

#include <set.h> #include <set_of_p.h> #include <bag.h> #include <setio.h> #include <set_of_pio.h> #include <bagio.h> namespace SCO_SC {class ostream; // Auxiliary types typedef implementation_dependent_integral_type Set_or_Bag_hashval; // Template classes for Bag_pair, Bag, Set, and Set_of_p: template <class T> struct Bag_pair{ T value; unsigned count; }; template <class T> class Bag{ public: // Constructors, destructor Bag(); Bag(const T& t1); Bag(const T& t1, const T& t2); Bag(const T& t1, const T& t2, const T& t3); Bag(const T& t1, const T& t2, const T& t3, const T& t4); ~Bag(); // Copy and assign Bag(const Bag<T>& b); Bag<T>& operator=(const Bag<T>& b); // Length unsigned size()const; unsigned size_unique()const; operator const void*()const; // Membership const Bag_pair<T>* contains(const T& t)const; unsigned count(const T& t)const; // Select an arbitrary element const Bag_pair<T>* select()const; // Insert and remove elements const Bag_pair<T>* insert(const T& t, int count = 1); unsigned remove(const T& t, int count=1); unsigned remove_all(const T& t); unsigned remove_all(); // Relations int operator==(const Bag<T>& b)const; int operator!=(const Bag<T>& b)const; int operator<=(const Bag<T>& b)const; int operator<(const Bag<T>& b)const; int operator>=(const Bag<T>& b)const; int operator>(const Bag<T>& b)const; // Algebra Bag<T> operator(const Bag<T>& b)const; Bag<T> operator&(const Bag<T>& b)const; Bag<T> operator(const Bag<T>& b)const; Bag<T> operator^(const Bag<T>& b)const; Bag<T>& operator=(const Bag<T>& b); Bag<T>& operator&=(const Bag<T>& b); Bag<T>& operator=(const Bag<T>& b); Bag<T>& operator^=(const Bag<T>& b); // Performance analysis void histogram( Map<Set_or_Bag_hashval,unsigned>& m)const; // Very simple hash function static Set_or_Bag_hashval hash(const T&); }; // Stream insertion template <class T> ostream& operator<<(ostream& os, const Bag<T>& b); template <class T> class Bagiter{ public: Bagiter<T>(const Bag<T>& b); const Bag_pair<T>* next(); int next(const Bag_pair<T>*& p); void reset(); const Bag<T>* the_bag()const; }; template <class T> class Set{ public: // Similar to Bag<T> }; template <class T> class Setiter{ public: Setiter(const Set<T>& s); const T* next(); int next(const T*& p); void reset(); const Set<T>* the_set()const; }; template <class T> class Set_of_p{ public: // Similar to Set<T> }; template <class T> class Set_of_piter{ public: Set_of_piter(const Set_of_p<T>& s); T* next(); int next(T*& p); void reset(); const Set_of_p<T>* the_set_of_p()const; }; }
A Bag<T> is an unordered homogeneous collection whose elements are objects of type T. A Set<T> is a Bag in which no two elements are equal. In either case, T can be any type having:
The implementation of Set<T> and Bag<T> is based on hashing. To optimize time complexity, a perfect hash function (a function for which different arguments yield different results) should be used (see Complexity). To integrate a userdefined hash function into a Set or Bag structure, the function should be defined as either Set_or_Bag_hashval Set<T>::hash(const T&) or Set_or_Bag_hashval Bag<T>::hash(const T&). If there is no such hash function provided, a default hash function which always returns zero will be used and it will result in all elements being stored internally in a single list.
typedef implementation_dependent_integral_type Set_or_Bag_hashval; This type denotes an unsigned integral type which for UnixWare and most other implementations is unsigned long but may be shorter or longer in some implementations. It is used as the return type of userdefined hash functions.
Mapdeclare<Set_or_Bag_hashval,unsigned> Defines the type Map<Set_or_Bag_hashval,unsigned> which is returned by the function histogram(). See Map(3C++).
