import java.applet.Applet;
import java.awt.*;
import java.lang.*;

public class Deriv extends Applet {

  DerivPanel mainpanel;
  Button restartButton, newStartButton, answerButton, errorButton;
  String buttonStatus, buttonOptions;
  Panel buttonpanel = new Panel();
  int point,temp;
  boolean startedDraw=false, doneDrawing=false, drawAnswer=false, fill=false, defaultCurve=true;

  public void init() {
    mainpanel = new DerivPanel();
    setLayout(new BorderLayout());
    add("Center",mainpanel);
    mainpanel.init();
    add("South",buttonpanel);
    buttonpanel.setLayout(new GridLayout(1,4));
    restartButton = new Button("A. Original start");
    buttonpanel.add(restartButton);
    newStartButton = new Button("B. New start");
    buttonpanel.add(newStartButton);
    answerButton = new Button("C. Answer (derivative)");
    buttonpanel.add(answerButton);
    errorButton = new Button("D. Show Error");
    buttonpanel.add(errorButton);
    buttonStatus = "justCurve"; 
  }

  public boolean action(Event e, Object o) {
    if (e.target.equals(restartButton)) {point=0; startedDraw = false; doneDrawing = false; 
      drawAnswer=false; fill=false; defaultCurve=true; buttonStatus ="justCurve";       mainpanel.init();
    }
    if (e.target.equals(newStartButton)) {mainpanel.components=!mainpanel.components;
      point=0; startedDraw = false; doneDrawing = false; drawAnswer=false; fill=false; 
      defaultCurve=false; buttonStatus = "justCurve"; mainpanel.init();
    }
    if (e.target.equals(answerButton) && (buttonStatus=="justCurve" ||       buttonStatus=="finishedDraw"))        {drawAnswer=true; 
      if (doneDrawing==true) {buttonStatus="all3";} else {buttonStatus="justCorrect";}
      doneDrawing=false; 
    }
    if (e.target.equals(errorButton)) { if (drawAnswer==true && buttonStatus=="all3") {fill=true; buttonStatus="filled"; }}
    mainpanel.repaint();
    return true;
  }


  public class DerivPanel extends Panel {

//    int transx(double x) {return (int) (5.5+x*31);}
//    int transy(double y) {return (int) (188.5-y*31);}


    double a[]={0.0,0.0,0.0,0.0,0.0,0.0}, b[]={0.0,0.0,0.0,0.0,0.0,0.0},
     c[]={0.0,0.0,0.0,0.0,0.0,0.0}, d[]={0.0,0.0,0.0,0.0,0.0,0.0};
    double aa[]={0.0,0.0,0.0,0.0,0.0,0.0}, bb[]={0.0,0.0,0.0,0.0,0.0,0.0},
     cc[]={0.0,0.0,0.0,0.0,0.0,0.0}, dd[]={0.0,0.0,0.0,0.0,0.0,0.0}, ee[]={0.0,0.0,0.0,0.0,0.0,0.0};
    int numzeros, doublezero, signum, zeroplace, zz, temp;
    double zeros[]={0.0,0.0,0.0,0.0,0.0,0.0};
    double maxx=19.0;
    double maxloc, maxvalue, miny, maxy, x, y, x2, y2, shift, area;
//    boolean startedDraw = false, doneDrawing = false;
    int[] xx = new int[600]; int[] yy= new int[600]; int[] xxt = new int[600]; int[] yyt = new int[600];
    int[] xxx = new int[600]; int[] yyy= new int[600];
//    int point;


    Image back; Graphics bg; Dimension bsize = size();
    boolean components=false;
    boolean busy = false;
    Color tan_col = new Color(.9f,.8f,.6f);

