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
#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;
}
}

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

// Display resultant List
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
This article is contributed by Akash Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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