// ConsoleApplication15.cpp: определяет точку входа для консольного приложения.
//

#include "stdafx.h"
#include <iostream>
#include <math.h>

using namespace std;

double Analiticfunc(double x) {
	return pow(x,2);
}

double* x(int n, double h, double a) {
	double *x = new double[n];
	for (int i = 0; i <= n; i++)
		x[i] = a + i*h;
	return x;
}

double RLeftrest(int n, double a, double b, double *y) {
	double I = 0, k;
	double h = (b - a) / h;
	for (int i = 0; i <= n - 1; i++)
		if (y != NULL) I += y[i];
		else I += Analiticfunc();
		k = I*h;
		return k;
}

double Leftrest(int n, double *x, double *y) {
	double I = 0;
	double *h = new double[n];
	for (int i = 0; i <= n; i++)
		h[i] = x[i + 1] - x[i];
	for (int i = 0; i <= n - 1; i++)
		I += y[i] * h[i];
	return I;
}

double RRightrest(int n, double *x, double *y) {
	double I = 0;
	double *h = new double[n];
	for (int i = 0; i <= n; i++)
		h[i] = x[i + 1] - x[i];
	for (int i = 1; i <= n; i++)
		I += y[i];
	return I *= h[0];
}

double Rightrest(int n, double *x, double *y) {
	double I = 0;
	double *h = new double[n];
	for (int i = 0; i <= n; i++)
		h[i] = x[i + 1] - x[i];
	for (int i = 0; i <= n - 1; i++)
		I += y[i + 1] * h[i];
	return I;
}

double RTrapeze(int n, double *x, double *y) {
	double I, z = 0;
	double *h = new double[n];
	for (int i = 0; i <= n; i++)
		h[i] = x[i + 1] - x[i];
	for (int i = 1; i <= n - 1; i++)
		z += y[i];
	I = h[0] * (y[0] + 2 * z + y[n]) / 2;
	return I;
}

double Trapeze(int n, double *x, double *y) {
	double I, z = 0;
	double *h = new double[n];
	for (int i = 0; i <= n; i++)
		h[i] = x[i + 1] - x[i];
	for (int i = 1; i <= n - 1; i++)
		z += y[i] * (h[i - 1] + h[i]);
	I = (y[0] * h[0] + z + y[n] * h[n - 1]) / 2;
	return I;
}

double RSimpsone(int n, double *x, double *y) {
	double I;
	double m = (double)(n / 2);
	double *h = new double[n];
	for (int i = 0; i <= n; i++)
		h[i] = x[i + 1] - x[i];
	double z = 0, s = 0;
	for (int i = 0; i <= m - 1; i++)
		z += y[2 * i + 1];
	for (int i = 1; i <= m - 1; i++)
		s += y[2 * i];
	I = (2 * h[0] / 6)*(y[0] + 4 * z + 2 * s + y[2 * (int)m]);
	return I;
}

double Simpsone(int n, double *x, double *y) {
	double I = 0;
	int m = n / 2 - 1;
	double *h = new double[n];
	for (int i = 0; i <= n; i++)
		h[i] = x[i + 1] - x[i];
	for (int i = 0; i <= m; i++)
		I += ((h[2 * i + 1] + h[2 * i]) / (6 * h[2 * i + 1] * h[2 * i]))*(h[2 * i + 1] * (2 * h[2 * i] - h[2 * i + 1])*y[2 * i] + pow(h[2 * i + 1] + h[2 * i], 2)*y[2 * i + 1] + h[2 * i] * (2 * h[2 * i + 1] - h[2 * i])*y[2 * i + 2]);
	return I;
}

void Rav(int n, int numb) {
	double a, b, h;
	int s;
	cout << "Введите границы отрезка: ";
	cin >> a >> b;
	h = (double)((b - a) / n);
	double *x = new double[n];
	for (int i = 0; i <= n; i++)
		x[i] = a + i*h;
	cout << endl << "Способ задания функции:" << endl << " 1 - табличная" << endl << " 2 - аналитическая ";
	cin >> s;
	switch (s) {
	case 1: {
		double *y = new double[n];
		cout << "Введите значения функции в узлах сетки: ";
		for (int i = 0; i <= n; i++) {
			cout << "y[" << i << "] ";
			cin >> y[i];
		}
		cout << endl << "Значение интеграла: ";
		switch (numb) {
		case 1: cout << RLeftrest(n, x, y);
			break;
		case 2: cout << RRightrest(n, x, y);
			break;
		case 3: cout << RTrapeze(n, x, y);
			break;
		case 4: cout << RSimpsone(n, x, y);
			break;
		}
	} break;
	case 2: {
		cout << endl << "Значение интеграла: ";
		switch (numb) {
		case 1: cout << RLeftrest(n, x, NULL);
			break;
		case 2: cout << RRightrest(n, x, NULL);
			break;
		case 3: cout << RTrapeze(n, x, NULL);
			break;
		case 4: cout << RSimpsone(n, x, NULL);
			break;
		}
	} break;
	}
}