    public void init() {
      buttonStatus = "justCurve"; maxy=11.0; miny=-11.0;
while (maxy-miny>12){  //get to fit vertically (omits troublesome about 5%)
      if (defaultCurve) { numzeros=4; zeros[0]=-1.0; zeros[numzeros+1]=maxx+1;
        for (int i=1;i<=numzeros;i++) zeros[i]=((double)i-0.5+((double)(i)/30.0))*maxx/numzeros;
        doublezero=3; signum=1; buttonStatus="justCurve";
      } else {  buttonStatus="justCurve";
        numzeros=4; //if (Math.random()<.5) numzeros=3;
        zeros[0]=-0.5-Math.random()*2;  zeros[numzeros+1]=maxx+.5+Math.random()*2;
        for (int i=1;i<=numzeros;i++) zeros[i]=((double)i-.5+(Math.random()-.5)*2/3)*maxx/numzeros;
        signum=1; if (Math.random()<.5) signum=-1; doublezero=(int)(Math.random()*numzeros+1);
      }
      for (int i=1;i<=numzeros+1;i++){
        d[i]=-zeros[i-1]*zeros[i]; c[i]=zeros[i-1]+zeros[i]; b[i]=-1; a[i]=0;
        maxloc=(zeros[i]+zeros[i-1])/2;
        if (doublezero==i-1){
          a[i]=b[i]; b[i]=c[i]-b[i]*zeros[i-1]; c[i]=d[i]-c[i]*zeros[i-1]; d[i]=-d[i]*zeros[i-1]; 
          maxloc=(2*zeros[i]+zeros[i-1])/3;
        }
        if (doublezero==i){
          a[i]=-b[i]; b[i]=-c[i]+b[i]*zeros[i]; c[i]=-d[i]+c[i]*zeros[i]; d[i]=d[i]*zeros[i]; 
          maxloc=(zeros[i]+2*zeros[i-1])/3;
        }
        maxvalue=((a[i]*maxloc+b[i])*maxloc+c[i])*maxloc+d[i];
        //normalize
        a[i]=a[i]/maxvalue*2*signum; b[i]=b[i]/maxvalue*2*signum; 
        c[i]=c[i]/maxvalue*2*signum; d[i]=d[i]/maxvalue*2*signum;
        if (doublezero!=i) signum=-signum;
      }
      //antiderivative
      for (int i=1;i<=numzeros+1;i++){aa[i]=a[i]/4; bb[i]=b[i]/3; cc[i]=c[i]/2; dd[i]=d[i];}
      miny=0.0; maxy=0.0; y=0.0;
      for (int i=1;i<=numzeros+1;i++){
        x=zeros[i-1]; ee[i]=y-((((aa[i]*x+bb[i])*x+cc[i])*x+dd[i])*x); x=zeros[i];
        y=(((aa[i]*x+bb[i])*x+cc[i])*x+dd[i])*x+ee[i]; miny=Math.min(miny,y); maxy=Math.max(maxy,y);
      }
}
      shift=(miny+maxy)/2; for (int i=1;i<=numzeros+1;i++) ee[i]=ee[i]-shift ;
      components=false; reset();
    }
  
    DerivPanel(){}

    public void reset() {
      repaint();
    }
  
    public boolean mouseDown(Event e, int x, int y) {
      if (startedDraw==false && x<5 && !drawAnswer) {buttonStatus = "startedDraw"; startedDraw=true; 
        point=1; xx[point]=x; yy[point]=y; 
      } else {
        if (startedDraw==true && x>xx[point] && doneDrawing==false) {point=point+1; xx[point]=x; yy[point]=y;
        buttonStatus = "startedDraw"; }
      }
      if (startedDraw==true && x>579) {doneDrawing=true; buttonStatus = "finishedDraw"; 
        }
      repaint();
      return true;
    }
  
    public boolean mouseDrag(Event e, int x, int y) {
      if (startedDraw==false && x<5 && !drawAnswer) {startedDraw=true; point=1; xx[point]=x; yy[point]=y;
        buttonStatus = "startedDraw"; 
      } else {
        if (startedDraw==true && x>xx[point] && doneDrawing==false) {point=point+1; xx[point]=x; yy[point]=y;
        buttonStatus = "startedDraw"; }
      }
      if (startedDraw==true && x>579) {doneDrawing=true; buttonStatus = "finishedDraw";
        }
      repaint();
      return true;
    }
  
    public void update(Graphics g) {
      if (!busy) {
        busy = true; 
        paint(g); 
      }
    }
  
    public void paint(Graphics g) {
      if (back == null || bsize.width!=size().width || bsize.height!=size().height) {
        back = createImage(size().width, size().height);
        bsize = size();
        bg = back.getGraphics();
      }
      if (back != null) {
        dopaint(bg);
        g.drawImage(back,0,0,this);
      } else {
        dopaint(g);
      }
      done();
    }
    
