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 = 5x^2 + 4x^1 + 2x^0
     2nd number = 5x^1 + 5x^0
Output:
        5x^2 + 9x^1 + 7x^0
Input:
     1st number = 5x^3 + 4x^2 + 2x^0
     2nd number = 5x^1 + 5x^0
Output:
        5x^3 + 4x^2 + 5x^1 + 7x^0

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

// C++ program for addition of two polynomials 
// using Linked Lists 
#include<bits/stdc++.h> 
using namespace std; 
  
// Node structure containing power and coefficient of variable 
struct Node 
{ 
    int coeff; 
    int pow; 
    struct Node *next; 
}; 
              
// Function to create new node 
void create_node(int x, int y, struct Node **temp) 
{ 
    struct Node *r, *z; 
    z = *temp; 
    if(z == NULL) 
    { 
        r =(struct Node*)malloc(sizeof(struct Node)); 
        r->coeff = x; 
        r->pow = y; 
        *temp = r; 
        r->next = (struct Node*)malloc(sizeof(struct Node)); 
        r = r->next; 
        r->next = NULL; 
    } 
    else
    { 
        r->coeff = x; 
        r->pow = y; 
        r->next = (struct Node*)malloc(sizeof(struct Node)); 
        r = r->next; 
        r->next = NULL; 
    } 
} 
  
// Function Adding two polynomial numbers 
void polyadd(struct Node *poly1, struct Node *poly2, struct Node *poly) 
{ 
while(poly1->next && poly2->next) 
    { 
        // If power of 1st polynomial is greater then 2nd, then store 1st as it is 
        // and move its pointer 
        if(poly1->pow > poly2->pow) 
        { 
            poly->pow = poly1->pow; 
            poly->coeff = poly1->coeff; 
            poly1 = poly1->next; 
        } 
          
        // If power of 2nd polynomial is greater then 1st, then store 2nd as it is 
        // and move its pointer 
        else if(poly1->pow < poly2->pow) 
        { 
            poly->pow = poly2->pow; 
            poly->coeff = poly2->coeff; 
            poly2 = poly2->next; 
        } 
          
        // If power of both polynomial numbers is same then add their coefficients 
        else
        { 
            poly->pow = poly1->pow; 
            poly->coeff = poly1->coeff+poly2->coeff; 
            poly1 = poly1->next; 
            poly2 = poly2->next; 
        } 
          
        // Dynamically create new node 
        poly->next = (struct Node *)malloc(sizeof(struct Node)); 
        poly = poly->next; 
        poly->next = NULL; 
    } 
while(poly1->next || poly2->next) 
    { 
        if(poly1->next) 
        { 
            poly->pow = poly1->pow; 
            poly->coeff = poly1->coeff; 
            poly1 = poly1->next; 
        } 
        if(poly2->next) 
        { 
            poly->pow = poly2->pow; 
            poly->coeff = poly2->coeff; 
            poly2 = poly2->next; 
        } 
        poly->next = (struct Node *)malloc(sizeof(struct Node)); 
        poly = poly->next; 
        poly->next = NULL; 
    } 
} 
  
// Display Linked list 
void show(struct Node *node) 
{ 
while(node->next != NULL) 
    { 
    printf("%dx^%d", node->coeff, node->pow); 
    node = node->next; 
    if(node->next != NULL) 
        printf(" + "); 
    } 
} 
  
// Driver  program 
int main() 
{ 
    struct Node *poly1 = NULL, *poly2 = NULL, *poly = NULL; 
      
    // Create first list of 5x^2 + 4x^1 + 2x^0 
    create_node(5,2,&poly1); 
    create_node(4,1,&poly1); 
    create_node(2,0,&poly1); 
      
    // Create second list of 5x^1 + 5x^0 
    create_node(5,1,&poly2); 
    create_node(5,0,&poly2); 
      
    printf("1st Number: ");  
    show(poly1); 
      
    printf("\n2nd Number: "); 
    show(poly2); 
      
    poly = (struct Node *)malloc(sizeof(struct Node)); 
      
    // Function add two polynomial numbers 
    polyadd(poly1, poly2, poly); 
      
    // Display resultant List 
    printf("\nAdded polynomial: "); 
    show(poly); 
  
return 0; 
} 

Output:

1st Number: 5x^2 + 4x^1 + 2x^0
2nd Number: 5x^1 + 5x^0
Added polynomial: 5x^2 + 9x^1 + 7x^0

Time Complexity: O(m + n) where m and n are number of nodes in first and second lists respectively.

Related Article: Add two polynomial numbers using Arrays
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