#define eps 0.00001
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
double area_by_rect(double left, double right);
double area_by_trapezia(double left, double right);
double area_by_simpson(double left, double right);
double steps_of_trapezia(double left, double right);
double steps_of_simpson(double left, double right);
double steps_of_rect(double left, double right);
double function(double param);
int main()
{
    char ch;
    double left, right;
    double res1, res2, res3;
    double(*func_pointer)(double,double) = NULL;
    printf("Enter left limit: ");
    scanf_s("%lf", &left);
    printf("Enter right limit: ");
    scanf_s("%lf", &right);
    start:printf("Which method will by chosen: ");
    scanf_s("%c",&ch);
    scanf_s("%c", &ch);
    getchar();
    switch(ch)
    {
        case 't':
        func_pointer = area_by_trapezia;
        func_pointer(left, right);
        break;

        case 's':
        func_pointer = area_by_simpson;
        func_pointer(left, right);
        break;

        case 'r':
        func_pointer = area_by_rect;
        func_pointer(left, right);
        break;

        default:
            goto start;
        break;
    }

    /*res2 = area_by_trapezia(left, right);
    res3 = area_by_simpson(left, right);
    res1 = area_by_rect(left, right);
    printf("Average area is %lf\n", (res1 + res2 + res3) / 3);*/
    getchar();
    getchar();
    return 0;
}
double function(double param)
{
    return 1 / pow(cos(param / 3), 2);
}

double steps_of_rect(double left, double right)
{
    double save1 = 0, temp, a1 = right;
    int rect_num = 4;
    double width1;
    double width = right - left;
    do
    {
        temp = save1;
        save1 = 0;
        width1 = width / rect_num;
        for (int i = 0; i < rect_num; i++)
        {
            save1 += width1 * (function(a1));
            a1 -= width1;
        }
        a1 = right;
        rect_num *= 2;
    } while (fabs(save1 - temp) > eps);
    return width1;
}

double area_by_rect(double left, double right)
{
    double step = steps_of_rect(left, right);
    double area = 0;
    while (left<right)
    {
        area += step*function(left);
        left += step;
    }
    printf("area by rectangle - %lf\n", area);
    return area;
}
double steps_of_trapezia(double left, double right)
{
    double save1 = 0, temp, a1 = right;
    int rect_num = 4;
    double width1;
    double width = right - left;
    do
    {
        temp = save1;
        save1 = 0;
        width1 = width / rect_num;
        for (int i = 0; i < rect_num; i++)
        {
            save1 += width1 * (function(a1) + function(a1 - width1)) / 2;
            a1 -= width1;
        }
        a1 = right;
        rect_num *= 2;
    } while (fabs(save1 - temp) > eps);
    return width1;
}

double area_by_trapezia(double left, double right)
{
    double area = 0;

    double step = steps_of_trapezia(left, right);
    while (left<right)
    {
        area += step * (function(left) + function(left + step)) / 2;
        left += step;
    }
    printf("area by trapezia - %lf\n", area);
    return area;
}
double steps_of_simpson(double left, double right)
{
    double width = right - left;
    double save2 = 0, temp2 = 0;
    double right2;
    right2 = right;
    double width1;
    width1 = width;
    double rect_num = 4;
    do
    {
        temp2 = save2;
        save2 = 0;
        width1 = width1 / rect_num;
        for (int i = 0; i <= rect_num; i++)
        {
            save2 += (width1 / 6)*(function(right) + function(2 * right - width1) + function(right - width));
            right -= width1;
        }
        right = right2;
        rect_num *= 2;
    } while (fabs(save2 - temp2)>eps);
    return rect_num;
}

double area_by_simpson(double left, double right)
{
    double i = 0, j = 0;
    double N = steps_of_simpson(left, right);
    double width = right - left;
    double area3 = 0, area4 = 0, part = width / N, part1 = left + part, part2 = left + 2 * part;
    for (i = 0; i<N / 2; i++)
    {
        area3 += 4 * function(part1);
        part1 = part1 + 2 * part;
        j++;
    }
    for (i = 0; i < j; i++)
    {
        area4 += 2 * function(part2);
        part2 = part2 + 2 * part;
    }
    double result = width / (3 * N)*(function(left) + function(right) + area3 + area4);
    printf("area by Simpson - %lf\n", result);
    return result;
}