Sets and Maps

1
Sets and Maps

• Andy Wang
• Data Structures, Algorithms, and Generic
  Programming

2
Sets

• Abstract associative containers
• Set
• Stores objects
• Unimodal duplicate objects not allows
• MultiSet
• Stores objects
• Multimodal duplicate objects OK
• Also known as bags

3
Maps

• Abstract associative containers
• Map
• Stores (key, object) pairs
• Unimodal duplicate keys not allows
• AKA table, associative array
• MultiMap
• Stores (key, object) pairs
• Multimodal duplicate keys OK

4
Client Needs

• Insert an object
• Remove a specified object
• Remove all copies of an object
• Inspect an object
• Iterate through all objects
• Optional
• Performance constraints
• Iteration order constraints

5
Client Does Not Need

• Implementation details
• Data structure used to implement the container

6
Example Set Clients

• Inventory
• struct StockItem
• // barcode, name, amount
• void print_inventory(stdostreamos, const
  setltStockItemgt inventory)
• setltStockItemgtIterator
• for (I inventory.Begin() I !
  inventory.End() I)
• os ltlt I

7
Example Set Clients

• Customer accounts
• class Customer
• // ssn, account_number, last_name, first_name
• int main()
• setltCustomergt customers

8
Example Set Clients

• Exceptional instances
• setltStringgt dictionary
• setltStringgt wordset
• setltStringgt unknown wordset dictionary
• for (setltStringgtIterator I unknown.Begin() I
  ! unknown.End() I)
• stdcout ltlt I ltlt endl // output possible
  mispelled words

9
Example Set Clients

• Instances in common
• setltwidgetgt S1, S2
• setltwidgetgt S S1 S2
• // S contains the widgets that are in both S1 and
  S2

10
Example Set Clients

• Password server
• struct User
• String username
• unsigned long signature
• class PWServer
• setltUsergt users

11
Example Set Clients

• Password server
• int PWServerCheckPW(const String uid, const
  String pw)
• String uid_pw(uid pw)
• unsigned long hash secure_hash_function(uid_pw)
  
• User u(uid, hash)
• setltUsergtIterator I users.Includes(u)
• if ((I).username u.username)
  (I).signature user.signature))
• return 1
• return 0

12
Example Set Clients

• Any map client
• typedef setltpairltK, Vgt gt mapltK, Vgt

13
Example Map Clients

• Password server
• typedef String username
• typedef unsigned long signature
• class PWServer
• map ltusername, signaturegt users
• int PWServerCheckPW(const String uid, const
  String pw)
• unsigned long hash secure_hash_function(uid
  pw)
• mapltusername, signaturegt Iterator I
  users.Includes(uid)
• if (I.Valid() (I).key uid (I).value
  signature)
• return 1
• return 0

14
Example Map Clients

• Internet router
• map ltDestIPNumber, NextHopIPNumbergt routemap
• Dictionary
• map ltWord, Definitiongt dictionary
• Keyword index
• map ltWord, Listltpage_numbersgt gt concordance

15
Set Tools (Sorted)

• Sorted sets
• CSetltT, Cgt adaptor
• Classic choices for C sorted list, binary
  search tree, or red-black tree
• Adaptation of sorted associative container
• Search operations LowerBound(), UpperBound(),
  and Includes()
• Sorted order traversal
• Operators union, intersection, difference,
  subset
• Modality determined by adaptee

16
Map Tools (Sorted)

• Sorted maps
• CMap and CMultiMap adaptors
• Adaptation of sorted associative container
• Search operations LowerBound(), UpperBound(),
  and Includes()
• Sorted order traversal
• Generic set algorithms apply
• Modality determined by adaptor

17
Set and Map Tools (Sorted)

• Client usage
• CSetltchar, TUSListltchargt gt S1
• Sorted list
• Unimodal
• CSetltchar, TMSListltchar, TGreaterThanltchargt gt gt
  S2
• Sorted list in reverse order
• Multimodal
• CMapltString, int, TUSListltTAssociationltString,
  intgt gt gt S3
• Sorted list
• Unimodal

