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Multiply two polynomials in C++
The coefficients of each term of the polynomial are given in an array. We need to multiply the two polynomials. Let's see an example.
Input
A = [1, 2, 3, 4] B = [4, 3, 2, 1]
Output
4x6 + 11x5 + 20x4 + 30x3 + 20x2 + 11x1 + 4
Algorithm
Initialise two polynomials.
Create a new array with a length of two polynomials.
Iterate over the two polynomials.
Take one term from the first polynomial and multiply it with all the terms in the second polynomial.
Store the result in the resultant polynomial.
Implementation
Following is the implementation of the above algorithm in C++
#include <bits/stdc++.h>
using namespace std;
int *multiplyTwoPolynomials(int A[], int B[], int m, int n) {
int *productPolynomial = new int[m + n - 1];
for (int i = 0; i < m + n - 1; i++) {
productPolynomial[i] = 0;
}
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
productPolynomial[i + j] += A[i] * B[j];
}
}
return productPolynomial;
}
void printPolynomial(int polynomial[], int n) {
for (int i = n - 1; i >= 0; i--) {
cout << polynomial[i];
if (i != 0) {
cout << "x^" << i;
cout << " + ";
}
}
cout << endl;
}
int main() {
int A[] = {1, 2, 3, 4};
int B[] = {4, 3, 2, 1};
int m = 4;
int n = 4;
cout << "First polynomial: ";
printPolynomial(A, m);
cout << "Second polynomial: ";
printPolynomial(B, n);
int *productPolynomial = multiplyTwoPolynomials(A, B, m, n);
cout << "Product polynomial: ";
printPolynomial(productPolynomial, m + n - 1);
return 0;
}Output
If you run the above code, then you will get the following result.
First polynomial: 4x^3 + 3x^2 + 2x^1 + 1 Second polynomial: 1x^3 + 2x^2 + 3x^1 + 4 Product polynomial: 4x^6 + 11x^5 + 20x^4 + 30x^3 + 20x^2 + 11x^1 + 4
Updated on: 26-Oct-2021
3K+ Views
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