Sets and MultiSets. Contents. Steven J. Zeil. July 19, Overview of Sets and Maps 4

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1 Steven J. Zeil July 19, 2013 Contents 1 Overview of Sets and Maps 4 1

2 2 The Set ADT The template header Internal type names Constructors & Assignment Status Insert & Erase Access Searching for Ranges of Equal Items A Simple Example of Using Set 34 CS361 2

3 The data structures and ADTs we have looked at so far in this course have been what are sometimes called sequential containers - they maintain elements in a known sequence and we access the elements by indicating a position in the sequence from which we wish to obtain an element. Sometimes we indicate this position numerically (e.g., a[23]), sometimes symbolically (e.g., myvector.front()), but always, in order to get an element, we have to know where it is in relation to the other elements. Now we turn our attention to associative containers, ones in which the container s implementation maintains the elements in a sequence that is intended to allow rapid access to elements based upon their value. This section of the course will be a bit different from the ones that have gone before. Previously, we have introduced an abstraction (vector, list, deque, etc) and also discussed how to implement it. The implementation of sets and maps is difficult enough, however, that we ll want to look at different possible underlying data structures, so for right now we ll only look at the set and map ADTs and how to use them, and we ll leave the imple- CS361 3

4 mentation for later. 1 Overview of Sets and Maps The major associative classes in the standard library are set map multiset multimap Sets are containers to which we can add elements (called keys ) and later check to see if certain key values are present in the set. CS361 4

5 Maps, also known in other contexts as lookup tables or dictionaries, allow us to store pairs consisting of a key value and associated data value 1 and to later look up the data value, if any, associated with a given key. In a set or a map, a given key value may appear only once. Attempting to add a key K to a set replaces any existing key equal to K. Adding a key-data pair (K,D1) to a map that already has (K,D2) replaces (K,D2) by (K,D1). But in a multiset or multimap, the same key can occur any number of times. For a multiset, this means that instead of just asking is K in this set? we can now ask how many K s are in this set?. For a multimap, adding a key-data pair (K,D1) to a multimap that already has (K,D2) results in multimap that has both (K,D1) and (K,D2). 1 In some contexts, especially more mathematical ones, the set of keys is called the domain of the map and the set of associated data values is called the range of the map. CS361 5

6 We ll look at sets and multisets first, and then turn to maps and multimaps in a later lecture. 2 The Set ADT A set collects elements and lets you check to see if an element is already in the collection. A given element can occur at most once in a set. Provides iterators that allow you to list the elements in sorted order. # ifndef SET_H #define SET_H #include <cstddef > CS361 6

7 template <class Key, class Compare=less <Key> > class set { private : Compare comparator ; public : / / typedefs : typedef Key key_type ; typedef Key value_type ; typedef Compare key_compare ; typedef Compare value_compare ; CS361 7

8 typedef const Key& reference ; typedef const Key& const_reference ; typedef... c o nst_iterator ; typedef c o nst_iterator i t e r a t o r ; typedef... const_reverse_iterator ; typedef const_reverse_iterator r e v e r s e _ i t e r a t o r ; typedef... size_type ; typedef... difference_type ; / / allocation / deallocation explicit set ( const Compare& comp = Compare ( ) ) ; CS361 8

9 set ( const set <Key, Compare>& x ) ; template <class InputIterator > set ( InputIterator f i r s t, InputIterator l a s t, const Compare& comp = Compare ( ) ) ; set <Key, Compare>& operator =( const set <Key, Compare>& x ) ; / / accessors : key_compare key_comp ( ) const { return comparator ; } value_compare value_comp ( ) const { return comparator ; } CS361 9

10 i t e r a t o r begin ( ) const ; i t e r a t o r end ( ) const ; r e v e r s e _ i t e r a t o r rbegin ( ) const { return t. rbegin ( ) ; } r e v e r s e _ i t e r a t o r rend ( ) const { return t. rend ( ) ; } bool empty ( ) const { return ( s i z e ( ) == 0 ) ; } size_type s i z e ( ) const ; size_ type max_size ( ) const ; void swap( set <Key, Compare>& x ) ; / / i n s e r t / erase pair < i t e r a t o r, bool> i n s e r t ( const value_type& x ) ; CS361 10

