# Program to add two polynomials

Given two polynomials represented by two arrays, write a function that adds given two polynomials.

Example:

```Input:  A[] = {5, 0, 10, 6}
B[] = {1, 2, 4}
Output: sum[] = {5, 10, 30, 26, 52, 24}

The first input array represents "5 + 0x^1 + 10x^2 + 6x^3"
The second array represents "1 + 2x^1 + 4x^2"
And Output is "6 + 2x^1 + 14x^2 + 6x^3"
```

We strongly recommend to minimize your browser and try this yourself first.
Addition is simpler than multiplication of polynomials. We initialize result as one of the two polynomials, then we traverse the other polynomial and add all terms to the result.

```add(A[0..m-1], B[0..n01])
1) Create a sum array sum[] of size equal to maximum of 'm' and 'n'
2) Copy A[] to sum[].
3) Travers array B[] and do following for every element B[i]
sum[i] = sum[i] + B[i]
4) Return sum[].```

The following is C++ implementation of above algorithm.

```// Simple C++ program to add two polynomials
#include <iostream>
using namespace std;

// A utility function to return maximum of two integers
int max(int m, int n) {  return (m > n)? m: n; }

// A[] represents coefficients of first polynomial
// B[] represents coefficients of second polynomial
// m and n are sizes of A[] and B[] respectively
int *add(int A[], int B[], int m, int n)
{
int size = max(m, n);
int *sum = new int[size];

// Initialize the porduct polynomial
for (int i = 0; i<m; i++)
sum[i] = A[i];

// Take ever term of first polynomial
for (int i=0; i<n; i++)
sum[i] += B[i];

return sum;
}

// A utility function to print a polynomial
void printPoly(int poly[], int n)
{
for (int i=0; i<n; i++)
{
cout << poly[i];
if (i != 0)
cout << "x^" << i ;
if (i != n-1)
cout << " + ";
}
}

// Driver program to test above functions
int main()
{
// The following array represents polynomial 5 + 10x^2 + 6x^3
int A[] = {5, 0, 10, 6};

// The following array represents polynomial 1 + 2x + 4x^2
int B[] = {1, 2, 4};
int m = sizeof(A)/sizeof(A[0]);
int n = sizeof(B)/sizeof(B[0]);

cout << "First polynomial is \n";
printPoly(A, m);
cout << "\nSecond polynomial is \n";
printPoly(B, n);

int *sum = add(A, B, m, n);
int size = max(m, n);

cout << "\nsumuct polynomial is \n";
printPoly(sum, size);

return 0;
}
```

Output:

```First polynomial is
5 + 0x^1 + 10x^2 + 6x^3
Second polynomial is
1 + 2x^1 + 4x^2
Sum polynomial is
6 + 2x^1 + 14x^2 + 6x^3```

Time complexity of the above algorithm and program is O(m+n) where m and n are orders of two given polynomials.