18
Set and Map Tools (Sorted)

• typedef String key_type
• typedef int data_type
• typedef TAssociationltkey_type, data_typegt
  pair_type
• typedef special_class predicate_type
• typedef TMBSTltpair_type, predicate_typegt
  container_type
• CMultiMapltkey_type, container_typegt M1
• Binary search tree
• Multimodal
• Special predicate class

19
Set and Map Tools (Unsorted)

• Unsorted sets and maps
• CHashSet, CHashMultiSet adaptors
• CHashMap, CHashMultiMap adaptors
• Adaption as vector of containers
• Search operation Includes()
• Random order traversal
• Modality determined by adaptor

20
The CSet Adaptor

• template lttypename T, class Cgt
• class CSet
• friend class CSetIteratorltK, V, Cgt
• public
• typedef T value_type
• typedef C container_type
• typedef CSetIteratorltT, Cgt Iterator
• // constructors
• CSet() c()
• CSet(const CSetltT, Cgt S) c(S.c)
• CSet() Clear()
• CSetltT, Cgtoperator(const CSetltT, Cgt S)
• if (this ! S)
• c S.c
• return this

21
The CSet Adaptor

• // element operations
• Iterator Insert(const value_type t)
• CSetltT, CgtIterator I
• I.i c.Insert(t)
• return I
• int Insert(Iterator I, const value_type t)
• return c.Insert(I.i, t)
• size_t Remove(const value_type t) return
  c.Remove(t)
• int Remove(Iterator I) return c.Remove(I.i)
  
• void Clear() c.Clear()

22
The CSet Adaptor

• // locator operations
• Iterator LowerBound(const value_type t) const
• CSetltT, CgtIterator I
• I.i c.LowerBound(t)
• return I
• Iterator UpperBound(const value_type t) const
• CSetltT, CgtIterator I
• I.i c.UpperBound(t)
• return I
• Iterator Includes(const value_type t) const
• CSetltT, CgtIterator I
• I.i c.Includes(t)
• return I

23
The CSet Adaptor

• Iterator Begin() const
• CSetltT, CgtIterator I
• I.i c.Begin(t)
• return I
• Iterator End() const
• CSetltT, CgtIterator I
• I.i c.End(t)
• return I
• Iterator rBegin() const
• CSetltT, CgtIterator I
• I.i c.Begin(t)
• return I
• Iterator rEnd() const
• CSetltT, CgtIterator I
• I.i c.rEnd(t)
• return I

24
The CSet Adaptor

• // size operations
• int Empty() const return c.Empty()
• size_t Size() const return c.Size()
• protected
• C c

25
Global Operators on CSet

• // containment operators
• bool operatorlt(const CSetltT, Cgt S1, const
  CSetltT, Cgt S2)
• return g_subset_of(S1.Begin(), S1.End(),
  S2.Begin(), S2.End()
• bool operatorlt(const CSetltT, Cgt S1, const
  CSetltT, Cgt S2)
• return (S1.Size() lt S1.Size() S1 lt S2)
• bool operatorgt(const CSetltT, Cgt S1, const
  CSetltT, Cgt S2)
• return S2 lt S1
• bool operatorgt(const CSetltT, Cgt S1, const
  CSetltT, Cgt S2)
• return S2 lt S1

26
Global Operators on CSet

• // union
• CSetltT, Cgt operator(const CSetltT, Cgt S1, const
  CSetltT, Cgt S2)
• CSetltT, Cgt S
• InsertIteratorltCSetltT, Cgt gt I(S)
• g_set_union(S1.Begin(), S1.End(), S2.Begin(),
  S2.End(), I)
• return S
• // difference
• CSetltT, Cgt operator-(const CSetltT, Cgt S1, const
  CSetltT, Cgt S2)
• CSetltT, Cgt S
• InsertIteratorltCSetltT, Cgt gt I(S)
• g_set_difference(S1.Begin(), S1.End(),
  S2.Begin(), S2.End(), I)
• return S

