1. Introduction
In mathematics, a polynomial is an expression that contains a sum of powersin one or morevariablesmultiplied bycoefficients. A polynomial in one variable,
, with constant coefficients is like:
. We call each item, e.g.,
, a term. If two terms have the same power, we call them like terms.
In this tutorial, we’ll show how to add and multiply two polynomials using a linked list data structure.
Adding two polynomials using Linked List
Given two polynomial numbers represented by a linked list. Write a function that add these lists means add the coefficients who have same variable powers.
Example:
Input:
1st number = 5x2 + 4x1 + 2x0
2nd number = -5x1 - 5x0
Output:
5x2-1x1-3x0
Input:
1st number = 5x3 + 4x2 + 2x0
2nd number = 5x^1 - 5x^0
Output:
5x3 + 4x2 + 5x1 - 3x0
Polynomial Addition | Polynomial Subtraction | Polynomial Multiplication — Using Linked List
What is Polynomial in Mathematics ?
Polynomial comes from poly [meaning “many”] and nomial [in this case meaning “term”] so it says “many terms”
In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7.
A polynomial can have:
- constants [like 3, −20, or ½]
- variables [like x and y]
- exponents [like the 2 in y2], but only 0, 1, 2, 3 etc are allowed.
Possible operations on Polynomials
- Addition
- Subtraction
- Multiplication
- Division
Except
- Division by a variable [ something like 2/x ]
A polynomial can have constants, variables and exponents, but never division by a variable.
Read more on Linked List…
What is Linked List ? | Advantages and Disadvantages of Linked List | Examples of Linked List using C Programming Language
Polynomial Operation using Linked List C Programs
1. Polynomial Addition using Linked List
2. Polynomial Subtraction using Linked List
3. Polynomial Multiplication using Linked List
4. Polynomial Addition and Multiplication using Linked List
Content: complete the addition operation of two polynomials. It is known that there are two polynomials PM [x] and QM [x]. Design an algorithm to realize the operation of Pm[x]+Qm[x] and Pm[x]-Qm[x]. Moreover, the wig operation does not reopen the storage space, and it is required to be realized by chain storage structure.
Steps:
- algorithm analysis
The implementation of the addition algorithm of two polynomials is to store the two polynomials in a linked list. Set two pointers LAI and LBI to move the first node of equations Pm[x] and Qm[x] respectively, and compare the exponential direction of the node referred to by LAI and LBI, which can be divided into the following three cases:
- If LAI - > exp < LBI - > exp, the node referred to by LAI is one of the polynomials, and the LAI pointer moves back one position on the original basis.
- If LAI - > exp = LBI - > exp, add the coefficients of the corresponding terms, and then deal with them in two cases: if the sum of the coefficient terms is zero, release the node pointed to by LAI and LBI; if the sum of the coefficient terms is not zero, modify the coefficient field of the node pointed to by LAI and release the LBI node.
- If Lai - > exp > LBI - > exp, the node referred to by LBI is one of the polynomials, and the LBI pointer moves back one position on the original basis.
Two polynomial subtraction algorithm, the first is to store the two polynomials in a linked list. Set two pointers LAI and LBI to move the first node of equations Pm[x] and Qm[x] respectively, and compare the exponential direction of the node referred to by LAI and LBI, which can be divided into the following three cases:
- If LAI - > exp < LBI - > exp, the node referred to by LAI is one of the polynomials, and the LAI pointer moves back one position on the original basis.
- If LAI - > exp = LBI - > exp, subtract the coefficients of the corresponding term, and then deal with it in two cases: if the sum of the coefficient terms is zero, release the node pointed to by LAI and LBI; if the sum of the coefficient terms is not zero, modify the coefficient field of the node pointed to by LAI and release the LBI node.
- If Lai - > exp > LBI - > exp, the node referred to by LBI is one of the polynomials, and the LBI pointer moves back one position on the original basis.
- Algorithm design
Five functions are designed in the program:
- Init[] is used to initialize the linked list;
- CreatFromTail[] creates a linked list by tail interpolation;
- Polyadd[] is used to realize the addition algorithm of two polynomials;
- Polysub[] is used to realize the subtraction of two polynomials;
- Print[] is used to output polynomials.
