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

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

List ADT Objects/data Operations A0, A1, A2, … 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

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

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<int> defined as vector<int>::iterator itr; Iterator type for list<string> defined as list<string>::iterator itr;

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<int>::iterator itr=v.begin(); itr!=v.end(); ++itr) cout << *itr << endl;

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

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)

Iterator example Removing every other elements in a list

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

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

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

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

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

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)

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]; } 16 16

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) Array old void push_back(T &x) { if(theSize==theCapacity) reserve(2*theSize); // Assumes theSize > 0 Array[theSize++] = x; } 17 17

Amortized Analysis of push_back Consider the time for N push_backs Time for copying the data = N*O(1) = O(N) Let 2k <= N < 2k+1 Time for call to reserve = O(1 + 2 + 4 + ... + 2k+1) = O(2k+2-1) = O(2N) = O(N) So, the total amortized time per push_back is O(1) 18 18