Some Bag operations (and Bag iteratorssee below) return pointers to constant objects of this type.
T value; The element value.
unsigned count; The number of occurrences.
Bag();
Bag(const T& t1);
Bag(const T& t1, const T& t2);
Bag(const T& t1, const T& t2, const T& t3);
Bag(const T& t1, const T& t2, const T& t3, const T& t4); Constructors for Bags of zero, one, two, three, or four elements, respectively.
~Bag(); Destructor. All iterators currently attached to the Bag will be informed of the Bag's destruction (see Bagiter<T>::the_bag()).
Bag(const Bag<T>& b);
Bag<T>& operator=(const Bag<T>& b); Copying or assigning a Bag<T> creates a copy of its value.
unsigned size()const; The number of elements in the Bag (counting multiple occurrences).
unsigned size_unique()const; The number of unique elements in the Bag.
operator const void*()const; Returns nonzero if the Bag contains one or more elements. Most useful in contexts where implicit conversion will take place, for example, while(b)....
const Bag_pair<T>* contains(const T& t)const; If an element t is in the Bag, returns a pointer to the corresponding Bag_pair; otherwise, returns zero.
unsigned count(const T& t)const; Returns the number of elements with the value t.
const Bag_pair<T>* select()const; Returns a pointer to an arbitrary Bag_pair.
const Bag_pair<T>* insert(const T& t, int count = 1); Inserts count elements with the value t into the Bag. Returns a pointer to the Bag_pair if the Bag actually changed and zero otherwise (no change will occur if count is nonpositive).
unsigned remove(const T& t, int count=1); Removes count elements with the value t from the Bag. If the number of elements with this value is less than count, then all such elements are removed. Returns the number of elements actually removed.
unsigned remove_all(const T& t); Removes all elements with the value t from the Bag. Returns the number of elements actually removed.
unsigned remove_all(); Removes all elements in the Bag. Returns nonzero if the Bag actually changed (no change will occur for an empty Bag).
All of the following operators return nonzero if the relation is true.
int operator==(const Bag<T>& b)const;
int operator!=(const Bag<T>& b)const; Equality and inequality relations. Two Bags are equal if they contain exactly the same elements.
int operator<=(const Bag<T>& b)const; Subbag relation. True if all of the elements of this Bag are also contained in b.
int operator<(const Bag<T>& b)const; Proper subbag relation. True if all of the elements of this Bag are also contained in b and, in addition, b has other elements.
int operator>=(const Bag<T>& b)const; Superbag relation. True if all of the elements of b are also contained in this Bag.
int operator>(const Bag<T>& b)const; Proper superbag relation. True if all of the elements b are also contained in this Bag and, in addition, this Bag has other elements.
Bag<T> operator(const Bag<T>& b)const; Bag union (the elements that are in this Bag or in b).
Bag<T> operator&(const Bag<T>& b)const; Bag intersection (the elements that are in both this Bag and b).
Bag<T> operator(const Bag<T>& b)const; Bag difference (the elements that are in this Bag but not in b).
Bag<T> operator^(const Bag<T>& b)const; Bag symmetric difference (the elements that are in this Bag or in b, but in not both).
Bag<T>& operator=(const Bag<T>& b);
Bag<T>& operator&=(const Bag<T>& b);
Bag<T>& operator=(const Bag<T>& b);
Bag<T>& operator^=(const Bag<T>& b); Assignment versions of the above.
ostream& operator<<(ostream& os,const Bag<T>& b); Inserts an ASCII representation of b into ostream os. The representation has the form {(n1,t1)(n2,t2)(n3,t3) ...} where ti is an element value and ni is its multiplicity.
void histogram(Map<Set_or_Bag_hashval,unsigned>& m)const; Returns (via the argument m) a Map(3C++) from hash values to collision list lengths. The shape of this "histogram" indicates the goodness of the hash function; for perfect hash functions, collision list lengths are never greater than 1.
