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"
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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 implementation of above algorithm.
C++
// 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
" ; printPoly(A, m); cout << "
Second polynomial is
" ; printPoly(B, n); int *sum = add(A, B, m, n); int size = max(m, n); cout << "
sum polynomial is
" ; printPoly(sum, size); return 0; } |
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); } } |
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
<?php // Simple PHP program to add two polynomials // A[] represents coefficients of first polynomial // B[] represents coefficients of second polynomial // m and n are sizes of A[] and B[] respectively function add( $A , $B , $m , $n ) { $size = max( $m , $n ); $sum = array_fill (0, $size , 0); // Initialize the porduct polynomial for ( $i = 0; $i < $m ; $i ++) $sum [ $i ] = $A [ $i ]; // Take ever term of first polynomial for ( $i = 0; $i < $n ; $i ++) $sum [ $i ] += $B [ $i ]; return $sum ; } // A utility function to print a polynomial function printPoly( $poly , $n ) { for ( $i = 0; $i < $n ; $i ++) { echo $poly [ $i ]; if ( $i != 0) echo "x^" . $i ; if ( $i != $n - 1) echo " + " ; } } // Driver Code // The following array represents // polynomial 5 + 10x^2 + 6x^3 $A = array (5, 0, 10, 6); // The following array represents // polynomial 1 + 2x + 4x^2 $B = array (1, 2, 4); $m = count ( $A ); $n = count ( $B ); echo "First polynomial is
" ; printPoly( $A , $m ); echo "
Second polynomial is
" ; printPoly( $B , $n ); $sum = add( $A , $B , $m , $n ); $size = max( $m , $n ); echo "
sum polynomial is
" ; printPoly( $sum , $size ); // This code is contributed by chandan_jnu ?> |
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.
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