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[] = {6, 2, 14, 6}

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.

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 implementation of above algorithm.

C++

 // Simple C++ program to add two polynomials #include 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

Java

 // Java program to add two polynomials    class GFG {    // A utility function to return maximum of two integers      static 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      static 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      static void printPoly(int poly[], int n) {         for (int i = 0; i < n; i++) {             System.out.print(poly[i]);             if (i != 0) {                 System.out.print("x^" + i);             }             if (i != n - 1) {                 System.out.print(" + ");             }         }     }    // Driver program to test above functions      public static void main(String[] args) {         // 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 = A.length;         int n = B.length;         System.out.println("First polynomial is");         printPoly(A, m);         System.out.println(" Second polynomial is");         printPoly(B, n);         int sum[] = add(A, B, m, n);         int size = max(m, n);         System.out.println(" sum polynomial is");         printPoly(sum, size);        } }

/div>

Python3

 # Simple Python 3 program to add two # polynomials    # A utility function to return maximum  # of two integers    # A[] represents coefficients of first polynomial # B[] represents coefficients of second polynomial # m and n are sizes of A[] and B[] respectively def add(A, B, m, n):        size = max(m, n);     sum = [0 for i in range(size)]        # Initialize the porduct polynomial            for i in range(0, m, 1):         sum[i] = A[i]        # Take ever term of first polynomial     for i in range(n):         sum[i] += B[i]        return sum    # A utility function to print a polynomial def printPoly(poly, n):     for i in range(n):         print(poly[i], end = "")         if (i != 0):             print("x^", i, end = "")         if (i != n - 1):             print(" + ", end = "")    # Driver Code if __name__ == '__main__':            # The following array represents     # polynomial 5 + 10x^2 + 6x^3     A = [5, 0, 10, 6]        # The following array represents     # polynomial 1 + 2x + 4x^2     B = [1, 2, 4]     m = len(A)     n = len(B)        print("First polynomial is")     printPoly(A, m)     print(" ", end = "")     print("Second polynomial is")     printPoly(B, n)     print(" ", end = "")     sum = add(A, B, m, n)     size = max(m, n)        print("sum polynomial is")     printPoly(sum, size)        # This code is contributed by # Sahil_Shelangia

C#

 // C# program to add two polynomials using System; class GFG {        // A utility function to return maximum of two integers      static 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      static 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      static void printPoly(int[] poly, int n)       {         for (int i = 0; i < n; i++)         {             Console.Write(poly[i]);             if (i != 0)              {                 Console.Write("x^" + i);             }             if (i != n - 1)              {                 Console.Write(" + ");             }         }     }        // Driver code      public static void 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 = A.Length;         int n = B.Length;         Console.WriteLine("First polynomial is");         printPoly(A, m);         Console.WriteLine(" Second polynomial is");         printPoly(B, n);         int[] sum = add(A, B, m, n);         int size = max(m, n);         Console.WriteLine(" sum polynomial is");         printPoly(sum, size);        } }    //This Code is Contributed  // by Mukul Singh

PHP



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.