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 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

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<int> defined as
vector<int>::iterator itr;
Iterator type for list<string> defined as
list<string>::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<int>::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 <typename T>
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]; } 16 16

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

18. 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( k+1) = O(2k+2-1) = O(2N) = O(N)
So, the total amortized time per push_back is O(1) 18 18