void neRav(int n, int numb) {
	double *x = new double[n];
	cout << "Введите узлы сетки: ";
	for (int i = 0; i <= n; i++) {
		cout << "x[" << i << "] ";
		cin >> x[i];
	}
	int s;
	cout << endl << "Способ задания функции:" << endl << " 1 - табличная" << endl << " 2 - аналитическая ";
	cin >> s;
	switch (s) {
	case 1: {
		double *y = new double[n];
		cout << "Введите значения функции в узлах сетки: ";
		for (int i = 0; i <= n; i++) {
			cout << "y[" << i << "] ";
			cin >> y[i];
		}
		cout << endl << "Значение интеграла: ";
		switch (numb) {
		case 1: cout << Leftrest(n, x, y);
			break;
		case 2: cout << Rightrest(n, x, y);
			break;
		case 3: cout << Trapeze(n, x, y);
			break;
		case 4: cout << Simpsone(n, x, y);
			break;
		}
	} break;
	case 2: {
		cout << endl << "Значение интеграла: ";
		switch (numb) {
		case 1: cout << Leftrest(n, x, Analiticfunc(n, x));
			break;
		case 2: cout << Rightrest(n, x, Analiticfunc(n, x));
			break;
		case 3: cout << Trapeze(n, x, Analiticfunc(n, x));
			break;
		case 4: cout << Simpsone(n, x, Analiticfunc(n, x));
			break;
		}
	} break;
	}
}

void Dinamic(int n, int numb) {
	int k = 1, q = 2, n1;
	double e, I, I1, d;
	double a, b, h, h1;
	n1 = q*n;
	cout << "Введите границы отрезка: ";
	cin >> a >> b;
	h = (double)((b - a) / n);
	h1 = (double)((b - a) / n1);
	cout << endl << "Введите точность вычисления интеграла: ";
	cin >> e;
	switch (numb) {
	case 1: {
		I = RLeftrest(n, x(n, h, a), Analiticfunc(n, x(n, h, a)));
		I1 = RLeftrest(n1, x(n1, h1, a), Analiticfunc(n1, x(n1, h1, a)));
	} break;
	case 2: {
		I = RRightrest(n, x(n, h, a), Analiticfunc(n, x(n, h, a)));
		I1 = RRightrest(n1, x(n1, h1, a), Analiticfunc(n1, x(n1, h1, a)));
	} break;
	case 3: {
		I = RTrapeze(n, x(n, h, a), Analiticfunc(n, x(n, h, a)));
		I1 = RTrapeze(n1, x(n1, h1, a), Analiticfunc(n1, x(n1, h1, a)));
	} break;
	case 4: {
		I = RSimpsone(n, x(n, h, a), Analiticfunc(n, x(n, h, a)));
		I1 = RSimpsone(n1, x(n1, h1, a), Analiticfunc(n1, x(n1, h1, a)));
	} break;
	default: break;
	}
	for (; abs((I1 - I) / I1) > e;) {
		n = n1;
		n1 = n*q;
		h = (double)((b - a) / n);
		h1 = (double)((b - a) / n1);
		if (numb == 1) {
			I = RLeftrest(n, x(n, h, a), Analiticfunc(n, x(n, h, a)));
			I1 = RLeftrest(n1, x(n1, h1, a), Analiticfunc(n1, x(n1, h1, a)));
		}
		if (numb == 2) {
			I = RRightrest(n, x(n, h, a), Analiticfunc(n, x(n, h, a)));
			I1 = RRightrest(n1, x(n1, h1, a), Analiticfunc(n1, x(n1, h1, a)));
		}
		if (numb == 3) {
			I = RTrapeze(n, x(n, h, a), Analiticfunc(n, x(n, h, a)));
			I1 = RTrapeze(n1, x(n1, h1, a), Analiticfunc(n1, x(n1, h1, a)));
		}
		if (numb == 4) {
			I = RSimpsone(n, x(n, h, a), Analiticfunc(n, x(n, h, a)));
			I1 = RSimpsone(n1, x(n1, h1, a), Analiticfunc(n1, x(n1, h1, a)));
		}
		k++;
	}
	d = abs((I1 - I) / I1);
	cout << "Значение интеграла: " << I1 << endl;
	cout << "Количество итераций: " << k << endl;
	cout << "Достигнутая точность: " << d << endl;
}

int main()
{
	setlocale(LC_ALL, "ru");
	int numb;
	cout << "Выберите формулу интегрирования:" << endl << " 1 - левосторонний прямоугольник" << endl << " 2 - правосторонний прямоугольник" << endl << " 3 - трапеция" << endl << " 4 - формула Симпсона ";
	cin >> numb;
	int m, n;
	cout << "Количество интервалов интегрирования (для формулы Симпсона n должна быть кратна 2): ";
	cin >> n;
	cout << "Выберите тип сетки:" << endl << " 1 - равномерная" << endl << " 2 - неравномерная" << endl << " 3 - динамическая ";
	cin >> m;
	switch (m) {
	case 1: Rav(n, numb);
		break;
	case 2: neRav(n, numb);
		break;
	case 3: Dinamic(n, numb);
		break;
	}
	cout << endl;
	system("pause");
}