Horner's Method for Polynomial Evaluation | GeeksforGeeks

Given a polynomial of the form c_nxⁿ + c_n-1x^n-1 + c_n-2x^n-2 + … + c₁x + c₀ and a value of x, find the value of polynomial for a given value of x. Here c_n, c_n-1, .. are integers (may be negative) and n is a positive integer.

Horner’s method can be used to evaluate polynomial in O(n) time. To understand the method, let us consider the example of 2x³ – 6x² + 2x – 1. The polynomial can be evaluated as ((2x – 6)x + 2)x – 1. The idea is to initialize result as coefficient of xⁿ which is 2 in this case, repeatedly multiply result with x and add next coefficient to result. Finally return result.

int horner(int poly[], int n, int x)

{

    int result = poly[0];  // Initialize result

 

    // Evaluate value of polynomial using Horner's method

    for (int i=1; i<n; i++)

        result = result*x + poly[i];

 

    return result;

}

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