秦九韶算法解多项式

对于多项式

传统的做法需要n(n+1)/2次乘法和n次加法，而秦九韶算法：

只需n次加法和n次乘法。

/**
 *秦九韶算法解多项式
 *假设ak=k
 *公式为：Sn=an；Sk=xSk-1+ak；P(x)=S0
**/ 
#include <iostream>
using namespace std;
double qinJiuShao(int n, double x){
	double s = 0.0;
	double k = n;
	s = k;
	while(n){
		s = x * s + --k;
	//	cout<<"s "<<s<<" k "<<k<<endl;
		n--;
	}
	s = s + k;	//k is k0
	return s;
}
int main(){
	int n;
	double x;
	cout << "Please input n: " << endl;	
	cin >> n;
	cout << "Please input x: " << endl;
	cin >> x; 
	cout << qinJiuShao(n, x);
}