Question

In this project you will design, implement and test the ADT set using both Arrays and Linked Lists and implement all the operations described in the following definitions in addition to the add and remove operations. Sets are one of the basic building blocks for the types of objects considered in discrete mathematics. A set is an unordered collection of objects. Sets do not allow duplicates. • • the students in this class the chairs in this room The objects in a set are called the elements, or members of the set. A set is said to contain its elements. The notation a E A denotes that a is an element of the set A. If a is not a member of A, write a A. Order not important Ex. S= {a,b,c,d} = {b,c,a,d} Definition: Two sets are equal if and only if they have the same elements. Therefore, if A and B are sets, then A and B are equal if and only if, V2(z A + c + B) We write A = B if A and B are equal sets. Definition: The set A is a subset of B, if and only if every element of A is also an element of B. The notation ASB is used to indicate that A is a subset of the set B. Definition: The cardinality of a finite set A, denoted by A, is the number of distinct) elements of A. Definition: Let A and B be sets. The union of the sets A and B, denoted by A UB, is the set: {x|x E A V X E B} Example: The Union of {1,2,3} and {3, 4, 5} is {1,2,3,4,5). Definition: The intersection of sets A and B, denoted by An B, is:

PLEASE ANSWER THE FOLLOWING IN C++!! PLEASE READ THE QUESTION CAREFULLY!!! AS WELL AS WHOEVER ANSWERS THIS CORRECTLY I WILL UPVOTE!!!

Answer 1

LinkedList.h

======================

#pragma once

template <typename T>
class LinkedList {
private:
   // private node class to store internal data
   class Node {
   public:
       T data;
       Node* next;
       Node(T item) {
           data = item;
           next = nullptr;
       }
   };
   Node* head; // head of list
   int count; // number of elements in the list
public:
   LinkedList(); // constructor
   ~LinkedList(); // destructor
   int size(); // returns size of list
   void add(T item); // add given item at start of list
   void remove(T item); // removes given item from the list if it present
   T get(int index); // returns item at given index from list
   bool contains(T item); // return true if given item is in list
};

template <typename T>
LinkedList<T>::LinkedList() {
   // initialize variables
   head = nullptr;
   count = 0;
}

template <typename T>
LinkedList<T>::~LinkedList() {
   while (head != nullptr) {
       Node* temp = head;
       head = head->next;
       delete temp;
   }
}

template <typename T>
void LinkedList<T>::add(T item) {
   // create new node
   Node* node = new Node(item);
   // assign new node to head
   node->next = head;
   // re-assign head
   head = node;
   count++;
}

template <typename T>
void LinkedList<T>::remove(T item) {
   // create iterator
   Node* itr = head;
   // check if head is need to be removed
   if (head->data == item) {
       head = head->next;
       delete itr;
       count--;
       return;
   }
   // loop the list to find item
   for (int i = 1; i < size(); i++) {
       if (itr->next->data == item) {
           // remove next node
           // check if next node is last node
           if (itr->next->next == nullptr) {
               Node* temp = itr->next;
               itr->next = nullptr;
               delete temp;
               count--;
               return;
           }
           else {
               Node* temp = itr->next;
               itr->next = itr->next->next;
               delete temp;
               count--;
               return;
           }
       }
       itr = itr->next;
   }
}

template <typename T>
int LinkedList<T>::size() {
   return count;
}

template <typename T>
T LinkedList<T>::get(int index) {
   // create iterator
   Node* itr = head;
   for (int i = 0; i < index; i++) {
       itr = itr->next;
   }
   return itr->data;
}

template <typename T>
bool LinkedList<T>::contains(T item) {
   // create iterator
   Node* itr = head;
   // loop the list
   for (int i = 0; i < count; i++) {
       if (itr->data == item) {
           return true;
       }
       itr = itr->next;
   }
   return false;
}

