//  Java code for parts 3 and 4 of checkpoint 1.  Comment, beautify, and comprehend.  We may ask you to change the code to do parts 1 and 2.

import java.io.*;
import display.*;
import VisualNumerics.math.Sfun;               
import gov.noaa.pmel.sgt.cplab.*;
import java.awt.*;
class Dice
{
    public static void main (String argv []) throws IOException
    {int nDice = 4;int nSides = 6;int nThrows;
        int[] histo = new int[nSides*nDice+1]; 
	    String title= " Multiple throws of "+nDice+" "+nSides+" sided dice";
DataSet data1 = new DataSet();DataSet data2 = new DataSet();DataSet data3 = new DataSet();
DataSet data4 = new DataSet();DataSet data5 = new DataSet();DataSet data6 = new DataSet();
	    for(nThrows=2;nThrows<1000;nThrows++){
	for(int h=0;h<nSides*nDice+1;h++) {histo[h]=0;} 
        for(int i=0;i<nThrows;i++){int sum = 0;
        for(int id=0;id<nDice;id++){sum = sum + diceThrow(6);}
            histo[sum]=histo[sum]+1;} 
        int total=0;int totalsq=0;
	for(int i=nDice;i<nSides*nDice+1;i++) {
        total = total+i*histo[i];
        totalsq = totalsq+i*i*histo[i];}
        double mean = (double)total/nThrows;
        double variance = (double)totalsq/nThrows - mean*mean;
        data2.addPoint(nThrows,mean); 
        data3.addPoint(nThrows,Math.sqrt(variance)); 
        data4.addPoint(nThrows,14+Math.sqrt(variance/nThrows)); 
        data5.addPoint(nThrows,14-Math.sqrt(variance/nThrows)); }
	/**        System.out.println("Trials: "+nThrows+"; Mean throw "+mean+"; Standard deviation "+Math.sqrt(variance)); **/	  
	SimpleGraph histoGram = new SimpleGraph(title,"Number Thrown","","Number of times",""); 
for(int i=nDice;i<nSides*nDice+1;i++){data1.addPoint(i,histo[i]);}
        histoGram.addData(data1,"Number");histoGram.showGraph();
	SimpleGraph graph1 = new SimpleGraph(title,"Number of Throws","T","Mean","14+-error"); 
        data2.setColor(Color.red);
        graph1.addData(data2,"Sample Mean"); 
        graph1.addData(data4,"Error +"); 
        graph1.addData(data5,"Error -"); 
        graph1.showGraph();
	SimpleGraph graph2 = new SimpleGraph(title,"Number of Throws","T","Mean","Standard deviation"); 
        graph2.addData(data2,"Sample Mean"); 
        graph2.addData(data3,"Standard deviation"); 
        graph2.showGraph();
    }
static int diceThrow(int S){double  randomNo = 1.0+S*Math.random();return (int)randomNo;} 
}