11 i t e r a t o r i n s e r t ( i t e r a t o r position, const value_type& x ) ; void clear ( ) ; void erase ( i t e r a t o r position ) ; size_ type erase ( const key_type& x ) ; void erase ( i t e r a t o r f i r s t, i t e r a t o r l a s t ) ; / / s e t operations : i t e r a t o r find ( const key_type& x ) const ; size_ type count ( const key_type& x ) const ; CS361 11

12 i t e r a t o r lower_bound ( const key_type& x ) const ; i t e r a t o r upper_bound ( const key_type& x ) const ; pair < i t e r a t o r, i t e r a t o r > equal_range ( const key_type& x ) const ; private :. / / declaration of implementing data structure } ; template <class Key, class Compare> bool operator ==( const set <Key, Compare>& x, const set <Key, Compare>& y ) ; CS361 12

13 template <class Key, class Compare> bool operator< ( const set <Key, Compare>& x, const set <Key, Compare>& y ) ; #endif The interface to multiset is identical to that of the set (aside from replacing the name set by multiset ) - it s only the behavior of a few of the operations that differ. So, as we look at the set interface, keep in mind that the same things apply to multisets as well. CS361 13

14 2.1 The template header Typically, you would declare a set by instantiating the template on the date type that template <class Key, class Compare=less <Key> > you want to use for the key: class set { set <string > mystringset ; But as you can see from the template header, this is an oversimplification. There is a second parameter, Compare, that supplies the comparison function to be used in comparing elements of the set. This parameter is given a default value, less<key>, so the above instantiation is actually equivalent to set <string, less <string > > mystringset ; What does less<...> do? It simply uses the Key s own operator< to do the compar- CS361 14

15 isons, and that s good enough 90% of the time. 2 Actually, even this template header is somewhat oversimplified. The real header has yet another parameter: template <class Key, class Compare=less <Key>, class Allocator = allocator <Key> > class set { but the Allocator parameter is only used in very rare situations where the application needs specialized control over how memory for the set will be allocated. We won t worry about that in this course. 2 less is a rather odd creature, however. It s actually a template for a class of functors (48), which we first encountered some time ago. CS361 15

16 2.2 Internal type names / / typedefs : Many standard containers provide a set of typedef Key key_type ; type names for programming convenience typedef Key value_type ; and to provide a standard way of declaring things without making direct reference typedef Compare key_compare ; typedef Compare value_compare ; to the data structures used to implement typedef const Key& reference ; them. We ve seen this with type names like typedef const Key& const_reference vector::const_iterator ; and list::size_type and typedef... const_iterator ; typedef c o nst_iterator i t e r a t o r ; we have used the same technique in our own programming (e.g., CS361Set::iterator). The associative containers add a couple of useful type names. The name key_type CS361 16

17 gives the data type of the keys in the container. The name value_type gives the data type that describes what we insert into the container and what is returned whenever we dereference (apply operator* to) an iterator. For set and multiset, the value_type is the same as the key_type, but that won t be true when we get to map and multimap. 2.3 Constructors & Assignment e x p licit set ( const Compare& comp = Compare ( ) ) ; set ( const set <Key, Compare>& x ) ; template <class InputIterator > set ( InputIterator f i r s t, InputIterator l a s t, const Compare& comp = Compare ( ) ) ; CS361 17

18 set <Key, Compare>& operator =( const set <Key, Compare>& x ) ; Looking at the constructors for set, the most interesting things are The first constructor takes a single parameter, a comparator. But we already supply a comparator when we instantiate the class! It turns out that when we instantiate the class, e.g., typedef set <string, less <string > > MySetType ; we re only telling the compiler what the default comparator should be. We can use that default: MySetType ascendingorder ; / / uses < to compare s t r i n g s or we can create objects that use a different comparator: MySetType descendingorder ( greater <string > ( ) ) ; / / uses > to compare s t r i n g s CS361 18

19 Note that, because this constructor has a default value for its only parameter, we can use it, as we did above, as the default constructor for the class. (If you don t remember what a default constructor is, go back to the ADTs lectures.) The third constructor lets us build a new set from any range specified by a pair of iterators. For example, vector <string > v ;. multiset <string > ms ( v. begin ( ), v. end ( ) ) ; CS361 19

