Question

The polynomial addition C function of Program 2.6 padd is the code when the polynomial is used to arrange the polynomial in the two arrangement methods of the polynomial described in the text 2.4.2. For the remaining method, when the expression polynomial is arranged by a coefficient, create a polynomial addition C function padd() corresponding to Program 2.6.

66 Arrays And Structures are zero are not displayed. The term with exponent equal to zero does not shouw able since x raised to a power of zero is 1. There are standard mathematicathe va for the sum and product of polynomials. Assume that we have two polynomial ents and all poly, nomial Z olen IsZe S. A G) ar and B(a)-bx then: A(a)+B(x)-a br Similarly, we can define subtraction and division on polynomials, as well as operations We begin with an ADT definition of a polynomial. The particular operations in are a reflection of what will be needed in our subsequent programs to manipulate polynomials. The definition is contained in ADT 2.2. Exponent Lea 2.4.2 Polynomial Representation PolmomialA We are now ready to make some representation decisions. A very reasonable first deci- sion requires unique exponents arranged in decreasing order. This requirement consider ably simplifies many of the operations. Using our specification and this stipulation, we yn can write a version of Add that is closer to a C function (Program 2.5), but is stil representation-independent. This algorithm works by comparing terms from the two polynomials until one or both of the polynomials becomes empty. The switch statement performs the comparis- ons and adds the proper term to the new polynomial, d. If one of the polynomials becomes empty, we copy the remaining terms from the nonempty polynomial into a. With these insights, we now consider the representation question more carefully. mial as below: d. Pibnomial S One way to represent polynomials in C is to use typedef to create the type polyno- Plmomial A #define MAX-DEGREE 101 /*Max degree of polynomial +1 */ typedef struct i tlmomial M int degree float coef (MAX-DEGREE] polynomial; Now if a is of type polhynomial and n 0 functions for all poly, poly 1,poly2 e Polynomial, coef e Coefficients, expon e Exponents Polynomial Zero0 Boolean IsZero(poly) well as man - return the polynomial, P(x) 0 else return TRUE coefficient else return zero poly ular operatin ams to if (poly) return FALSE ::: if (expon e poly) return its :::: return the largest exponent in ::: İf (export e poly) return error thanip Coeficient Coef(poly expon) Exponent LeadExp(poly) Polynomial Attach(poly, coef, expon) onable first rement consit else return the polynomial poly with the term inserted . atisPolnomial Remove(palb, expom if (expon e poly) 2.5), but return the polynomial poly with the term whose exponent is expon deleted else return error until one s the comp e polynomi nomial into efully als Polynonnial SingleMult(poly, coef, expon) Polynomial Add(poly1, poly2) Polynomial Mult(poly1, poly2) - return the polynomial :-return the polynomial := return the polynomial poly coef poly1 + poly2 polyl poly2 e type pohn 1end Polynomial al+1/ ADT 2.2: Abstract data type Polynomial In this representation, we store the coeficients in order of decreasing exponents, Phacoef i] is the coefficient of x- provided a term with exponent n-i exists; for most a coef li]0. Although this representation leads to very simple algorithms llGEE (the double "less than" should be read as "is much less than"), then we MAX-DEGREE, (the double e operations, it wastes a lot of space. For instance, if a. degree

Answer 1

Your question only require the function padd but I am including other code for testing

#include<stdio.h>

#define MAX_DEGREE 101
typedef struct {
   int degree;
   float coef[MAX_DEGREE];
  
}polynomial;

/// ONLY REQUIRE BY YOUR QUESTION

void padd(polynomial* A,polynomial* B,polynomial *C){
   C->degree=A->degree>B->degree?A->degree:B->degree;
   //printf("%d",C->degree);
   int i=0,j=0,x=0;
   while(i<=A->degree && j<=B->degree){
           if(A->degree-i==B->degree-j){
               C->coef[x++]=A->coef[i++]+B->coef[j++];
           }
           else
           C->coef[x++]=A->degree-i>B->degree-j?A->coef[i++]:B->coef[j++];
  
      
   }
   while(i<=A->degree)C->coef[x++]=A->coef[i++];
   while(j<=B->degree)C->coef[x++]=B->coef[j++];
  
  
}

//END OF ANSWER

int main(){
   polynomial A,B,C;
   int i;
   //let's take A=x^3+x^2+1  
   A.degree=3;
   float a[MAX_DEGREE]={1,1,0,1};
   for(i=0;i<MAX_DEGREE;i++)A.coef[i]=a[i];
  
   // lets take B=X^2+X^1
   B.degree=2;
   float b[MAX_DEGREE]={1,1};
   for(i=0;i<MAX_DEGREE;i++)B.coef[i]=b[i];
   padd(&A,&B,&C);
   for(i=0;i<A.degree;i++)printf("%f   ",A.coef[i]);
   printf("\n");
   for(i=0;i<B.degree;i++)printf("%f   ",B.coef[i]);
   printf("\ndegree of C %d \n",C.degree);
   for(i=0;i<=C.degree;i++)printf("%f   ",C.coef[i]);
   printf("\n");
   return 0;
  
}