#include <iostream>
#include <vector>
#include <cmath>
using namespace std;

vector<float> l;
vector<float> x;
vector<float> c;
vector<float> b;
vector<float> d;
vector<float> lambda_;
vector<float> sigma_;

float y(float t) {
    return t * exp(t);
}

void interpolate(float left, float right, int step) {
    float h = (right - left) / (float)step;
    float xx  = left;
    while (xx < right + h) {
        x.push_back(xx);
        xx += h;
    }

    for (int i = 1; i < x.size(); i++) {
        l.push_back((y(x[i]) - y(x[i - 1])) / h);
    }

    l.push_back(right);

    c.resize(step);
    b.resize(step);
    d.resize(step);

    lambda_.push_back(1.5 *((l[2] - l[1]) / h));
    sigma_.push_back(- 1 / 4);

    //прогонка
    for (int i = 2; i < x.size(); i++) {
        sigma_.push_back((-h) / (2 * h + 2 * h + h * sigma_[i - 2]));
        lambda_.push_back((3 * l[i] - 3 * l[i - 1] - h * lambda_[i - 2]) / (2 * h + 2 * h + h * sigma_[i - 2]));
    }

    //обратная прогонка
    for (int i = step - 1; i > 0; i--) {
        c[i - 1] = sigma_[i - 1] * c[i] + lambda_[i - 1];
    }

    for (int i = 1; i < step; i++) {
        b[i] = (l[i] + (2 * c[i] * h + h * c[i - 1]) / 3);
        d[i] = ((c[i] - c[i - 1]) / (3 * h));
    }
}

float getV(float v) {
    for (int i = 1; i < x.size(); i++) {
        if (v == x[0]) {
            return y(x[0]);
        } else if (i == x.size() - 1) {
            return y(x.back());
        } else if (x[i - 1] <= v && v <= x[i]) {
            float u = (v - x[i]);
            return y(x[i]) + b[i] * u + c[i] * u * u + d[i] * u * u * u;
        }
    }
}

int main() {
    interpolate(0, 1, 10);
    vector<float> t;
    float k = 0;
    cout << "x: ";
    while (k < 1.0) {
        cout << k << " ";
        k += 0.05;
    }
    cout << endl;

    k = 0;
    cout << "y: ";
    while (k < 1.0) {
        cout << y(k) << " ";
        k += 0.05;
    }
    cout << endl;


    k = 0;
    cout << "y*: ";
    while (k < 1.0) {
        cout << getV(k) << " ";
        k += 0.05;
    }
    cout << endl;

    k = 0;
    cout << "delta: ";
    while (k < 1.0) {
        cout << y(k) - getV(k) << " ";
        k += 0.05;
    }
    cout << endl;

    return 0;
}