==============================

MathSet.h

==============================

#pragma once
#include "LinkedList.h"

template <typename T>
class MathSet {
private:
   LinkedList<T>* list; // linked list to store elements in set
public:
   MathSet(); // constructor
   ~MathSet(); // destructor
   void add(T element); // adds given element to set if it doesn't exist in set
   void remove(T element); // removes given element from set
   bool contains(T element) const; // returns true if given element is in the set
   bool is_equal(const MathSet<T>& set); // returns true if this set is equal to given set
   bool is_subset(const MathSet<T>& set); // returns true if this set is subset of given set
   int cardinality() const; // return total number of elements in set
   MathSet<T>& make_union(const MathSet<T>& set); // returns a new set that is union of current set and given set
   MathSet<T>& intersection(const MathSet<T>& set); // returns a new set that is intersection of current set and given set
   MathSet<T>& difference(const MathSet<T>& set); // returns a new set that contains elements of this set that are not present in given set
   T get(int index); // returns element t given index
};

template <typename T>
MathSet<T>::MathSet() {
   // initialize variables
   list = new LinkedList<T>();
}

template <typename T>
MathSet<T>::~MathSet() {
   delete list;
}

template <typename T>
void MathSet<T>::add(T element) {
   // check if given element is not in list
   if (!list->contains(element)) {
       list->add(element);
   }
}

template <typename T>
void MathSet<T>::remove(T element) {
   // remove element from list
   list->remove(element);
}

template <typename T>
bool MathSet<T>::contains(T element) const{
   return list->contains(element);
}

template <typename T>
bool MathSet<T>::is_equal(const MathSet<T>& set) {
   // check size of sets
   if (cardinality() != set.cardinality()) {
       return false;
   }
   // loop current set
   for (int i = 0; i < cardinality(); i++) {
       // check if each elemnt is present in given set
       if (!set.contains(this->list->get(i))) {
           return false;
       }
   }
   return true;
}

template <typename T>
bool MathSet<T>::is_subset(const MathSet<T>& set) {
   // check size of sets
   if (this->cardinality() > set.cardinality()) {
       return false;
   }
   // loop current set
   for (int i = 0; i < cardinality(); i++) {
       // check if each elemnt is present in given set
       if (!set.contains(this->list->get(i))) {
           return false;
       }
   }
   return true;
}

template <typename T>
int MathSet<T>::cardinality() const{
   return list->size();
}

template <typename T>
MathSet<T>& MathSet<T>::make_union(const MathSet<T>& set) {
   // create a new set to return
   MathSet<T>* result = new MathSet<T>();
   // first add elements from current set
   for (int i = 0; i < this->cardinality(); i++) {
       result->add(this->list->get(i));
   }
   // add element from second set
   for (int i = 0; i < set.cardinality(); i++) {
       result->add(set.list->get(i));
   }
   // return the resulting set
   return *result;
}

template <typename T>
MathSet<T>& MathSet<T>::intersection(const MathSet<T>& set) {
   // create a new set to return
   MathSet<T>* result = new MathSet<T>();
   // loop the current set
   for (int i = 0; i < this->cardinality(); i++) {
       // check if elemet from current set present on both set
       if (set.contains(this->list->get(i))) {
           // add element to the result set
           result->add(this->list->get(i));
       }
   }
   // return the resulting set
   return *result;
}

template <typename T>
MathSet<T>& MathSet<T>::difference(const MathSet<T>& set) {
   // create a new set to return
   MathSet<T>* result = new MathSet<T>();
   // first add all elements from current set
   for (int i = 0; i < this->cardinality(); i++) {
       result->add(this->list->get(i));
   }
   // remove all element from second set
   for (int i = 0; i < set.cardinality(); i++) {
       result->remove(set.list->get(i));
   }
   // return the resulting set
   return *result;
}

template <typename T>
T MathSet<T>::get(int index) {
   return list->get(index);
}