27
Global Operators on CSet

• CSetltT, Cgt operator(const CSetltT, Cgt S1, const
  CSetltT, Cgt S2)
• CSetltT, Cgt S
• InsertIteratorltCSetltT, Cgt gt I(S)
• g_set_intersection(S1.Begin(), S1.End(),
  S2.Begin(), S2.End(), I)
• return S
• bool operator(const CSetltT, Cgt S1, const
  CSetltT, Cgt S2)
• if (S1.Size() ! S2.Size())
• return 0
• CSetltT, CgtIterator I1(S1), I2(S2)
• while (I1.Valid()
• if ((I1) ! (I2))
• return 0
• return 1

28
Global Operators on CSet

• bool operator!(const CSetltT, Cgt S1, const
  CSetltT, Cgt S2)
• return !(S1 S2)
• templatelttypename T, class Cgt
• stdostream operatorltlt(stdostream os, const
  CSetltT, Cgt S)
• CSetltT, CgtIterator I
• for (I S.Begin() I ! S.End() I)
• os ltlt I
• return os

29
The CSetIterator Adaptor

• template lttypename T, class Cgt
• class CSetIterator
• friend class CSetltT, Cgt
• public
• // constructors
• CSetIterator() i()
• CSetIterator(const CSetltT, Cgt S) i() i
  S.c.Begin()
• CSetIterator(const CSetIteratorltT, Cgt I)
  i(I.i)
• // initializers
• void Initialize(const CSetltT, Cgt S)
  i.Initialize(S.c)
• void rInitialize(cocnst CSetltT, Cgt S)
  i.rInitialize(S.c)
• // informationals
• value_type Retrieve() const return
  i.Retrieve()
• int Valid() const return i.Valid()

30
The CSetIterator Adaptor

• // operators
• int operator(const CSetIteratorltT, Cgt I2)
  const return i I2.i
• int operator!(const CSetIteratorltT, Cgt I2)
  const return i ! I2.i
• value_type operator() const return i
• CSetIteratorltT, Cgt operator(const
  CSetIteratorltT, Cgt I)
• i I.i
• return this
• CSetIteratorltT, Cgt operator()
• i
• return this
• CSetIteratorltT, Cgt operator(int)
• CSetIteratorltT, Cgt I this
• CSetIteratorltT, Cgtoperator()
• return I

31
The CSetIterator Adaptor

• CSetIteratorltT, Cgt operator--()
• --i
• return this
• CSetIteratorltT, Cgt operator--(int)
• CSetIteratorltT, Cgt I this
• CSetIteratorltT, Cgtoperator--()
• return I
• protected
• typename CIterator i

32
The CMap Adaptor

• template lttypename K, class V, class Cgt
• class CMap
• friend class CMapIteratorltK, V, Cgt
• public
• typedef K key_type
• typedef C container_type
• typedef typename Cvalue_type value_type
• typedef CMapIteratorltK, V, Cgt Iterator
• // proper type
• CMap() c()
• CMap(const CMapltK, V, Cgt M) c(M.c)
• CMap() c.Clear()
• CMap operator(const CMapltK, V, Cgt M)
• if (this ! M)
• c M.c
• return this

33
The CMap Adaptor

• // associative array operator unimodal
• V operator(const K k)
• TAssociationltK, Vgt p
• p.key k
• typename CIterator i c.LowerBound(p)
• if (!i.Valid() p ! i) // if not in map
  or not identical key
• c.Insert(i, p)
• return (i).value

34
The CMap Adaptor

• Iterator Insert(const K k, const V v)
• TAssociationltK, Vgt p
• Iterator I
• I.i c.LowerBound(p)
• if (!I.Valid() p ! I) // not found
• if (c.Insert(I.i, p)
• return I
• else
• return End()
• (I).value v // overwrite if found
• return I
• int Insert(Iterator I, const K k, const V v)
  
• TAssociationltK, Vgt p(k, v)
• return c.Insert(I.i, p)

35
The CMap Adaptor

• unsigned int Remove(const K k)
• TAssociationltK, Vgt p
• p.key k
• return c.Remove(p)
• int Remove(Iterator I) return c.Remove(I.i)
  
