Admin: /* Flags */

2017-06-29T04:03:09Z

Flags

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	==Flags==		=Flags=

	{{MapsFlag}}		{{MapsFlag}}
	[[Category:Sets]]		[[Category:Sets]]

Admin: /* Computer science sets */

2017-06-29T04:02:55Z

Computer science sets

← Older revision		Revision as of 04:02, 29 June 2017
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	* Remove all - if any items in the current set are in the passed set, remove them		* Remove all - if any items in the current set are in the passed set, remove them
	* Retain all - if any items in the current set are not contained in the passed set, remove them		* Retain all - if any items in the current set are not contained in the passed set, remove them



			==Flags==

			{{MapsFlag}}
			[[Category:Sets]]

Admin: Created page with "=Notes= ==Mathematical sets== Begin with a review of the mathematical concept of a set: A set is a collection of objects or numbers that are specified in some well-defined..."

2017-06-29T03:47:49Z

Created page with "=Notes= ==Mathematical sets== Begin with a review of the mathematical concept of a set: A set is a collection of objects or numbers that are specified in some well-defined..."

New page

=Notes=

==Mathematical sets==

Begin with a review of the mathematical concept of a set:

A set is a collection of objects or numbers that are specified in some well-defined manner. Each item in the set is called an element.

Various properties of sets can be enumerated, such as notation for constructing sets, how we determine if two sets are equal, set operations, etc.

==Computer science sets==

Sets are data structures that correspond to the mathematical set object.

Sets are defined by their chief characteristic, which is that sets cannot contain duplicates. They are not indexed, and items are accessed directly. The set data structure works similar to the map data structure with its key-value lookup, but the set has no keys - the values are their own keys.

The Set class defines an abstract data type. This abstract data type must provide the following five public methods:
* S.add(e) - add element e to set
* S.discard(e) - remove e from set
* e in S - returns true if e is in S
* len(S) or S.size() - size of set
* iter(S) or S.iterator() - get an iterator over set elements

To see more details about the Set ADT, see [[Sets/ADT]].

Other utility methods include remove (passing a specific element) and pop (remove one element), as well as the usual size, check if empty, clear.

Finally, there are several operations that need to be redefined for sets. These include both set operations and algebraic operations (e.g., equality).

Operations:
* Equals - returns true if two sets have identical contents
* Subset / proper subset - returns true if set S is proper subset of set T. This is convenient to implement using the <= or < operators
* Superset / proper superset - returns true if set S is proper superset of set T. Convenient to implement using >= or > operators.
* Disjoint - returns true if S and T contain no common elements

Other set operations:
* Union operation - the union of two sets S and T consists of all elements that are in S or T or both
* Intersection operation - the intersection of two sets S and T consists of all elements that are in both S and T
* Symmetric difference - consists of all elements that are in S but not T, or in T but not S
* Remove all - if any items in the current set are in the passed set, remove them
* Retain all - if any items in the current set are not contained in the passed set, remove them

Sets - Revision history

Admin: /* Flags */

Admin: /* Computer science sets */

Admin: Created page with "=Notes= ==Mathematical sets== Begin with a review of the mathematical concept of a set: A set is a collection of objects or numbers that are specified in some well-defined..."