Linear List

Array representation

Data structures

• A data structure is a particular way of storing and manipulating data in a computer so that it can be used efficiently.

• Simple data types (storing data and manipulated by build-on operators)

• Structured data types (member variables and functions)– Structs– Classes

Linear Lists

• Each instance of the data structure linear list (or ordered list) is an collection of ordered elements.

• Instances of a linear list are of the form– (e0, e1, e2, …, en-1)

– where ei denotes a list element– n >= 0 is finite– list size is n (the number of elements in the list)

Linear Lists

L = (e0, e1, e2, e3, …, en-1)

relationshipse0 is the zero’th (or front) element

en-1 is the last element

Linear List Examples/Instances

StudentsinCSC307=(Jack, Jill, Abe, Henry, Mary, …, Judy)

ExamsinCSC307=(exam1, exam2, exam3)

DaysofWeek = (S, M, T, W, Th, F, Sa)

Months = (Jan, Feb, Mar, Apr, …, Nov, Dec)

Linear List Operations—size()the number of elements in the list

determine list size

L = (a,b,c,d,e)

L.size() is 5

Linear List Operations—get(theIndex)get element with given index

L = (a,b,c,d,e)

L.get(0) is aget(2) is cget(4) is eCheck if the index is valid before get operation(theIndex >=0 and theIndex<=listSize)get(-1) is errorget(9) is error

Linear List Operations—indexOf(theElement)

determine the index of a given element

L = (a,b,d,b,a)indexOf(d) is 2indexOf(a) is 0indexOf(z) is -1 //element is not in the list

The index of a nonexistent element is defined to be –1. When theElement is in the list an index between 0 and size()-1 is the result. So –1 would be an invalid index and is used to represent the case when theElement is not in the list

Linear List Operations—erase(theIndex)

Remove/delete element with given index

L = (a,b,c,d,e,f,g)erase(2) removes cand L becomes (a,b,d,e,f,g)

index of d,e,f, and g decrease by 1Size of the list decrease by 1

Linear List Operations—erase

Remove/delete element from the list6

L = (a,b,c,d,e,f,g)erase(indexof(c)) removes cand L becomes (a,b,d,e,f,g)L.size() becomes 5

index of d,e,f, and g decrease by 1Size of the list decrease by 1

Linear List Operations—erase(theIndex)

Remove/delete element with given index

L = (a,b,c,d,e,f,g)Check if theIndex is valid before erase operation

erase(-1) => error

erase(20) => error

Linear List Operations—insert(theIndex, theElement)

add an element so that the new element has a specified index

L = (a,b,c,d,e,f,g)

insert(0,h) => L = (h,a,b,c,d,e,f,g)index of a,b,c,d,e,f, and g increase by 1Size of the list increase by 1

Linear List Operations—insert(theIndex, theElement)

L = (a,b,c,d,e,f,g)

insert(2,h) => L = (a,b,h,c,d,e,f,g)index of c,d,e,f, and g increase by 1Check if theIndex is valid before insert

insert(10,h) => error

insert(-6,h) => error

Abstract Data Type (ADT)

• Abstraction: separating the design details from its use of called abstraction. E.g. how the car’s engine works is abstraction, how the car’s engine is designed is implementation

• Abstract Data Type (ADT): a data type that separates the logical properties from the implementation details.

• Classes are a convenient way to implement an ADT.

Data Structure Specification

Language independentAbstract Data Type Abstract Data Type (ADT): a data type that separates the logical

properties from the implementation details and is a model for a certain class of data structures that have similar behavior;

C++Abstract Class is used for the class of data

structures.

Linear List Abstract Data TypeAbstractDataType LinearList{ instances ordered finite collections of zero or more elements operations empty(): return true iff the list is empty, false otherwise size(): return the list size (i.e., number of elements in the list) get(index): return the indexth element of the list indexO f(x): return the index of the first occurrence of x in the list, return -1 if x is not in the list erase(index): remove the indexth element, elements with higher index have their index reduced by 1 insert(theIndex, x): insert x as the indexth element, elements with theIndex >= index have their index increased by 1 output(): output the list elements from left to right}

Linear List As C++ Abstract Class

template<class T>class linearList { public: virtual ~linearList() {}; virtual bool empty() const = 0; virtual int size() const = 0; virtual T& get(int theIndex) const = 0; virtual int indexOf(const T& theElement) const = 0; virtual void erase(int theIndex) = 0; virtual void insert(int theIndex, const T& theElement) = 0; virtual void output(ostream& out) const = 0;};

cannot be instantiated.