• void Clear() return c.Clear()
• // size operations
• unsigned long Size() const return c.Size()
• int Empty() const return c.Empty()

36
The CMap Adaptor

• // locator operations
• Iterator Includes(const K k) const
• CMapIteratorltK, V, Cgt I
• TAssociationltK, Vgt p
• p.key k
• I.i c.LowerBound(p)
• if (I.Valid() (k (I).key)
• return I
• return End()
• Iterator LowerBound(const K k) const
• Iterator UpperBound(const K k) const

37
The CMap Adaptor

• Iterator Begin() const
• CMapIteratorltK, V, Cgt I
• I.i c.Begin()
• return I
• Iterator End() const
• Iterator rBegin() const
• Iterator rEnd() const
• protected
• C c

38
The CMapIterator

• templatelttypename K, class V, class Cgt
• class CMapIterator
• friend class CMapltK, V, Cgt
• public
• // bidirectional iterator interface
• protected
• typename CIterator i

39
The CMultiMap Adaptor

• templatelttypename K, class V, class Cgt
• class CMultiMap
• friend class CMapIteratorltK, V, Cgt
• public
• typedef K key_type
• typedef C container_type
• typedef typename Cvalue_type value_type
• typedef CMapIteratorltK, V, Cgt Iterator
• // proper type
• CMultiMap() c()
• CMultiMap(const CMultiMapltK, V, Cgt MM)
  c(MM.c)
• CMultiMap() c.Clear()
• CMultiMap operator(const CMultiMap MM)

40
The CMultiMap Adaptor

• // operators
• Iterator Insert(const K k, const V v)
• TassociationltK, Vgt p(k, v)
• Iterator I
• I.i c.Insert(p)
• return I
• int Insert(Iterator I, const K k, const V v)
  
• TAssociationltK, Vgt p(k, v)
• return c.Insert(I.i, p)
• unsigned int Remove(const K k)
• TAssociationltK, Vgt p
• p.key k
• return c.Remove(p)
• int Remove(Iterator I) return c.Remove(I.i)
  
• void Clear() return c.Clear()

41
The CMultiMap Adaptor

• // size operations
• unsigned long Size() const return c.Size()
• int Empty() const return c.Empty()
• // locator operations
• Iterator Includes(const K k) const
• Iterator I
• TAssociationltK, Vgt p
• p.key k
• I.i c.Includes(p)
• return I
• Iterator LowerBound(const K k) const
• Iterator UpperBound(const K k) const

42
The CMultiMap Adaptor

• Iterator Begin() const
• CMultiMapIteratorltK, V, Cgt I
• I.i c.Begin()
• return I
• Iterator End() const
• Iterator rBegin() const
• Iterator rEnd()
• protected
• C c

43
The CHashSet Adaptor

• template lttypename T, class H, class Cgt
• class CHashSet
• friend class CHashSetIteratorltT, H, Cgt
• public
• typedef T value_type
• typedef H hash_type
• typedef C bucket_type
• typedef CHashSetIteratorltT, H, Cgt Iterator
• // constructor
• CHashSet(size_t number_of_buckets)
• CHashSet()
• // element operations
• Iterator Insert(const value_type t)
• int Insert(Iterator I, const value_type t)
• size_t Remove(const value_type t)
• int Remove(Iterator I)

44
The CHashSet Adaptor

• // locator operations
• Iterator Includes(const value_type t) const
• Iterator Begin() const
• Iterator End() const
• Iterator rBegin() const
• Iterator rEnd() const
• // size operations
• int Empty() const
• size_t Size() const
• protected
• size_t numBuckets
• TVectorltCgt bucketVector
• H hashObject
• private
• CHashSet(const CHashltT, H, Cgt)
• CHashSet operator(const CHashSet)

45
The CHashSetIterator Adaptor

• template lttypename T, class H, class Cgt
• class CHashSetIterator
• friend class CHashSetltT, H, Cgt
• public
• // bidirectional iterator public interface
• protected
• const CHashSetltT, H, Cgt setPtr
• typename CIterator bucketItr
• size_t bucketNum