=================================

main.cpp

=================================

#include <iostream>
#include "mathSet.h"
using namespace std;

int main() {
   // test all function from MathSet
   cout << "for testing create sets of characters" << endl;
   cout << "create empty set" << endl;
   MathSet<char> set1;
   cout << "size of set : " << set1.cardinality() << " expected : 0" << endl;
   cout << "adding elements to list" << endl;
   set1.add('A');
   set1.add('B');
   set1.add('A');
   cout << "size of set : " << set1.cardinality() << " expected : 2" << endl;
   cout << "creating second set" << endl;
   MathSet<char> set2;
   set2.add('C');
   set2.add('B');
   set2.add('D');
   cout << "set contains : ";
   for (int i = 0; i < set2.cardinality(); i++) {
       cout << set2.get(i) << " ";
   }
   cout << "expected : D B C" << endl;

   MathSet<char> set3;
   set3.add('B');
   set3.add('A');

   cout << "testing equality on set {B A} and {A B} :";
   if (set1.is_equal(set3)) {
       cout << " true ";
   }
   else {
       cout << " false ";
   }
   cout << "expected : true" << endl;
   cout << "testing equality on set {B A} and {D B C} :";
   if (set1.is_equal(set2)) {
       cout << " true ";
   }
   else {
       cout << " false ";
   }
   cout << "expected : false" << endl;

   cout << "testing union on set {B A} and {D B C} : ";
   MathSet<char> set4 = set1.make_union(set2);
   for (int i = 0; i < set4.cardinality(); i++) {
       cout << set4.get(i) << " ";
   }
   cout << "expected : B A D C" << endl;

   cout << "testing subset on set ";
   for (int i = 0; i < set2.cardinality(); i++) {
       cout << set2.get(i) << " ";
   }
   cout << "and set ";
   for (int i = 0; i < set4.cardinality(); i++) {
       cout << set4.get(i) << " ";
   }
   cout << ": ";
   if (set2.is_subset(set4)) {
       cout << " true ";
   }
   else {
       cout << " false ";
   }
   cout << "expected : true" << endl;

   cout << "testing subset on set ";
   for (int i = 0; i < set4.cardinality(); i++) {
       cout << set4.get(i) << " ";
   }
   cout << "and set ";
   for (int i = 0; i < set2.cardinality(); i++) {
       cout << set2.get(i) << " ";
   }
   cout << ": ";
   if (set4.is_subset(set2)) {
       cout << " true ";
   }
   else {
       cout << " false ";
   }
   cout << "expected : false" << endl;

   MathSet<char> set5 = set1.intersection(set4);
   cout << "testing intersection on set ";
   for (int i = 0; i < set1.cardinality(); i++) {
       cout << set1.get(i) << " ";
   }
   cout << "and set ";
   for (int i = 0; i < set4.cardinality(); i++) {
       cout << set4.get(i) << " ";
   }
   cout << ": ";
   for (int i = 0; i < set5.cardinality(); i++) {
       cout << set5.get(i) << " ";
   }
   cout << "expected : A B" << endl;

   MathSet<char> set6 = set4.difference(set2);
   cout << "testing difference on set ";
   for (int i = 0; i < set4.cardinality(); i++) {
       cout << set4.get(i) << " ";
   }
   cout << "and set ";
   for (int i = 0; i < set2.cardinality(); i++) {
       cout << set2.get(i) << " ";
   }
   cout << ": ";
   for (int i = 0; i < set6.cardinality(); i++) {
       cout << set6.get(i) << " ";
   }
   cout << "expected : A" << endl;

   return 0;
}

- 0 x G Microsoft Visual Studio Debug Console for testing create sets of characters create empty set size of set : 0 expected : 0 adding elements to list size of set : 2 expected : 2 creating second set set contains : DB C expected : DBC testing equality on set {B A} and {A B} : true expected : true testing equality on set {B A} and {D B C} : false expected : false testing union on set {B A} and {D BC}: CDAB expected : BADG testing subset on set DB C and set CDAB: true expected: true testing subset on set CDAB and set DBC: false expected : false testing intersection on set B A and set CDAB: A B expected : AB testing difference on set CDAB and set DBC: A expected : A C:\Users\ASUS FX505 source repos\MathSet Debug MathSet.exe (process 20304) exited with code 0. To automatically close the console when debugging stops, enable Tools->Options ->Debugging->Automatically close the conso le when debugging stops. Press any key to close this window ...

let me know if you have any problem. thank you.