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 – (e 0, e 1, e 2, …, e n-1 ) – where e i denotes a list element – n >= 0 is finite – list size is n (the number of elements in the list)

Linear Lists L = (e 0, e 1, e 2, e 3, …, e n-1 ) relationships e 0 is the zero’th (or front) element e n-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 a get(2) is c get(4) is e Check if the index is valid before get operation (theIndex >=0 and theIndex<=listSize) get(-1) is error get(9) is error

Linear List Operations— indexOf(theElement) determine the index of a given element L = (a,b,d,b,a) indexOf(d) is 2 indexOf(a) is 0 indexOf(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 c and L becomes (a,b,d,e,f,g) index of d,e,f, and g decrease by 1 Size 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 c and L becomes (a,b,d,e,f,g) L.size() becomes 5 index of d,e,f, and g decrease by 1 Size 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 1 Size 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 1 Check 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 independent  Abstract 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 Type AbstractDataType 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 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 arrayList : public linearList { // 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}; Linear List Array Representation abcde 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. abcdef 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. abcdefabcdef copy(element, element + 6, newArray);

Increasing Array Length Finally, delete old array and rename new array. delete [] element; element = newArray; arrayLength = 15; abcdef element[0]

Change Array Length template 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 arrayList template class arrayList : public linearList { public: // constructor, copy constructor and destructor arrayList(int initialCapacity = 10); arrayList(const arrayList &); //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;

Constructor template arrayList ::arrayList(int initialCapacity) {// Constructor. if (initialCapacity < 1) { cout << “wrong intinitial capacity” << endl; } arrayLength = initialCapacity; element = new T[arrayLength]; listSize = 0; }

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

Copy Constructor arrayList(const arrayList & theList); Now copy elements from old array to new one. abcdef arrayLength = theList.arrayLength; listSize = theList.listSize; element = new T[arrayLength]; copy(theList.element, theList.element + listSize, element); abcdef theList element

Copy constructor template arrayList ::arrayList(const arrayList & theList) { // Copy constructor. arrayLength = theList.arrayLength; listSize = theList.listSize; element = new T[arrayLength]; copy(theList.element, theList.element + listSize, element); }

constructor // test constructor arrayList *x = new arrayList (20); arrayList y(2), z; //test copy constructor arrayList w(y);

The Method checkIndex template void arrayList ::checkIndex(int theIndex) const {// Verify that theIndex is between 0 and // listSize - 1. if (theIndex = listSize) {cout << “invalid index” << endl; return ;} }

The Method get template T& arrayList ::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; abcdef element

The Method indexOf template int arrayList ::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;

Erase erase(int theIndex) erase(2) abdef copy(element + theIndex + 1, element + listSize, element + theIndex); element[--listSize].~T(); // invoke destructor abcdef element

The Method erase template void arrayList ::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;

insert insert(int theIndex, const T& theElement) insert(2,’c’) abdef copy_backward(element + theIndex, element + listSize, element + listSize + 1); element[theIndex] = theElement; listSize++; abcdef element

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

Overloading << // overload << template ostream& operator & 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 account on Next Tuesday (2/08) before 1pm.