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PHP Class MathPHP\SetTheory\Set

https://en.wikipedia.org/wiki/Set_(mathematics) Sets can contain numbers, strings, arrays, objects, and other sets. Implementation: For performance reasons, PHP arrays are used as a hash for quick access via hash keys. The hash keys are as follows: - Numbers and strings: value itself - Sets: Set as a string. - Arrays: Array(array_serialization) - Objects: Object\Name(object_hash) - Resource: Resource(Resource id: #) - Null: '' The values of the associative array (hash) are the actual values or objects themselves. If the set is iterated in a foreach loop you will get back the original value, set, array, or object. An object cannot be in the set multiple times. For a regular value, like a number or string, this is straight forward. For arrays and objects, the behavior is based on whether they are the same thing. What that means depends on whether it is an array or object. Example (arrays): $array1 = [1, 2, 3]; $array2 = [1, 2, 3]; $set = new Set([$array1, $array2]); The set will have only one element, because the arrays are equal. $array2 === $array2 evaluates to true. Example (different objects): $object1 = new \StdClass(); $object2 = new \StdClass(); $set = new Set([$object1, $object2]); The set will have two elements, because they are different objects. $object1 === $object2 evaluates to false. Example (same objects): $object1 = new \StdClass(); $object2 = $object1; $set = new Set([$object1, $object2]); The set will have only one element, because the objects are the same. $object1 === $object2 evaluates to true. Example (Sets, a special case of object) $set1 = new Set([1, 2, 3]); $set2 = new Set([1, 2, 3]); $set3 = new Set([$set1, $set2]); Set3 will have only one element, because sets 1 and 2 are the same. Sets are not based on whether the object is the same, but whether the content of the set are the same. Sets and arrays act similarly. When storing a Set object as a member of a set, its key will be a string that uses mathematical set notation with the addtion of the word 'Set'. For example: Set{1, 2, 3} The one edge case of this, is that the Set object {1, 2, 3} and the string 'Set{1, 2, 3}' would appear identical in the case of adding one when the other already is a member of the set. When accessing the actual set member, you will always get back the original one added, whether it was a Set object or a string. ファイルを表示 Open project: markrogoyski/math-php Class Usage Examples

Protected Properties

Property	Type	Description
$A	array	Keys are a representation of the members of the set. Values are the values/objects themselves.
$iterator_keys	array	Iterator interface array to iterate over
$iterator_position	mixed	Iterator interface position of iterator keys we are at (the key)

Public Methods

Method	Description
__construct ( array $members = [] )	Constructor - Initialize set members
__toString ( ) : string	Return the set as a string Set{a, b, c, .
add ( mixed $x ) : Set	Add an element to the set Does nothing if element already exists in the set.
addMulti ( array $members ) : Set	Add an array of elements to the set Does nothing if element already exists in the set.
asArray ( ) : array	Get the set as an array
cartesianProduct ( Set $B ) : Set	Cartesian product (A×B) Produces a new set by associating every element of the set with every element of the other set.
clear ( ) : Set	Clear the set. Removes all members.
copy ( ) : Set	Copy Produces a new set with the same elements as the set.
count ( ) : integer	Countable interface Computes cardinality of a set S, |S|
current ( )	Current (Iterator interface)
difference ( variadic $Bs ) : Set	Difference (relative complement) (A ∖ B) or (A - B) Produces a new set with elements that are not in the other sets.
intersect ( variadic $Bs ) : Set	Intersect (A ∩ B) Produces a new set with all the elements common to all sets.
isDisjoint ( Set $other ) : boolean	Disjoint Does the set have no elements in common with the other set?
isEmpty ( ) : boolean	************************************************************************ SET PROPERTIES - Empty set ************************************************************************
isMember ( mixed $x ) : boolean	Set membership (x ∈ A) Is x a member of the set?
isNotMember ( mixed $x ) : boolean	Set non-membership (x ∉ A) Is x not a member of the set?
isProperSubset ( Set $B ) : boolean	Proper subset (A ⊆ B & A ≠ B) Is the set a proper subset of the other set? In other words, does the other set contain all the elements of the set, and the set is not the same set as the other set?
isProperSuperset ( Set $B ) : boolean	Superset (A ⊇ B & A ≠ B) Is the set a superset of the other set? In other words, does the the set contain all the elements of the other set, and the set is not the same set as the other set?
isSubset ( Set $B ) : boolean	Subset (A ⊆ B) Is the set a subset of the other set? In other words, does the other set contain all the elements of the set?
isSuperset ( Set $B ) : boolean	Superset (A ⊇ B) Is the set a superset of the other set? In other words, does the the set contain all the elements of the other set?
key ( )	Key (Iterator interface)
length ( ) : integer	Get length of set (number of members in set)
next ( )	Next (Iterator interface)
powerSet ( ) : Set	Power set P(S) The set of all subsets of S, including the empty set and S itself.
remove ( mixed $x ) : Set	Remove an element from the set Does nothing if the element does not exist in the set.
removeMulti ( array $x ) : Set	Remove elements from the set Does nothing if the element does not exist in the set.
rewind ( )	Rewind (Iterator interface)
symmetricDifference ( Set $B ) : Set	Symmetric Difference (A Δ B) = (A ∖ B) ∪ (B ∖ A) Produces a new set with elements that are in the set or the other, but not both.
union ( variadic $Bs ) : Set	Union (A ∪ B) Produces a new set with all elements from all sets.
valid ( ) : boolean	Valid (Iterator interface)

Protected Methods

Method	Description
getKey ( mixed $x ) : string	Determine the key for the member to be added

Method Details

Property Details