Tridiagonal matrix algorithm

#include <iostream>
#include <vector>

using namespace std;

void tridiagonal(vector <double> a, vector <double> b, vector <double> c, vector <double> d, vector <double> & x){
    int N = a.size();

    vector <double> alpha(N), beta(N);
    for(int i = 1; i < N; ++i){
        alpha[i] = -c[i - 1] / (a[i - 1] * alpha[i - 1] + b[i - 1]);
        beta[i] = (d[i - 1] - a[i - 1] * beta[i - 1]) / (a[i - 1] * alpha[i - 1] + b[i - 1]);
    }

    x[N - 1] = (d[N - 1] - a[N - 1] * beta[N - 1]) / (b[N - 1] + a[N - 1] * alpha[N - 1]);
    for(int i = N - 2; i >= 0; --i){
        x[i] = alpha[i + 1] * x[i + 1] + beta[i + 1];
    }
}

int main(){
    cout << "Enter N:\n";
    int N;
    cin >> N;

    cout << "Enter a (i != 0), b, c (i != N - 1) and d:\n";
    vector <double> a(N), b(N), c(N), d(N);
    for(int i = 0; i < N; ++i){
        if(i != 0){
            cin >> a[i];
        }
        cin >> b[i];
        if(i != N - 1){
            cin >> c[i];
        }
        cin >> d[i];
    }

    vector <double> x(N);
    tridiagonal(a, b, c, d, x);

    cout << "Solutions:\n";
    for(auto & res : x){
        cout << res << " ";
    }

    return 0;
}