DS: Polynomial Addition - 2

Polynomial Representation:

The polynomial can be represented using following methods:

1. Using structure of arrays

2. Using array of structures

1. Using structure of arrays:

syntax:

struct polynomial{

int degree;

float coeff[100];

} ;

typedef struct polynomial POLY;

POLY a,b;

a(x)=25x⁴ +12x² +2x +7

a.degree=4;

a.coeff[0]=7

a.coeff[1]=2;

a.coeff[2]=12;

a.coeff[3]=0;

a.coeff[4]=25;

b(x)=28x⁵ +6

b.degree=5;

b.coeff[0]=6

b.coeff[1]=0;

b.coeff[2]=0;

b.coeff[3]=0;

b.coeff[4]=28;

Advantage:

1.This representation is simple

2.Using this we can write easy algorithms.

3.If few terms with zero coefficients are present, this uses less space.

Disadvantage:

If more terms with zero coefficients are present, this uses more space.

2.Using Array of structures

In this we use an array of structures. Instead of using one array for each polynomial as in the previous method, here we use one array to store all the polynomials.

Syntax:

typedef struct{

float coeff;

int expon;

}POLY;

POLY p[100];

example:

Concider two polynomials

a(x)=25x⁴ +12x² +2x +7

and b(x)=28x⁵ +6

 

advantage:

If more terms with zero coefficients are present, this uses less space.

Disadvantage:

If more terms with non-zero coefficients are present, this uses more space(usually twice the memorey used by previous method).

ARRAY OF STRUCTURES PROGRAM

Write a program to add two polynomials

#include<stdio.h>

#include<stdlib.h>

#define MAX_SIZE 100

#define COMPARE(x,y)(((x)==(y))?0:((x)>(y))?1:-1)

int avail;

typedef struct{

float coeff;

int exp;

}POLY;

void attach(POLY *p, float coeffei, int expei){

if(avail==MAX_SIZE){

printf("Too many items");

exit(0);

}

p[avail].coeff=coeffei;

p[avail].exp=expei;

avail++;

}

void addpoly(POLY *p,int startA,int startB,int *startC,int endA,int endB,int *endC){

*startC=avail;

int expe;

float coeffe;

while(startA<=endA&&startB<=endB)

{

switch(COMPARE(p[startA].exp,p[startB].exp))

{

case 0: coeffe=p[startA].coeff+p[startB].coeff;

if(coeffe!=0)attach(p,coeffe,p[startA].exp);

startA++;

startB++;

break;

case 1: attach(p,p[startA].coeff,p[startA].exp);

startA++;

break;

default:attach(p,p[startB].coeff,p[startB].exp);

startB++;

}

}

*endC=avail-1;

}

readpoly(POLY *p,int *start,int *end)

{

int expe;

float coeffe;

int i=0;

*start=avail;

for(;;){

printf("Term number %d \n",++i);

printf("coeff "); scanf("%f",&coeffe);

printf("exponent "); scanf("%d",&expe);

attach(p,coeffe,expe);

if(expe==0) break;

}

*end=avail-1;

}

void printpoly(POLY *p,int start,int end){

while(start<=end)

{

if(p[start].coeff<0){ printf(" - ");}

else {printf(" + ");}

printf("%fx^%d ",p[start].coeff,p[start].exp);

start++;

}

}

void main()

{

POLY p[MAX_SIZE];

int startA,startB,startC;

int endA,endB,endC;

printf("ENTER THE FIRST POPPLPPYPOMIAL \n");

readpoly(p,&startA,&endA);

printf("ENTER THE SEC POPPLPPYPOMIAL \n");

readpoly(p,&startB,&endB);

addpoly(p,startA,startB,&startC,endA,endB,&endC);

printf("Sum of two polynomials \n");

printpoly(p,startC,endC);

}

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