with the value itself. Once the elements are inserted in the set, they cannot be modified; however, they can be inserted or removed from the container.
The purpose of sets is to house a collection of related objects. They are important everywhere in mathematics because every field of mathematics uses or refers to sets in some way. They are important for building more complex mathematical structure.
Sets are used to get information of an object by providing all the information, usually used to check if the data exists. A map is used to get the information of an object by using a key (single data).
As mentioned above, sets in C++ are the type of STL containers that are used for storing elements in a sorted way. The operations allowed to be performed on sets are insertion and deletion. The elements are internally sorted according to a strict weak ordering in a set type container.
Don't feel bad if you have trouble understanding sets in general. Most of a degree in mathematics is spent coming to terms with set theory:
http://en.wikipedia.org/wiki/Set_theory
Think of a set as a collection of unique, unordered objects. In many ways it looks like a list:
{ 1, 2, 3, 4 }
but order is unimportant:
{ 4, 3, 2, 1} = { 1, 2, 3, 4}
and repetitions are ignored:
{ 1, 1, 2, 3, 4 } = { 1, 2, 3, 4}
A C++ set is an implementation of this mathematical object, with the odd feature that is is sorted internally. But this is just a detail of implementation, and is not relevant to understanding the data structure. The sorting is just for speed.
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