// Interactive lesson on the vertex of a quadratic curve.
// Quick and dirty - needs to be revised, and things would certainly
// be easier with a Rational class.
import java.applet.Applet;
import java.awt.*;
import java.util.*;
class VertexCanvas extends Canvas{
	private int a, b, c;
	private int state;
	private Font f;

	public void init(){
		f = new Font("TimesRoman", Font.PLAIN, 14);
	}

	public void setCoefficients(int aco, int bco, int cco, int s)
	{
		a = aco;
		b = bco;
		c = cco;
		state = s;
		repaint();
	}

	public void paint( Graphics g)
	{
		String part2, part3;
		String part1 = "For the equation   y = " + a + " x";
		g.setFont( f );
		g.drawString(part1, 10, 28);
		FontMetrics fm = g.getFontMetrics();
		int newPosition = fm.stringWidth(part1) + 10;
		g.drawString("2", newPosition, 20);
		newPosition += fm.stringWidth("2");
		if(b > 0){
			part2 = " + " + b + " x";
		}
		else if(b < 0){
			part2 = " - " + Math.abs(b) + " x";
		}
		else {
			part2 = "";
		}
		g.drawString(part2, newPosition, 28);
		newPosition += fm.stringWidth(part2);
		if(c > 0){
			part3 = " + " + c + ",";
		}
		else if(c < 0){
			part3 = " - " + Math.abs(c) + ",";
		}
		else{
			part3 = "";
		}
		g.drawString(part3, newPosition, 28); 
	}
}

// State dictionary
// state 1 :
//		Awaiting answer to the first question - is there a maximum
//		or a minimum? Exit is to state2 on selecting either checkbox.
//
// state2 :
//		Allows user to read response. Exit is to state3 on a mousedown.
//
// state3 :	
//		Awaiting entry of vertex answer. On syntactically invalid
//		input, transition is to state4. If the answer is correct or
//		just off by a sign or twice the right answer, the transition
// 		is to state5. Otherwise the transition is to state6.
//
// state4 :
//		Lets user read response and then retry vertex answer.
//		Transition is to state3.
//
// state5 :
//		Lets user read response. Transition on a mousedown is to
//		state1.
//
// state6 :
//		Await input of b. Syntactically incorrect - go to state8.
//		b correct - go to state7. b incorrect - go to state 5.
//
// state7 : 
//		Await input of a. On syntactically invalid input, go to
//		state9. Otherwise go to state 5.
//
// state8:
//		Let user read message that b is syntactically invalid. 
//		Transition is to state6.
//
// state9:
//		Let user read message that a is syntactically invalid.
//		Transition is to state7.
//		
public class Vertex extends Applet {
	private TextArea text1;
	private VertexCanvas equation;
	private CheckboxGroup maxmin;
	private Checkbox maxbox, minbox;
	private TextField text2;
	private int a, b, c;
	private int state;
	private	int numerator, denominator;
	private Random r;

	public void init()
	{
		
		setBackground(Color.cyan);
		equation = new VertexCanvas();
		equation.resize(50,200);		
		text1 = new TextArea(6,200);
		text1.setEditable( false);
		text2 = new TextField(100);
		text2.setEditable( true);
		text2.setBackground(Color.yellow);
				
		setLayout( new GridLayout(5,1) );

		add(equation);
		add(text1);

		maxmin = new CheckboxGroup();
		add( maxbox = new Checkbox("maximum", maxmin, false));
		add( minbox = new Checkbox("minimum", maxmin, false));

		state = 1;		
		r = new Random();
		a = 0;
		while(a == 0){
			a = Math.abs(r.nextInt()) % 10 - 5;
		}
		b = Math.abs(r.nextInt()) % 20 - 10;
		c = Math.abs(r.nextInt()) % 20 - 10;
		equation.setCoefficients(a,b,c,1);
	
		text1.setText("   first decide whether the curve has a maximum or minimum.");
	}

	public void setUpState1(){
		state = 1;
		text2.setText("");
		a = 0;
		while(a == 0){
			a = Math.abs(r.nextInt()) % 10 - 5;
		}
		b = Math.abs(r.nextInt()) % 20 - 10;
		c = Math.abs(r.nextInt()) % 20 - 10;
		equation.setCoefficients(a,b,c,1);
	
		text1.setText("   first decide whether the curve has a maximum or minimum.");
		remove(text2);

		add(maxbox);
		add(minbox);	
		maxbox.setState(false);
		minbox.setState(false);	
		repaint();
	}
				
	public void okstate1(boolean good){
		String badstring;
		if(a < 0){
			badstring = a + " is negative, the curve has a maximum.";
		}
		else{
			badstring = a + " is positive, the curve has a minimum.";
		}

		if(good){
			text1.setText("   That's right.\nClick away from the checkboxes for the next question.");
		}
		else{
			text1.setText("   Incorrect - since a = " + badstring + "\nClick away from the boxes for the next question.");
		}
		state = 2;
		repaint();
	}

	public void goodAnswer(){
		state = 5;
		text1.setText("That's right. Click anywhere for another problem.");
		
		repaint();
	}

	public void offBySign(){
		state = 5;
		text1.setText("You are off by a sign. The answer should be -b/2a,\nbut you have b/2a. Click anywhere for another problem.");
		repaint();
	}

	public void forgot2(){
		state = 5;
		text1.setText("Maybe you forgot the 2 in -b/2a. Click anywhere for another problem.");
		repaint();
	}

