import java.awt.*;
import java.applet.*;
import java.util.*;
import java.awt.event.*;
import java.lang.String;




public class BirthdayProb extends Applet {  
	
	Button Run, Reset;
	Image backImg, offScreenImg;
	Graphics offScreenG;

	int randomBirthDate;
	int numPeople, numTrials;
	int numDateMatchesFound;
	int oneDateMatch, atleastOneDateMatch, atleastTwoDateMatch;

	boolean showProb;

	TextField people, trials;

	int dates[] = new int[365];

	
	public void init() 
	{
		backImg = getImage(getCodeBase(),"back.gif");
		offScreenImg = createImage(this.size().width, this.size().height);
		offScreenG = offScreenImg.getGraphics();
		repaint();

		randomBirthDate = 0;
		numPeople = numTrials = 0;
		numDateMatchesFound = 0;
		oneDateMatch = atleastOneDateMatch = atleastTwoDateMatch = 0;

		setLayout(null);
		Run = new Button("Find Probabilities");
		Reset = new Button("Reset");
		Run.setBounds(350, 70, 110, 25);
		Reset.setBounds(350, 110, 110, 25);
		add(Run);
		add(Reset);

		people = new TextField(4);
		trials = new TextField(7);
		trials.setBounds(165,70,75,30);
		people.setBounds(165,110,75,30);
	
		add(people); 
		add(trials); 

		people.setText("10");
		trials.setText("50000");

		showProb = false;

		for (int i = 0; i < 365; i++)
			dates[i] = 0;
	}

	public void paint (Graphics g)
	{
		offScreenG.drawImage(backImg,0,0,this);
		show(offScreenG);
		g.drawImage(offScreenImg,0,0,this);

	}

	public void findProb()
	{
		oneDateMatch = atleastOneDateMatch = atleastTwoDateMatch = 0;

		numPeople = Integer.parseInt(people.getText());
		numTrials = Integer.parseInt(trials.getText());

		for (int i = 0; i < numTrials; i++)
		{
			for (int j = 0; j < numPeople; j++)
			{
				randomBirthDate = (int) (Math.random() * 365);
				dates[randomBirthDate]++;
			}

			for (int j = 0; j < 365; j++)
				if (dates[j] >= 2)
					numDateMatchesFound++;

			if (numDateMatchesFound == 1)
				oneDateMatch++;

			if (numDateMatchesFound >= 1)
				 atleastOneDateMatch++;

			if (numDateMatchesFound >= 2)
				atleastTwoDateMatch++;

			numDateMatchesFound = 0;

			for (int k = 0; k < 365; k++)
				dates[k] = 0;
		}

		showProb = true;

		repaint();

	}

	public double actual()
	{
		double ans = 1;

		for(int i = 365; i >= (366 - numPeople); i--)
			ans = ans*i;

		ans = ans/(Math.pow(365, numPeople));

		ans = 1 - ans;

		for (int i = 2; i <= numPeople; i++)
		{
			double comb = 1;

			for (int j = numPeople; j > i; j--)
				comb = comb*j;

			for (int k = 2; k <= (numPeople - i); k++)
				comb = comb/k;

			for (int l = 365; l >= (365 - numPeople + i); l--)
				comb = comb*l;

			comb = comb/(Math.pow(365, numPeople));

			ans = ans - comb;
		}

		return ans*100;

//		answer:  P(Multiple Birthdays >= 2) = 1 - (365) (364) (363) (362) *** (365 - numPeople + 1)/365^numPeople  
//                                                      - The Sum For q=2 to numPeople (C(numPeople, q) (365) (364) (363) (362) *** (365 - numPeople + q) / 365^numPeople)
//
//		This equation is explained on the webpage along with this applet

	}

		

	public float round(float x)
	{
		x *= 10000;
		x = (int)x;
		x = x/10000;

		return x;
	}

	public double round(double x)
	{
		x *= 10000;
		x = (int)x;
		x = x/10000;

		return x;
	}
			

	public void reset()
	{

		people.setText("10");
		trials.setText("50000");

		showProb = false;	

		repaint();
	
	}	

	public void update (Graphics g) 
	{
		paint(g);
	}

	public boolean mouseDown(Event evt, int x, int y)
	{
		
	
		return true;
	}

	public void show(Graphics offScreenG)
	{
		Font f = new Font("Comic Sans MS", Font.BOLD, 15);

		offScreenG.setFont(f);

		offScreenG.drawString("Number of trials:", 25, 90);
		offScreenG.drawString("Number of people: ", 25, 130);

		if (showProb == true)
		{
			offScreenG.setColor(Color.blue);
			offScreenG.drawString("" + round(((float)oneDateMatch/numTrials)*100) + "%" +
			 			" of your trials resulted in exactly one duplicated birthday.", 25, 230);

			offScreenG.setColor(Color.red);
			offScreenG.drawString("" + round(((float)atleastOneDateMatch/numTrials)*100) + "%" +
			 			" of your trials resulted in atleast one duplicated birthday.", 25, 260);

			offScreenG.setColor(Color.blue);
			offScreenG.drawString("" + round(((float)atleastTwoDateMatch/numTrials)*100) + "%" +
			 			" of your trials resulted in atleast two duplicated birthdays.", 25, 290);
			offScreenG.drawString("Mathematical Probability: " + round(actual()) + "%", 25, 310);

			offScreenG.setColor(Color.black);	
		}
	}

	public boolean action(Event evt, Object arg) 
	{

		if (arg.equals("Find Probabilities"))
			findProb();

		if (arg.equals("Reset"))
			reset();

		return true;
	}			
}