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 ` `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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