Question

Implementing Polynomials using Singly Linked List in C++

1. The Term Class
   
   Create a class to represent a term in an algebraic expression. As defined here, a term consists of an integer coefficient and a nonnegative integer exponent. E.g.
   
   • in the term 4X², the coefficient is 4 and the exponent 2
   • in -6X⁸, the coefficient is -6 and the exponent 8
   
   Your class will have a constructor that creates a Term object with a coefficient and exponent passed as parameters, and accessor methods that return the coefficient and the exponent
   
   
   II. The Polynomial Class
   
   Now create a class to represent a polynomial. As defined here, a polynomial is a sequence of terms. E.g.
   
   1. 3X² + 4X⁴ + X⁶
   2. 2 + 5X² + 6X³ + 2X⁷
   3. 4X¹⁰
   
   The terms of polynomial 1 are (3,2), (4,4) and (1,6). The terms of polynomial 2 are (2,0), (5,2), (6,3) and (2,7). Polynomial 3 has only one term (4,10)
   
   F To receive credit for this assignment, your class must use a generic “List of Term” to store the terms of a Polynomial object
   
   Your class will have a constructor that creates an empty list and additional methods to do each of the following:
   
   1. insert a new term in its proper place in a polynomial (see “Additional Specifications,” below)
   
   2. return all the terms of a polynomial as a single line string, as shown here:
   
   3x^2 + 4x^4 + x^6
   
   3. delete a term from a polynomial (see “Additional Specifications,” below)
   
   4. Compute and return the derivative of all the polynomial

5. reverse the order of the terms in a polynomial (see “Additional Specifications,” below)


III. The Test Class

The main method of your test class will create a Polynomial object and then read and process a series of operations

The operations are:

1. INSERT X Y

Insert a new term with coefficient X and exponent Y into its proper place in the polynomial

(insert method : adds terms to the list in descending order of power)

2. DELETE X Y

Remove the term with coefficient X and exponent Y from the polynomial

3. REVERSE

Reverse the order of the terms of the polynomial

4. 1^st DEV

          to find the first derivatives of the polynomial

   2^nd DEV

         to find the second derivatives of the polynomial

Each operation is to be carried out by calling a method of the Polynomial class

Each operation read must be “echo printed” to the screen

After each operation, print the updated polynomial by calling the toString() method

For the Derivatives operation, print the string returned
-----------------------------------------------------------------------------

Answer 1

#include<iostream>
#include<string>
using namespace std;
class Term
{
   private :
       int coeff;
       int expo;
   public :
       Term *next;
       Term()
       {
           next=NULL;
       }
       Term(int c,int e)
       {
           coeff=c;
           expo=e;
           next=NULL;
       }
       int getCoeff(void)
       {
           return coeff;
       }
       int getExpo(void)
       {
           return expo;
       }
      
};

class Polynomial
{

  
   public :
       Term *head;
       Polynomial()
       {
           head=NULL;
       }
      
   void insert(int x,int y)
   {
      Term *temp=head;
      Term *pre=NULL;
     
          while(temp!=NULL&&temp->getExpo()>y)
          {
              pre=temp;
              temp=temp->next;
           }
       Term *node=new Term(x,y);
       if(pre==NULL)
       {
           head=node;
       }
       else
       {
           pre->next=node;
           node->next=temp;
       }
         
   }
   string printPolynomial(Term *Head)
   {
      Term *temp=Head;
      int count=0;
      string str("");
      if(temp==NULL)
      return str;
      while(temp->next!=NULL)
      {
          int coeff=temp->getCoeff();
          int expo=temp->getExpo();
          if(coeff<0)
          coeff=coeff*-1;
          string s("");
          s.append(to_string(coeff)).append("x^").append(to_string(expo));
          if(coeff<0)
          {
              str.append(" - ").append(s).append(" ");
           }
           else if(count>0)
           {
              str.append(" + ").append(s).append(" ");
           }
           else
           {
              str.append(s).append(" ");
           }
           count++;
          temp=temp->next;
       }
          int coeff=temp->getCoeff();
          int expo=temp->getExpo();
       str.append(to_string(coeff)).append("x^").append(to_string(expo));
       return str;
   }
   void reverse()
   {
      Term* current = head;
Term *prev = NULL, *next = NULL;
  
while (current != NULL) {
  
next = current->next;

current->next = prev;
prev = current;
current = next;
}
head = prev;
   }
   Term* derivation(Term *Head)
   {
      Term *temp=Head;
      Term *p=NULL,*pre=NULL;
      while(temp!=NULL)
      {
          if(temp->getExpo()>1)
          {
              Term *node=new Term(temp->getExpo()*temp->getCoeff(),temp->getExpo()-1);
              if(p==NULL)
              {
                  p=node;
                  pre=node;
               }
               else
               {
                  pre->next=node;
                  pre=node;
               }
           }
           temp=temp->next;
       }
       return p;
   }
     
   void deleteTerm(int x,int y)
   {
      Term *pre=NULL,*temp=head;
      if(head!=NULL&&head->getCoeff()==x&&head->getExpo()==y)
      {
          head=head->next;
          delete(temp);
          return ;
       }
       while(temp!=NULL&&temp->getCoeff()!=x&&temp->getExpo()!=y)
       {
          pre=temp;
          temp=temp->next;
       }
         
       if(temp==NULL)
       return;
       pre->next=temp->next;
       delete(temp);
         
   }
     
      
};

int main()
{
   Polynomial p1;
   p1.insert(4,5);
   p1.insert(-3,2);
   p1.insert(2,4);
   string str=p1.printPolynomial(p1.head);
   cout<<str<<endl;
   p1.reverse();
   str=p1.printPolynomial(p1.head);
   cout<<str<<endl;
   Term *node=p1.derivation(p1.head);
   cout<<p1.printPolynomial(node)<<endl;
   p1.deleteTerm(2,4);
   str=p1.printPolynomial(p1.head);
   cout<<str<<endl;
  
}