#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
//#define endl '\n'
#define boostIO() ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
ll gcd(ll a, ll b) { return (b == 0 ? a : gcd(b, a % b)); }


vector<double> x = { -2, -1, 0, 1, 2, 3, 4 };
vector<double> y = { -8.78, -5.36, -0.49, -7.81, 4.07, -6.77, -2.17 };

vector<double> b(7);

double f(double cur_x) {
    double ans = 0;
    for (int i = 0; i < y.size(); ++i) {
        double pr = y[i];
        for (int j = 0; j < x.size(); ++j) {
            if (i != j) {
                pr *= (cur_x - x[j]) / (x[i] - x[j]);
            }
        }
        ans += pr;
    }
    return ans;
}

void get_b() {
    b[0] = y[0];
    for (int i = 1; i < 7; ++i) {
        b[i] = y[i] - b[0];
        double k = x[i] - x[0];
        for (int j = 1; j <= i - 1; ++j) {
            b[i] -= b[j] * k;
            k *= x[i] - x[j];
        }
        b[i] /= k;
    }
}

double N(double cur_x) {
    double ans = b[0];
    double k = 1;
    for (int i = 0; i < 6; ++i) {
        k *= cur_x - x[i];
        ans += k * b[i + 1];
    }
    return ans;
}
signed main() {
    for (int i = -2; i <= 4; ++i) {
        cout << "f(" << i << ") = " << f(i) << endl;
    }
    cout << "f(" << -1.3 << ") = " << f(-1.3) << endl;
    cout << "f(" << 1.75 << ") = " << f(1.75) << endl;


    cout << endl << endl;
    get_b();
    for (int i = 0; i < 7; ++i) {
        cout << "B" << i + 1 << " = " << b[i] << endl;
    }


    cout << endl << endl;
    for (int i = -2; i <= 4; ++i) {
        cout << "f(" << i << ") = " << N(i) << endl;
    }
    cout << "f(" << -1.3 << ") = " << N(-1.3) << endl;
    cout << "f(" << 1.75 << ") = " << N(1.75) << endl;
}