20 2.4 Status bool empty ( ) const { return ( s i z e ( ) == 0 ) ; } No surprises here... size_type s i z e ( ) const ; size_ type max_size ( ) const ; CS361 20

21 2.5 Insert & Erase / / i n s e r t / erase pair < i t e r a t o r, bool> i n s e r t ( const value_type& x ) ; i t e r a t o r i n s e r t ( i t e r a t o r position, const value_type& x ) ; As described in your text, void clear ( ) ; s. i n s e r t ( " def " ) ; void erase ( i t e r a t o r position ) ; adds a new element, "def", into s. size_ type erase ( const key_type& x ) ; void erase ( i t e r a t o r f i r s t, i t e r a t o r l a s t ) ; CS361 21

22 If something equal to "def" is already in the set, nothing happens. But in a multiset, we would go ahead and add a second copy of "def". The return type from this operation is a bit interesting. There s two things you might want to know after trying to add something to a set: 1. Did it go in? (i.e., was this key already in the set), or 2. Where is it in the set? Rather than choose between these two equally valuable pieces of information, the insert operation actually returns both of them in a pair. (The std::pair template was one of our first examples of a class template (77).) It returns a pair (b,p) where b is a bool indicating whether an insertion occurred, and p is the position where the key was inserted. You are supposed to ignore the value of p if b is false. CS361 22

23 The second of the two insert functions is a bit odd: s. i n s e r t ( position, " def " ) ; Since this is an associative container, it s supposed to decide where to put things. Why then might we supply a position? The position is taken as a "hint" of where to begin searching for position to insert. The set implementation may ignore the hint if a quick check shows that the new key really does not belong at that position. But the C++ standard says that we are guaranteed that this hint version of insert will have an amortized O(1) worst case if we have data that is already in order and we use the position where one key was inserted as the hint for the next larger key, e.g.: CS361 23

24 vector <int > v ;. sort ( v. begin ( ), v. end ( ), less <int > ( ) ) ; / / we know the elements of v are in order set <int > myset ; set <int > : : i t e r a t o r hint = myset. begin ( ) ; for ( int i = 0 ; i < v. s i z e ( ) ; ++ i ) { hint = myset. i n s e r t ( hint, v [ i ] ) ; / / amortized O(1) i n s e r t s ++hint ; } Many generic algorithms expect an insert operation of this form. In particular, suppose we wanted to copy a list into a set. You may remember that we can t do this: CS361 24

25 l i s t <Foo> foolist ;. set <Foo> fooset ; copy ( f o o L i s t. begin ( ), foolist. end ( ), fooset. begin ( ) ) ; Question: Why doesn t this copy work? CS361 25

26 Answer: l i s t <Foo> foolist ;. set <Foo> fooset ; copy ( f o o L i s t. begin ( ), foolist. end ( ), fooset. begin ( ) ) ; The copy does not work here because copy simply writes into its destination positions it doesn t allocate new space for stuff, it assumes that the space already exists When we faced this problem copying into vectors and lists, we got around it by using back_inserter: l i s t <Foo> foolist ;. vector <Foo> foovect ; copy ( f o o L i s t. begin ( ), foolist. end ( ), back_inserter ( foovect ) ) ; CS361 26

27 back_inserter is a function that returns a special iterator that uses push_back whenever we try to store something at the iterator. Now that won t help for copying into sets, because sets don t have a push_back function. But another iterator-returning function is inserter, that returns an iterator that uses insert(position,value) whenever we try to store to it. For example, we can copy into the middle of a vector this way: l i s t <Foo> foolist ; vector <Foo> foovect ;. copy ( f o o L i s t. begin ( ), foolist. end ( ), i n s e r t e r ( foovect, foovect. begin ( ) + foovect. s i z e ( ) / 2 ) ) ; And, to finally get to the point of all this, because set and multiset have a member function that looks like insert(position,value), we can use inserter with them as well: CS361 27

28 l i s t <Foo>. foolist ; set <Foo> fooset ; copy ( f o o L i s t. begin ( ), foolist. end ( ), i n s e r t e r ( fooset, fooset. end ( ) ) ) ; If the list is unsorted, then the position supplied to inserter is only a hint. But if the list were sorted already, then this copy would get the amortized O(1) hint benefit, and the entire copy would be accomplished in O(fooList.size()) time. 2.6 Access i t e r a t o r find ( const key_type& x ) const There ; are two ways to see if an element is size_ type count ( const key_type& x ) const present ; in a set: CS361 28