#include
#include
#include
typedef struct poly
{
int exp; //index
int coef; //coefficient
struct poly *next;
}PNode,*PLinklist;
/*Linked list initialization*/
int Init[PLinklist *head]
{
*head=[PLinklist]malloc[sizeof[PNode]];
if[*head]
{
[*head]->next=NULL;
return 1;
}
else
return 0;
}
/*Creating linked list by tail interpolation*/
int CreateFromTail[PLinklist*head]
{
PNode *pTemp,*pHead;
int c; //Storage factor
int exp; //Storage index
int i=1 ; //Counter
pHead=*head;
scanf["%d,%d",&c,&exp];
while[c!=0]//When the coefficient is zero, end the input
{
pTemp=[PLinklist]malloc[sizeof[PNode]];
if[pTemp]
{
pTemp->exp=exp; //Acceptance index
pTemp->coef=c; //Acceptance coefficient
pTemp->next=NULL;
pHead->next=pTemp;
pHead=pTemp;
scanf["%d,%d",&c,&exp];
}
else
return 0;
}
return 1;
}
/*Add two polynomials*/
void Polyadd[PLinklist LA,PLinklist LB]
{
PNode*LAI=LA->next; //Pointer LAI moves in polynomial A
PNode*LBI=LB->next;
PNode*temp; //Pointer temp saves the node to be deleted
int sum=0; //Sum of preservation factors
/*Compare the exponential terms of the nodes referred to by LAI and LBI*/
while[LAI&&LBI]
{
if[LAI->expexp]{
LA->next=LAI;
LA=LA->next;
LAI=LAI->next;
}
else if[LAI->exp==LBI->exp]
{
sum=LAI->coef+LBI->coef;
if[sum]
{
LAI->coef=sum;
LA->next=LAI;
LA=LA->next;
LAI=LAI->next;
temp=LBI;
LBI=LBI->next;
free[temp];
}
else
{
temp=LAI;
LAI=LAI->next;
free[temp];
temp=LBI;
LBI=LBI->next;
free[temp];
}
}
else
{
LA->next=LBI;
LA=LA->next;
LBI=LBI->next;
}
}
if[LAI]
LA->next=LAI;
else
LA->next=LBI;
}
/*Subtraction of two polynomials*/
void Polysub[PLinklist LA,PLinklist LB]
{
PNode*LAI=LA->next; //Pointer LAI moves in polynomial A
PNode*LBI=LB->next;
PNode*temp; //Pointer temp saves the node to be deleted
int difference=0; //Preservation factor
/*Compare the exponential terms of the nodes referred to by LAI and LBI*/
while[LAI&&LBI]
{
if[LAI->expexp]{
LA->next=LAI;
LA=LA->next;
LAI=LAI->next;
}
else if[LAI->exp==LBI->exp]
{
difference=LAI->coef-LBI->coef;
if[difference]
{
LAI->coef=difference;
LA->next=LAI;
LA=LA->next;
LAI=LAI->next;
temp=LBI;
LBI=LBI->next;
free[temp];
}
else
{
temp=LAI;
LAI=LAI->next;
free[temp];
temp=LBI;
LBI=LBI->next;
free[temp];
}
}
else
{
LA->next=LBI;
LA=LA->next;
LBI=LBI->next;
}
}
if[LAI]
LA->next=LAI;
else
LA->next=LBI;
}
void Print[PLinklist head]
{
head=head->next;
while[head]
{
if[head->exp]
printf["[%dx^%d]",head->coef,head->exp];
else
printf["%d",head->coef];
if[head->next]
printf["+"];
else
break;
head=head->next;
}
}
int main[void]
{
PLinklist LA;
PLinklist LB;
Init[&LA];
Init[&LB];
printf["Please enter the coefficient of the first polynomial,index,Enter 0,0 End input\n"];
CreateFromTail[&LA];
printf["Please enter the coefficient of the second polynomial,index,Enter 0,0 End input\n"];
CreateFromTail[&LB];
Print[LA];
printf["\n"];
Print[LB];
printf["\n"];
int i;
printf["[Please enter 1 for addition polynomial and 0 for subtraction polynomial]\n"];
scanf["%d",&i];
if[1==i]{
Polyadd[LA,LB];
printf["The result of adding two polynomials:\n"];
Print[LA];
printf["\n"];
}
else if[0==i]{
Polysub[LA,LB];
printf["The result of subtracting two polynomials:\n"];
Print[LA];
printf["\n"];
}
else
printf["Please enter the correct characters"];
return 0;
}