#include "stdio.h"
#include "math.h"
#include "stdlib.h"
#include "time.h"

#define VAL 0.001f
#define MyMax 10000

float mult(float var)
{
  return var * var;
}

float MethodOfRectangle(float start, float last)
{
  float integVal = 0;
  float step = VAL;
  for (float i = start; i < last; i+=step)
    integVal += mult(i);
  integVal *= step;
  return integVal;
}

float MethodOfTrap(float start, float last)
{
  float integVal = 0;
  float step = VAL;
  for (float i = start; i < last; i += step)
    integVal += 2 * mult(i);
  integVal = (integVal + mult(start) + mult(last)) * step / 2;
  return integVal;
}

float MethodOfSimson(float start, float last)
{
  int n = 1;
  float step = VAL;
  float integVal = 0;
  float fstInteg = 0;
  float sndInteg = 0;
  for (float i = start; i < last; i += step)
  {
    if (n % 2 == 0)
    {
      fstInteg += mult(i);
    }
    else
    {
      sndInteg += mult(i);
    }
    n++;
  }
  integVal = (integVal + mult(start) + mult(last) + 4 * sndInteg + 2 * fstInteg) * step / 3;
  return integVal;
}

double MonteCarlo(double start, double last)
{
  double a, b, x, y, sum, integVal = 0;
  int step = last - start, nums = 0;

  if (mult(start) > mult(last))
  {
    b = mult(start);
    a = last - start;
  }
  else
  {
    b = mult(last);
    a = last - start;
  }
  sum = a * b;

  //int val = (last-start)/VAL;
  //for(int i = 0; i < val; i++)
  for (double i = start; i < last; i+=VAL)
  {
    x = (rand()*1.0 / RAND_MAX)*step + start;
    y = (rand()*1.0 / RAND_MAX) * (b);
    if (y <= mult(x))
    {
      nums++;
    }
  }
  integVal = sum*(((double)nums) / MyMax);
  return integVal / 2;
}

int main()
{
  srand(time(NULL));
  int start = 1;
  int last = 21;
  printf("Start value: %d, Last value: %d\n", start, last);
  printf("Method of Rectangle: %f\nMethod of Trapezium: %f\nMethod of Simpson: %f\nMethod of Monte Carlo: %lf\n", MethodOfRectangle(start, last), MethodOfTrap(start, last), MethodOfSimson(start, last), MonteCarlo(start , last));
  return 0;
}