Description

In numerical analysis, the Horner scheme or Horner algorithm, named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form. Horner’s method describes a manual process by which one may approximate the roots of a polynomial equation. The Horner scheme can also be viewed as a fast algorithm for dividing a polynomial by a linear polynomial with Ruffini’s rule.

Application

The Horner scheme is often used to convert between different positional numeral systems — in which case x is the base of the number system, and the ai coefficients are the digits of the base-x representation of a given number — and can also be used if x is a matrix, in which case the gain in computational efficiency is even greater.

History

Even though the algorithm is named after William George Horner, who described it in 1819, the method was already known to Isaac Newton in 1669, and even earlier to the Chinese mathematician Ch’in Chiu-Shao in the 13th century. TASK: write a program to calculate sum of Polynomial by Horner scheme.

Input

tow lines. The first line have tow numbers,n and x, n<=20, x<=10 The second line have n+1 numbers, a0,a1…an.

Output

The sum of Polynomial

Sample Input

5 2

0 1 2 3 4 5

Sample Output

258

#include<iostream>
using namespace std;
int qinjiushao(int a[], int n, int x)
{
    int sum = a[n];
    for (int i = n - 1; i >= 0; i--)
    {
        sum = sum*x + a[i];
    }
    return sum;
}
int main()
{
    int arr[1005], n, x;
    cin >> n >> x;
    for (int i = 0; i < n+1;i++)
        cin >> arr[i];
    cout << qinjiushao(arr, n, x) << endl;
    return 0;
}