# 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

`// 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; ` `} ` |

*chevron_right*

*filter_none*

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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