	public void talkToUser(){
		state = 6;
		text1.setText("Your answer isn't right. Let's see if you are identifying a and b correctly\nEnter b in the yellow text field.");
		text2.setText("");
		text2.requestFocus();
		repaint();
	}

	public void talkToUser1(){
		state = 6;
		text1.setText("Try entering b in the yellow text field again.");
		text2.setText("");
		text2.requestFocus();
		repaint();
	}

	public void analyzeAnswer(){
	// Was user's answer correct? If not, try to figure out
	// what went wrong.
		// Answer should equal -b/2a
		if( 2*a*numerator == -b*denominator){
			goodAnswer();
			return;
		}
		// Maybe answer is off by a sign.
		if( 2*a*numerator == b*denominator){
			offBySign();
			return;
		}
		// Maybe user forgot the 2 in -b/2a.
		if(a*numerator == -b*denominator){
			forgot2();
			return;
		}
		// Maybe user misidentifies the coefficients.
		// See what user thinks a and b are.
		talkToUser();
	}
		



	public void badInput(){
		text1.setText("Invalid input. Click anywhere to retry.");
		state = 4;
		repaint();
	}

	public void badDenominator(){
		text1.setText("Denominators can't be zero. Click anywhere to retry.");
		state = 4;
		repaint();
	}
	
	public void validateInput(String input){
		Integer num, den;
		StringTokenizer tokens = new StringTokenizer( input, "/\n\r");
		int numberof = tokens.countTokens();
		if(numberof == 1){
			try{
				num = new Integer(input);
			}
			catch(Exception e)
			{
				badInput();
				return;
			}
			numerator = num.intValue();
			denominator = 1;
		}
		else if(numberof == 2){
			String next = tokens.nextToken();
			try{
				num = new Integer(next);
			}
			catch(Exception e)
			{
				badInput();
				return;
			}
			numerator = num.intValue();
			next = tokens.nextToken();
			try{
				den = new Integer(next);
			}
			catch(Exception e)
			{
				badInput();
				return;
			}
			denominator = den.intValue();
			if(denominator == 0){
				badDenominator();
				return;
			}
		}
		else{
			badInput();
			return;
		}

		// If we get here, the input was syntactically valid, anyhow.
		// Let's see if the user's answer is correct.
			analyzeAnswer();
	}

	public void badCheckb(){
		text1.setText("Invalid input. Click anywhere to retry.");
		state = 8;
		repaint();
	}


	public void checkValueb(String bString){
		Integer bMaybe;
		int bb;
		try{
			bMaybe = new Integer(bString);
		}
		catch(Exception e)
		{
			badCheckb();
			return;
		}
		bb = bMaybe.intValue();
		if( bb != b){
			text1.setText("Oh! b should be " + b + ". Click anywhere for another problem.");
			state = 5;
			repaint();			
			return;
		}
		else{
			state = 7;
			text1.setText("b is right. Let's see about a.\nEnter a in the yellow text field.");
			text2.setText("");
			text2.requestFocus();
			repaint();
		}
	}

	public void badChecka(){
		text1.setText("Invalid input. Click anywhere to retry.");
		state = 9;
		repaint();
	}

	public void tryaAgain(){
		state = 7;
		text1.setText("Try entering a again in the yellow text field.");
		text2.setText("");
		text2.requestFocus();
		repaint();
	}

	public void checkValuea(String aString){
		Integer aMaybe;
		int aa;
		try{
			aMaybe = new Integer(aString);
		}
		catch(Exception e)
		{
			badChecka();
			return;
		}
		aa = aMaybe.intValue();
		if( aa != a){
			text1.setText("Oh! a should be " + a + ". Click anywhere for another problem.");
			state = 5;
			repaint();			
			return;
		}
		else{
			state = 5;
			text1.setText("Well, you have coefficient a right. I don't know how you went wrong.\nClick anywhere for another problem.");
			repaint();
			return;
		}
	}
					
	public boolean action( Event e, Object o)
	{
		if(state == 1){
			if( e.target instanceof Checkbox){
				if( maxbox.getState() == true && a < 0){
					okstate1(true);
				}
				else if( minbox.getState() == true && a > 0){
					okstate1(true);
				}
				else{
					okstate1(false);
				}				
			}
		}

		else if(state == 3 && e.target == text2){
			String input = e.arg.toString();
			validateInput(input);
		}

		else if(state == 6 && e.target == text2){
			String input = e.arg.toString();
			checkValueb(input);
		}	
		else if(state == 7 && e.target == text2){
			String input = e.arg.toString();
			checkValuea(input);
		}	
			
		return(true);
	}
		
	public boolean mouseDown( Event e, int x, int y){
		if(state == 2){
			state = 3;
			remove(maxbox);
			remove(minbox);
			add(text2);
			text2.reshape(10,150,100,30);		
			text1.setText("Now, what is the x coordinate of the vertex?\nEnter in the yellow text field either as a fraction, like 5/4 or -1/6,\nor an integer, like 3 or -2.");					
			text2.requestFocus();
			repaint();
		}
		else if(state == 4){
			state = 3;
			text2.setText("");
			text1.setText("Now, what is the x coordinate of the vertex?\nEnter in the yellow text field either as a fraction, like 5/4 or -1/6,\nor an integer, like 3 or -2.");					
			text2.requestFocus();
			repaint();
		}		
		else if(state == 5){
			state = 1;
			setUpState1();
		}
		else if(state == 8){
			talkToUser1();
		}
		else if(state == 9){
			tryaAgain();
		}
		return(true);
	}


}