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//Horner's evaluaation
#include <iostream>
#include <cmath>
using namespace std;
#define EPS 0.00001


void horner(int n, float a[], float x0, float p[]) {
	int i;
	p[0] = a[n];
	p[1] = a[n];
	for (i = n - 1; i >= 1; i--) {c
		p[0] = a[i] + p[0] * x0;
		p[1] = p[0] + p[1] * x0;
	}
	p[0] = a[0] + p[0] * x0;
}


int main() {
	float a[10], p[2], x0, x1;
	int i, n, count = 1;
	
	cout << "Enter the degree of the polynomial:\n";
	cin >> n;
	
	cout << "Enter the coefficients of the polynomial starting from the highest degree:\n";
	for (i = n; i >= 0; i--) {
		cin >> a[i];
	}
	
	cout << "Enter a valid initial point x0:\n";
	cin >> x0;
	horner(n, a, x0, p);
	x1 = x0 - (p[0] / p[1]);
	
	while (fabs((x1 - x0) / x1) > EPS) {
		count++;
		x0 = x1;
		horner(n, a, x0, p);
		x1 = x0 - (p[0] / p[1]);
	}
	cout << "The approximate root of given function is "
	<< x1 << " with " << count<< " number of iterations." << endl;
	return 0;
}