Lagrange polynomial

#include <iostream>
#include <vector>

using namespace std;

double P(double x0, vector <double> x, vector <double> y){
    int N = x.size();
    double S = 0;

    for(int i = 0; i < N; ++i){
        double L = 1;

        for(int j = 0; j < N; ++j){
            if(i != j){
                L *= (x0 - x[j]) / (x[i] - x[j]);
            }
        }

        S += y[i] * L;
    }

    return S;
}

vector <double> get_coefficients(vector <double> x, vector <double> y){
    int N = x.size();
    vector <double> a(N);

    for(int i = 0; i < N; ++i){
        a[i] = y[i];
        for(int j = 0; j < N; ++j){
            if(i != j){
                a[i] /= x[i] - x[j];
            }
        }
    }

    return a;
}

int main(){
    int N;
    cin >> N;

    vector <double> x(N);
    vector <double> y(N);

    for(int i = 0; i < N; ++i){
        cin >> x[i] >> y[i];
    }

    for(auto a : get_coefficients(x, y)){
        cout << a << " ";
    }

    return 0;
}