// This program calculates a series of n values using iterative formula
// x(1) = 0.3, x(2) = -0.3, ..., x(i) = i + sin(x(i-2)), i = 3, 4 ...n
#include<iostream.h>
#include<math.h>
#include<Array.h>

const int MAXSIZE = 100;

// function prototype
double diff(double x);

int main() 
{
// ---------------------------------begin solution for part (1)

// declarations
 int n;
 Array<double> x;  
 x.setSize(MAXSIZE);

// input value
 cout << "Enter your value n (n>=3) "; 
 cin >> n; 
 cout << endl;

 x(0) = 0.3;
 x(1) = -0.3;

// main iteration to generate x(i) 
 for (int i=2; i < n; i++)
 {
   x(i) = (i+1) + sin(x(i-2));
 }
// ----------------------------------end  solution for part (1)

                           // begin diagnostic output
                              cout << "\t\t Begin DIAGNOSTIC\n";
                              for (int i=0; i < n; i++)
                              {
                                 cout << "\t\tx(" 
                                      << (i+1) 
                                      << ") = " 
                                      << x(i) << endl;
                               }
                              cout << "\t\t End DIAGNOSTIC\n";
                           // end diagnostic output

// ----------------------------------begin solution to part (2)
// find the nearest to its whole neighbour
 double mindiff = diff(x(0));
 double mindiffx = x(0);

 for(int i = 1; i < n ; i++)
 { 
   if (mindiff > diff(x(i)))  
   {
      mindiff = diff(x(i));
      mindiffx = x(i);
   }
 }


                          // begin diagnostic output
                          cout << "\t\t Begin DIAGNOSTIC\n"; 
                          for (int i=0; i < n; i++)
                          {
                             cout << "\t\tDiff(" 
                                  << (i+1) 
                                  << ") = " 
                                  << diff(x(i)) << endl;
                          }
                          cout << "\t\t End DIAGNOSTIC\n"; 
                          // end diagnostic output

cout << "The following number has smallest difference with its whole neighbour:\n"
      << mindiffx << endl;
                         // begin  diagnostic output
                         cout << "\t\t Begin DIAGNOSTIC\n";  
                         cout << "\t\tThe difference is: " 
                              << mindiff << endl;
                          cout << "\t\t End DIAGNOSTIC\n"; 
                         // end diagnostic output

} // end main()

// function to calculate the abs value of the difference 
// between a double and its nearest whole rounding
 
double diff(double x)
{
  double difference;
  if (fabs(x-floor(x)) >= fabs(x-ceil(x)))   
  {
   difference = fabs(x-ceil(x));  
   }
  else
  {
   difference = fabs(x-floor(x)); 
  }
  return difference;
} // end diff

//---------------------------------- end of solution to part (2)