#include <iostream>
#include <vector>
#include <functional>

using namespace std;

template <class T>
T lagrange(vector<T> xs, vector<T> ys, T x) {
    T res = 0;
    T mul;
    size_t len = xs.size();
    for (size_t i=0; i<len; i++) {
        mul = 1;
        for(size_t j=0; j<len; j++) {
            if (i != j) {
                mul *= (x-xs[j])/(xs[i]-xs[j]);
            }
        }
        res += mul * ys[i];
    }
}

int main()
{
    vector<double> xs = {8, 9, 9.5, 10, 11};
    vector<double> ys = {0,0,1,0,0};

    double x;

    while(true) {
        cout << "x ? ";
        cin >> x;
        cout << "lagrange(" << x << ") = " << lagrange(xs, ys, x) << '\n';
    }
}