//numerical differences
//this takes experimental data for x and f(x)
//the data is used to calculate the values for 
//the function in areas where we have no data


//this example hard codes the data for x^3 at the values
//x = 0, 1, 3, 4, 7, 9
//getting x and f(x) from the user will be more useful




public class differences
{
    
    public static void main ( String args[] )
    {
	int arraysize = 6;
	int x[] = { 0, 1, 3, 4, 7, 9 };
	int f_of_x[] = { 0, 1, 27, 64, 343, 729 };
	
	int x1[] = new int[arraysize];
	int x2[] = new int[arraysize];
	int x3[] = new int[arraysize];
	int x4[] = new int[arraysize];
		
	//initialize stuff
	for ( int i=0; i<arraysize; i++){
	    x1[i] = 0;
	    x2[i] = 0;
	    x3[i] = 0;
	    x4[i] = 0;
	
	}
	
	//calculate differences
	for ( int i=0; i<(arraysize-1); i++ ){
	    x1[i] = (f_of_x[i] - f_of_x[i+1])/(x[i] - x[i+1]);
	}
	
	for ( int i=0; i<(arraysize-2); i++ ){
	    x2[i] = (x1[i] - x1[i+1])/(x[i] - x[i+2]);
	}
	
	for ( int i=0; i<(arraysize-3); i++ ){
	    x3[i] = (x2[i] - x2[i+1])/(x[i] - x[i+3]);
	}
	
	for ( int i=0; i<(arraysize-4); i++ ){
	    x4[i] = (x3[i] - x3[i+1])/(x[i] - x[i+4]);
	}
	
	
	
	
	
	for ( int i=0; i<arraysize; i++){
	    System.out.println ( x[i] + "\t" + f_of_x[i]);
	    
	    if ( x1[i] != 0 ) System.out.println ( "\t\t" + x1[i] );
	    if ( x2[i] != 0 ) System.out.println ( "\t\t\t" + x2[i] );
	    if ( x3[i] != 0 ) System.out.println ( "\t\t\t\t" + x3[i] );
	    if ( x4[i] != 0 ) System.out.println ( "\t\t\t\t\t" + x4[i] );
	}
	
	
    
    }
    
    
}