1 Chapter 3 Lists, Stacks, and Queues Abstract Data Types, Vectors Sections 3.1, 3.2, 3.3, 3.4 Abstract Data Types (ADT) Iterators Implementation of Vector

2 Abstract Data Type (ADT) High-level definition of data types An ADT specifies –A collection of data –A set of operations on the data or subsets of the data ADT does not specify how the operations should be implemented Examples –list, stack, queue, deque, priority queue, table (map), associative array, set, graph, digraph How are they different? –Class –Class template –ADT

3 List ADT Objects/data –A 0, A 1, A 2, … A N-1 –Size of the List is N Operations –Up to the designer of a List, for example, –printList() –makeEmpty() –Find() –Insert() –Remove() –findKth() –etc

4 Iterators: Motivation Need a way to navigate through the items in a container. An example: navigating over vector v. for (int i = 0; i != v.size(); i++ ) cout << v[i] << endl; However, doubly-linked list would need a different form We want a general approach to navigate elements for different implementations of an ADT

5 Iterators A generalized type that helps in navigating a container –A way to initialize at the front and back of a list –A way to move to the next or previous position –A way to detect the end of an iteration –A way to retrieve the current value Implemented as nested types of containers in STL Examples: –Iterator type for vector defined as vector ::iterator itr; –Iterator type for list defined as list ::iterator itr;

6 Getting an Iterator Two methods in all STL containers –iterator begin ( ) Returns an iterator to the first item in the container –iterator end ( ) Returns an iterator representing end marker in the container (that is, the position after the last item) Example for (int i = 0; i != v.size(); i++ ) cout << v[i] << endl; can be written using iterators as for(vector ::iterator itr=v.begin(); itr!=v.end(); itr++) cout << itr++ << endl;

7 Iterator Methods Iterators have methods Many methods use operator overloading –itr++ and ++itr  advance the iterator to next location –*itr  return reference to object stored at iterator itr’s location – itr1 == itr2  true if itr1 and itr2 refer to the same location, else false – itr1 != itr2  true if itr1 and itr2 refer to different locations, else false

8 Container Operations Requiring Iterators Adding element –iterator insert(iterator pos, const object &x) –Add x in list before interator pos –Returns iterator representing position of inserted item Removing element –iterator erase(iterator pos) –Remove element at position pos –Returns iterator representing position of item following pos Removing elements in a range –iterator erase(iterator start, iterator end) –Remove elements from start to end (not including end )

9 Iterator example Removing every other elements in a list

10 The Vector Implementation of List ADT Extends the notion of array by storing a sequence of arbitrary objects –Informally, we call it Vector ADT Elements of vector ADT can be accessed by specifying their index

11 vector in C++ STL Collection  Elements of some proper type T Operations –int size ( )  returns the number of elements in the vector –void clear ( )  removes all elements from the vector –bool empty ( )  returns true if the vector has no elements –void push_back ( const Object &x ) adds x to the end of the vector –void pop_back ( ) Removes the object at the end of the vector –Object & back ( ) Returns the object at the end of the vector –Object & front ( ) Returns the object at the front of the vector

12 vector in C++ STL (contd.) More Operations –Object & operator[] ( int index ) Returns the object at location index (without bounds checking) Both accessor and mutator versions –int capacity ( ) Returns the internal capacity of the vector Number of elements the container can hold without further memory allocation –void resize ( int newSize, const Object& val = Object() ) Change the size of the vector Newly created elements will be initialized to val

13 Implementing the vector Class Implementing Vector as first-class type –Can be copied –Memory it uses is automatically reclaimed Vector maintains –A primitive C++ array –The array capacity –The current number of items stored in the vector Operations –Copy constructor –operator= –Destructor to reclaim primitive array –All the other operators we saw earlier

14 vector Implementation template class vector { public: // lots of member functions typedef T * iterator; private: int theSize; int theCapacity T *Array };

15 vector Member Functions - 1 vector(int initialSize=1) : theSize(initialSize),theCapacity(initialSize+1) {Array = new T[theCapacity];} ~vector() {delete [] Array;} void pop_back() {theSize--;} O(1) iterator begin() {return Array;} iterator end() {return Array + theSize;} T &operator[](int index) {return Array[index];} O(1)

16 vector Member Functions - 2 vector &operator=(vector &rhs) { if(this != &rhs) // Prevents self-copy { delete Array; theSize = rhs.size(); theCapacity = rhs.theCapacity; Array = new T[ capacity() ]; for(int k=0; k<size(); k++) Array[k] = rhs.Array[k]; }

17 vector Member Functions - 3 void reserve(int N) { if(N < theSize) return; T *old = Array; Array = new T[N]; for(int k=0;k<theSize;k++) Array[k] = old[k]; theCapacity = N; delete [] old; } O(N) void push_back(T &x) { if(theSize==theCapacity) reserve(2*theSize); // Assumes theSize > 0 Array[theSize++] = x; } Array old

18 Amortized Analysis of push_back Consider the time for N push_backs –Time for copying the data = N*O(1) = O(N) –Let 2 k <= N < 2 k+1 –Time for call to reserve = O( k+1 ) = O(2 k+2 -1) = O(2N) = O(N) –So, the total amortized time per push_back is O(1)