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18.08.2022
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#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

int main() {
	setlocale(LC_ALL, "RUS");
	int N, n;
	cout << "Введите ваш номер варианта: ";
	cin >> n;
	system("cls");
	cout << "Введите N: ";
	cin >> N;
	system("cls");
	cout << "=== Введите значения X ===\n" << endl;
	vector <float> x, y;
	
	for (int i = 0; i < N; i++) {
		cout << "Введите X [" << i << "]: ";
		int m;
		cin >> m;
		x.push_back(m);
		cout << endl;
	}
	
	for (int i = 0; i < N; i++) {
		float m = (x[i] * x[i] * x[i]) / (n + 1);
		y.push_back(m);
	}

	cout << "X: ";

	for (int i = 0; i < N; i++)
		cout << x[i] << " ";

	cout << endl;
	
	cout << "Y: ";

	for (int i = 0; i < N; i++)
		cout << y[i] << " ";

	cout << "\n" << endl;

	vector <vector <float>> XX;

	for (int i = 0; i < N; i++) {
		XX.push_back(vector<float>());
		for (int j = 0; j < N - 1; j++) {
			float m = (x[j] + x[j + 1]) / 2;
			
			float M = m;
			for (int k = 0; k < N ; k++) {
				XX[i].push_back(M);
			//cout << " " << M; //!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
				M *= m;
			}
		}
	}
	for (int t = 0; t < N - 1; t++) {
		float res = 0;
		int l = 0;
		do {
			float m = 1, k = 1;
			for (int i = 0; i < N; i++) {
				if (l != i) {
					//cout << XX[0][t] << " И " << XX[1][t] << endl;
					m *= XX[l][t] - x[i];
					k *= x[l] - x[i];
					//cout << "[" << l << "]\n" << m << "\n" << k << "\n" << endl;

				}
			}
			res += (m / k) * y[l];
		//	cout << "RES =" << res << endl;
			l++;
		} while (l < N);
		cout << "Результат [" << t << "]: " << res << endl;
	}


	//float l = ((XX[0][1] - x[1]) * (XX[0][1] - x[2]) * (XX[0][1] - x[3])) / ((x[0] - x[1]) * (x[0] - x[2]) * (x[0] - x[3]));
	//float ll = ((XX[0][1] - x[0]) * (XX[0][1] - x[2]) * (XX[0][1] - x[3])) / ((x[1] - x[0]) * (x[1] - x[2]) * (x[1] - x[3]));
	//float lll = ((XX[0][1] - x[0]) * (XX[0][1] - x[1]) * (XX[0][1] - x[3])) / ((x[2] - x[0]) * (x[2] - x[1]) * (x[2] - x[3]));

	//cout << "L(1): " << l << "\n L(2): " << ll << "\n L (3): " << lll << endl;
	system("pause");
	return 0;
}
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