For every class Bag<T>, there is a class Bagiter<T> whose objects, called iterators, are used for iterating over elements. The order in which elements are returned by an iterator is purposely unspecified. Several iterators may be active simultaneously over a single Bag. If an element is inserted into a Bag, it may or may not be seen by an active iterator. The behavior of all iterator operations except the_bag() is undefined when the Bag to which the iterator is attached ceases to exist.
Bagiter(const Bag<T>& b); Creates a Bagiter<T> to iterate over the elements of b.
const Bag_pair<T>* next(); Returns a pointer to the next Bag_pair<T>; returns 0 if all pairs have been returned.
int next(const Bag_pair<T>*& p); Assigns a pointer to the next Bag_pair<T> (if there is one) to p and returns nonzero if the value of p is meaningful.
void reset(); Resets the iterator so that it can be reused.
const Bag<T>* the_bag()const; Returns a pointer to the Bag being iterated over, or zero if there is no such Bag (this can happen if the Bag is destroyed).
The description of Bag<T> and Bagiter<T> hold, mutatis mutandis, for Set<T> and Setiter<T> with the following exceptions:
Set<T>, Bag<T>, and Set_of_p<T> were designed to achieve minimum acrosstheboard order estimates for time complexity. Naturally, speed was achieved at a cost of space. Even so, space complexity for all three classes remains O(N). Operations are further accelerated by cacheing the results of each search of the internal data structure. Thus, for example, testing for containment and then deleting an element requires only a single search. Similarly, iteration is accelerated by cacheing. In view of this, expect degraded performance if you do anything to destroy the utility of the cache, for example
if(x.contains(a) && x.contains(b)) x.remove(a);
Similarly, iterators maintain private caches, but these are invalidated by operations that modify the object to which the iterator is attached.
Set_of_p<T> Time complexity of operations involving a single element (for example, insert(), remove(), contains()) is O(1); the time for operations involving all the elements in the set (for example, iteration) is O(N), where N is the size of the set. The time for operations involving two sets (for example, the algebraic and relational operations) is O(N+M), where N and M are the sizes of the two sets. Space complexity is approximately O(N).
Set<T> Time complexity depends on the average length of collision lists. For a perfect hash function (one which hashes unique keys to unique hash values), time complexity is O(1), O(N), and O(N+M) (as above), with a somewhat higher constant multiplier, owing, for example, to the copying overhead of operations like insert. For a lessthanperfect hash function, the time complexity must be multiplied by the average length of collision lists; if L is the average list length, then average complexity is O(L), O(N*L), and O(L*(N+M)), respectively. Space complexity is also O(N), also with a somewhat higher constant multiplier.
Bag<T> Time complexity is roughly equal to that of Set<T>. Space complexity is O(N), where N is the number of unique elements (multiple occurrences are not actually stored).
Iterators for certain other container classes, like List(3C++), yield pointers to their elements, allowing the elements to be modified in place. Bag and Set iterators, on the other hand, yield pointers to constants because it is dangerous to modify their elements in place (since the location of an element within the internal data structure is a function of its hash value, changing an element in place corrupts the data structure). The only time it is safe to cast away the constant is when default hash function is used, since an element's storage location in such a Set or Bag is independent of its value.
If you need integer sets, Bits(3C++) may be more efficient, both in time and space, than Set<int>. For small sets where linear time complexity is not a problem, consider using Block Algorithms (see Array_alg(3C++) and Block(3C++)).
The elements pointed to by a pointer set must reside on even byte boundaries. (That is, the low order bit of every pointer in a pointer set must be zero.) Violating this restriction will result in unpredictable behavior. Since character pointers do not in general satisfy this restriction, pointer sets can not be used to keep track of arbitrary character strings. However, pointer sets can always be used to keep track of dynamically allocated objects (including dynamically allocated character strings), since pointers obtained from operator new always are guaranteed to satisfy the most stringent alignment restrictions.