29 set <string, less <string > > : : i t e r a t o r i ; i = s. find ( "abc" ) ; We can search the set for "abc". If the key is found, find returns the position where that element resides. If not found, it returns s.end(). So it s not unusual to see code that looks like: i f ( myset. find (yourname)! = myset. end ( ) ) cout << " I found " << yourname << " in my set. " << endl ; Alternatively, we can count the number of times we find an element. i f ( myset. count (yourname) > 0) { cout << " I found " << yourname << " in my set. " << endl ; cout << " I found there " << myset. count (yourname) << " times. " << endl ; } CS361 29

30 Of course, for sets, count(...) will always return 0 or 1, because either the key isn t in there at all, or there s only one copy of it in the set. But for multiset, count may return any non-negative number Searching for Ranges of Equal Items Suppose that we re interested, not i t e r a t o r lower_bound ( const key_type& x ) const ; so much in whether or not an element is present, but in where it i t e r a t o r upper_bound ( const key_type& x ) const ; pair < i t e r a t o r, i t e r a t o r > equal_range ( const key_type& might be. x ) const ; We can, as we have seen, use find to get the position of an element in a set. But if we have a multiset, there may be many instances of the same key. How do we know which instance will be pointed out by find? CS361 30

31 The functions shown here allow us to get the positions of all keys equal to some specified value. lower_bound returns the position of the first element in the set/multiset with the indicated value. upper_bound returns the position just after the last element equal to a given value. equal_range returns a pair consisting of both the lower_bound and the upper_bound. For example, a library system, having many copies of the same book, might keep track of its books by ISBN number: class Book { public :. s t r i n g author ( ) const ; s t r i n g t i t l e ( ) const ; s t r i n g isbn ( ) const ; int copynumber ( ) const ; CS361 31

32 bool ischeckedout ( ) const ; } ; bool operator < ( const Book& l e f t, const Book& r i g h t ) { return l e f t. isbn ( ) < r i g h t. isbn ( ) ; } Then, given a multiset of books: typedef multiset <Book, less <Book> > Holdings ; Holdings l i b r a r y ; we could list all the copies of a given book that are checked out this way: const s t r i n g textisbn = " " ; pair <Holdings : : i t e r a t o r, Holdings : : i t e r a t o r > rng CS361 32

33 = l i b r a r y. equal_range ( textisbn ) ; for ( Holdings : : i t e r a t o r i = rng. f i r s t ; i!= rng. second ; ++ i ) { i f ( i >ischeckedout ( ) ) cout << "Copy " << i >copynumber ( ) << " i s checked out. " << endl ; } Both set and multiset support these operations, though they aren t really very useful for sets. By the way, this is a good example of a place where the new C++11 auto type declaration and range-based for loop can simplify the code: const s t r i n g textisbn = " " ; auto rng = l i b r a r y. equal_range ( textisbn ) ; CS361 33

34 for ( auto i : rng ) { i f ( i >ischeckedout ( ) ) cout << "Copy " << i >copynumber ( ) << " i s checked out. " << endl ; } The first auto matches the pair type and the second matches the iterator type. 3 A Simple Example of Using Set As part of a program to be presented in a later example, we need to read an English language document in plain text form and collect all the words that are used to begin sentences. For example, if we read CS361 34

35 Hello! How are you? I haven t seen you in a long time. How is your family? we would want a set with the words Hello!, How, and I. 3 This is a pretty straightforward application for set, and here is the code to collect the sentence-starting words: void readdocument ( const char * docfilename, set <string >& startingwords,... ) { ifstream docin ( docfilename ) ; char lastchar =. ;. 3 Unlike in our spell checker, this particular application will need us to preserve all upper/lower case distinctions and to treat punctuation as part of the preceding word. CS361 35

36 s t r i n g word ; } while ( docin >> word) { i f ( lastchar ==. lastchar ==? lastchar ==! ) { startingwords. i n s e r t (word ) ; } lastchar = word [ word. length ( ) 1];. } CS361 36