#include <iostream>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
#include <vector>
#define start 1
#define N 15
#pragma warning (disable:4996)
using namespace std;
long double yy[N+1];
long double xx[N+1];
long double p(long double e)
{
    int random;
    random = 1 + rand() % 20000;
    return e*random*0.001;
}
void masx(double h, double a, double b)
{
    for (int i = 0; i <= N; i++)
    {
        xx[i] = a + h*i;
    }
}
long double fact(long double x)
{
    return (sin(x) + cos(x));
}
long double f(long double x, long double y)
{
    return ((1 / cos(x)) - y*(sin(x) / cos(x)));
}
long double calc(long double x, long double y, long double h)
{
    long double yy;
    long double ff;
    ff = f(x, y);
    yy = y + h*ff;
    return (y + h*(ff + f(x + h, yy)) / 2);
}
int k=1; //количество отрезков, h - длина одного
long double hh;
vector<pair<long double, long double>> RK(long double e, long double a, long double b, long double y) //возвращает значение для точки с заданной точностью
{
    vector<pair<long double, long double>> vec;
    long double y0_1, y0_2, y1, y2;
    k = 1;
    do
    {
        hh = 0;
        vec.clear();
        y0_1 = y;
        y0_2 = y;
        vec.push_back(make_pair(a, y0_2));
        long double h = (b - a) / k;
        for (int i = 0; i < k; i++)
        {
            y1 = calc(a + i*h, y0_1, h);
            //y1 = y0_1 + (h / 2.0)*(f(a + (i+1)*h, y1) + f(a + i*h, y0_1));
            y0_1 = y1;
        }
        for (int j = 0; j < 2 * k; j++)
        {
            y2 = calc(a + (j*h) / 2, y0_2, h / 2);
            vec.push_back(make_pair(a + ((j+1)*h) / 2, y2));
            //y2 = y0_2 + (h / 4.0)*(f(a + (j + 1)*h, y1) + f(a + j*h, y0_2));
            y0_2 = y2;
        }
        k *= 2;
        hh = h / 2;
    } while (fabs((y1 - y2)) > e);
    return vec;
}
void adams(long double e, long double a, long double b, long double h, long double y_start, FILE *F)
{
    int maxx = 0;
    int min = INT_MAX;
    long double max=0;
    long double max2 = 0;
    yy[0] = y_start;
    for (int n = 1; n <= N; n++)
    {
        vector <pair<long double, long double>> yyy = RK(e, xx[n - 1], xx[n], yy[n - 1]); //по р-к находится точка
        if (k < min) min = k;
        if (k > maxx) maxx = k;
        long double pogr2 = fabs(yyy[yyy.size() - 1].second - fact(xx[n]));
        if (max2 < pogr2) max2 = pogr2;
        for (unsigned int i = 1; i < yyy.size(); i++)
        {
            yyy[i].second = yyy[i - 1].second + (hh / 2.0)*(f(yyy[i-1].first, yyy[i - 1].second) + f(yyy[i].first, yyy[i].second));
        }
        yy[n] = yyy[yyy.size() - 1].second;
        long double pogr = fabs(fact(xx[n]) - yy[n]);
        if (max < pogr) max = pogr;
    }
    //fprintf(F, "%i ", min);
    printf("%e ", max);
    printf("%e \n", max2);
    //fprintf(F, "%e ", max);
    //fprintf(F, "%e ", max2); //р-к
}
long double RK1(long double e, long double a, long double b, long double y) //возвращает значение для точки с заданной точностью
{
    long double y0_1, y0_2, y1, y2;
    do
    {
        y0_1 = y;
        y0_2 = y;
        long double h = (b - a) / k;
        for (int i = 0; i < k; i++)
        {
            y1 = calc(a + i*h, y0_1, h);
            y1 = y0_1 + (h / 2.0)*(f(a + (i + 1)*h, y1) + f(a + i*h, y0_1));
            y0_1 = y1;
        }
        for (int j = 0; j < 2 * k; j++)
        {
            y2 = calc(a + (j*h) / 2, y0_2, h / 2);
            y2 = y0_2 + (h / 4.0)*(f(a + (j + 1)*h, y1) + f(a + j*h, y0_2));
            y0_2 = y2;
        }
        k *= 2;
    } while (fabs((y1 - y2)) > e);
    k = 1;
    return y2;
}
void adams1(long double e, long double a, long double b, long double h, long double y_start, FILE *F)
{
    int maxx = 0;
    int min = INT_MAX;
    long double max = 0;
    yy[0] = y_start;
    for (int n = 1; n <= N; n++)
    {
        yy[n] = RK1(e, xx[n-1], xx[n], yy[n-1]);
        long double pogr = fabs(fact(xx[n]) - yy[n]);
        if (max < pogr) max = pogr;
    }
    //fprintf(F, "%i ", min);
    printf("%e ", max);
    //fprintf(F, "%e ", max);
    //fprintf(F, "%e ", max2); //р-к
}
void main()
{
    long double a = 0, b = 1.5;
    long double e;
    long double l = 0.01;
    long double h = (b - a) / (double) N;
    FILE *f;
    f = fopen("file3.txt", "a");
    masx(h, a, b);
    /*e = 0.1;
    for (int i = 0; i < 10; i++)
    {
        fprintf(f, "%e ", e);
        e *= 0.1;
    }
    fprintf(f, "\n");*/
    //e = pow(10, -10);
    e = 0.1;
    fprintf(f, "\n");
    for (int i = 0; i < 10; i++)
    {
        adams1(e, a, b, h, start, f);
        l *= 0.1;
        e *= 0.1;
    }
    //fprintf(f, "\n");
    fclose(f);
}