Linear list data store

• Array• Linked list

Extending A C++ Class

template<class T>class arrayList : public linearList<T> { // code for all abstract methods of linearList must come here}

If arrayList does not provide an implementation for all abstract methods of linearList, arrayList also is abstract and so cannot be instantiated.

use a one-dimensional array element[]element[15] = {a,b,c,d,e};

0 1 2 3 4 5 6

Linear List Array Representation

a b c d e

L = (a, b, c, d, e)

Store element i of list in element[i].

14

Data Type Of Array element[]

• Data type of list elements is unknown.• To use this representation in C++, we must

know/provide a data type and length of the array element[].

• Use template type T to get a generic class that works for all data types.

• Define element[] to be of template type T.

Length of Array element[]

Don’t know how many elements will be in list.

Must pick an initial length and dynamically increase as needed.

Use variable arrayLength to store current length of array element[].

Increasing Array Length(length vs size)

What is different between size and length?Length/size of array element[] is 6.

a b c d e f

arrayLength = 15;

T* newArray = new T[arrayLength];

First create a new and larger array

Increasing Array Length

Now copy elements from old array to new one.

a b c d e f

a b c d e f

copy(element, element + 6, newArray);

Increasing Array Length

Finally, delete old array and rename new array.delete [] element;element = newArray;arrayLength = 15;

a b c d e f

element[0]

Change Array Length

template<class T>void changeLength1D(T*& a, int oldLength, int newLength){ if (newLength < 0)

{ cout << “wrong length!\n”; return -1;} T* temp = new T[newLength]; // new array int number = min(oldLength, newLength); // number to copy copy(a, a + number, temp); // function copy from algorithm.h delete [] a; // deallocate old memory a = temp;}

Class arrayListtemplate<class T>class arrayList : public linearList<T> { public: // constructor, copy constructor and destructor arrayList(int initialCapacity = 10); arrayList(const arrayList<T>&); //copy constructor ~arrayList(); // ADT methods from class linearList bool empty() const {return listSize == 0;} int size() const {return listSize;} T& get(int theIndex) const; int indexOf(const T& theElement) const; void erase(int theIndex); void insert(int theIndex, const T& theElement); void output(ostream& out) const; // additional method int capacity() const {return arrayLength;} protected: void checkIndex(int theIndex) const; // throw illegalIndex if theIndex invalid T* element; // 1D array to hold list elements int arrayLength; // capacity of the 1D array int listSize; // number of elements in list};

Constructor arrayList(int initialCapacity = 10);

arrayLength = initialCapacity;element = new T[arrayLength];listSize = 0;

Constructortemplate<class T>arrayList<T>::arrayList(int initialCapacity){// Constructor. if (initialCapacity < 1) {

cout << “wrong intinitial capacity” << endl;}

arrayLength = initialCapacity; element = new T[arrayLength]; listSize = 0;}

constructor

// test constructor arrayList<double> *x = new arrayList<double>(20); arrayList<int> y(2), z;

Copy Constructor arrayList(const arrayList<T>& theList);Now copy elements from old array to new one.

a b c d e f

arrayLength = theList.arrayLength;listSize = theList.listSize;element = new T[arrayLength];copy(theList.element, theList.element + listSize, element);

a b c d e ftheList

element

element

Copy constructor

template<class T>arrayList<T>::arrayList(const arrayList<T>& theList){

// Copy constructor. arrayLength = theList.arrayLength; listSize = theList.listSize; element = new T[arrayLength]; copy(theList.element, theList.element + listSize, element);}

constructor

// test constructor arrayList<double> *x = new arrayList<double>(20); arrayList<int> y(2), z;

//test copy constructorarrayList<int> w(y);

The Method checkIndex

template<class T>void arrayList<T>::checkIndex(int theIndex) const{// Verify that theIndex is between 0 and // listSize - 1. if (theIndex < 0 || theIndex >= listSize)

