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

// 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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