{cout << “invalid index” << endl; return ;}}

The Method get

template<class T>T& arrayList<T>::get(int theIndex) const{// Return element whose index is theIndex. // Throw illegalIndex exception if no such // element. checkIndex(theIndex); return element[theIndex];}

get(theIndex)

// test get cout << "Element with index 0 is " << y.get(0)

<< endl; cout << "Element with index 3 is " << y.get(3)

<< endl;

int indexOf(const T& theElement) const;

• indexOf(‘c’);• find(element, element + listSize, ‘c’) //algorithm.h• Find Return element+2;• indexOf(‘c’) is (element+2) – element

• indexOf(‘h’);• find(element, element + listSize, ‘h’)• Return element+listSise;• If indexOf(‘h’) is listSize // no element is in the list;

a b c d e felement

The Method indexOftemplate<class T>int arrayList<T>::indexOf(const T& theElement) const{// Return index of first occurrence of theElement. // search for theElement int theIndex = (int) (find(element, element + listSize, theElement) -

element); // check if theElement was found if (theIndex == listSize)

return -1; // not found else

return theIndex; }

// test indexOf int index = y.indexOf(‘a’); if (index < 0) cout << “a not found" << endl; else cout << "The index of a is " << index << endl;

index = y.indexOf(‘z’); if (index < 0) cout << “z not found" << endl; else cout << "The index of z is " << index << endl;

Eraseerase(int theIndex)

erase(2)

a b d e f

copy(element + theIndex + 1, element + listSize, element + theIndex);  element[--listSize].~T(); // invoke destructor

a b c d e felement

element

The Method erase

template<class T>void arrayList<T>::erase(int theIndex){

// Delete the element whose index is theIndex. checkIndex(theIndex); // valid index, shift elements with higher index copy(element + theIndex + 1, element + listSize, element + theIndex); element[--listSize].~T(); // invoke destructor}

// test erase y.erase(1); cout << "Element 1 erased" << endl; cout << "The list is " << y << endl; y.erase(2); cout << "Element 2 erased" << endl; cout << "The list is " << y << endl;

cout << "Size of y = " << y.size() << endl; cout << "Capacity of y = " << y.capacity() << endl; if (y.empty()) cout << "y is empty" << endl; else cout << "y is not empty" << endl;

insertinsert(int theIndex, const T& theElement)

insert(2,’c’)

a b d e f

copy_backward(element + theIndex, element + listSize, element + listSize + 1);

element[theIndex] = theElement;

listSize++;

a b c d e f

element

element

The Method insert

template<class T>void arrayList<T>::insert(int theIndex, const T& theElement){ // Insert theElement.

checkIndex(theIndex) ; // valid index, make sure we have space if (listSize == arrayLength) {// no space, double capacity changeLength1D(element, arrayLength, 2 * arrayLength); arrayLength *= 2;

}// shift elements right one position copy_backward(element + theIndex, element + listSize, element +

listSize + 1); element[theIndex] = theElement;

listSize++;}

// test insert y.insert(0, 2); y.insert(1, 6); y.insert(0, 1); y.insert(2, 4); y.insert(3, 5); y.insert(2, 3); cout << "Inserted 6 integers, list y should be 1 2 3 4 5 6" << endl; cout << "Size of y = " << y.size() << endl; cout << "Capacity of y = " << y.capacity() << endl; if (y.empty()) cout << "y is empty" << endl; else cout << "y is not empty" << endl; y.output(cout); cout << endl << "Testing overloaded <<" << endl; cout << y << endl;

The Method output

template<class T>void arrayList<T>::output(ostream& out) const{// Put the list into the stream out.copy(element, element + listSize, ostream_iterator<T>(cout, “ “));}

Overloading <<

// overload <<template <class T>ostream& operator<<(ostream& out, const arrayList<T>& x){

x.output(out); return out;

}

// test output cout << "Y is printed by output :\n"; y.output(cout); cout << "Y is printed by << :\n"; cout << y;

Next class – Lab 1 assignment

• See lab1 presentations and material on course webpage.

• Submit your lab assignment 1 to class email account on Next Tuesday (2/08) before 1pm.