    public void dopaint(Graphics g) {
      g.setColor(Color.white);       g.setFont(new Font("Dialog",0,15)); 
      g.fillRect(0,0,size().width,size().height);
      g.setColor(Color.blue);
      for (int i=1; i<=numzeros+1; i++){
        double stepsize=(zeros[i]-zeros[i-1])/20;
        for (int stepnum=0; stepnum<20; stepnum++){
          x=zeros[i-1]+stepnum*stepsize;  y=(((aa[i]*x+bb[i])*x+cc[i])*x+dd[i])*x+ee[i];
          x2=x+stepsize;  y2=(((aa[i]*x2+bb[i])*x2+cc[i])*x2+dd[i])*x2+ee[i];
          g.drawLine((int)(5.5+x*31),(int)(188-y*31),(int)(5.5+x2*31),(int)(188-y2*31));
          g.drawLine((int)(5.5+x*31),(int)(189-y*31),(int)(5.5+x2*31),(int)(189-y2*31));
        }
      }
      g.setColor(Color.black);
	g.drawRect(0,0,599,376); //boxit
      //axes
      g.drawLine(4,188,595,188); g.drawLine(4,187,595,187); g.drawLine(4,189,595,189);
	g.drawLine(5,4,5,372); g.drawLine(4,126,595,126); g.drawLine(4,250,595,250);
	g.drawString("2",7,124); g.drawString("-2",7,248); g.drawString("0",7,185);
      for (int i = 2; i<20; i+=2) {
        int y=5+31*i;
        g.drawLine(y,193,y,183);
        g.drawString(""+i,y,182);
      }
      g.setColor(Color.black);
      String s;
      if (defaultCurve)  s = "Original Curve"; 
      else s = "New Random Curve";
      g.drawString(s,10,20);
      g.setColor(Color.red);
      if (startedDraw) {for (int i=2; i<=point; i++) g.drawLine(xx[i-1],yy[i-1],xx[i],yy[i]);}
      if (drawAnswer) {g.setColor(Color.green);
        for (int i=1; i<=numzeros+1; i++){
          double stepsize=(zeros[i]-zeros[i-1])/20;
          for (int stepnum=0; stepnum<20; stepnum++){
            x=zeros[i-1]+stepnum*stepsize;  y=((a[i]*x+b[i])*x+c[i])*x+d[i];
            x2=x+stepsize;  y2=((a[i]*x2+b[i])*x2+c[i])*x2+d[i];
            g.drawLine((int)(5.5+x*31),(int)(188.5-y*31),(int)(5.5+x2*31),(int)(188.5-y2*31));
          }
        }
        if (fill){temp=0;
          for (int i=1;i<=point;i++){temp++; xxt[temp]=xx[i]; yyt[temp]=yy[i];
            if (i<point) { 
              while (xxt[temp]+1<xx[i+1]) {temp++; xxt[temp]=xxt[temp-1]+1; 
                yyt[temp] = (int)(yy[i] + ((double)(xxt[temp]-               
                xx[i]))/((double)(xx[i+1] - xx[i]))*((double)(yy[i+1]-yy[i])) +0.5);
              }
            }
          }
          point=temp/3;
          for (int i=1;i<=point;i++) {xx[i]=xxt[3*i-2]; yy[i]=yyt[3*i-2];} 
            point++; xx[point]=xxt[temp]; yy[point]=yyt[temp];
            zeroplace=0;
            for (int i=1;i<=point;i++){ 
              while ((double)(xx[i])>=5.5+31*zeros[zeroplace+1]) zeroplace++ ;
              xxx[i]=xx[i]; x=((double)(xx[i])-5.5)/31.0; zz=zeroplace+1;
              yyy[i]=(int)(188.5-(((a[zz]*x+b[zz])*x+c[zz])*x+d[zz])*31);
              g.drawLine(xx[i],yy[i],xxx[i],yyy[i]);
            }
            area=0; 
            for (int i=1;i<point;i++) {
              temp = (xx[i+1]-xx[i])*(Math.abs(yyy[i+1]-yy[i+1])+Math.abs(yyy[i]-yy[i]));
              area=area+((double)(temp))/(31.0*31.0*2);  area=(double)((int)(1000*area+.5))/1000;
            }
            g.setColor(Color.black);
            s="Total (unsigned) shaded area = " + String.valueOf(area);                       g.drawString(s,200,20);
          }
        }
g.setColor(Color.black);
if (buttonStatus=="justCurve") buttonOptions="Draw or Buttons A, B, or C";
if (buttonStatus=="startedDraw") buttonOptions = "Continue to draw, or Buttons A or B";
if (buttonStatus=="finishedDraw") buttonOptions = "Buttons A, B, or C";
if (buttonStatus=="all3") buttonOptions = "Buttons A, B, or D";
if (buttonStatus=="justCorrect") buttonOptions = "Buttons A or B";
if (buttonStatus=="filled") buttonOptions = "Buttons A or B";
g.drawString("Options: " + buttonOptions,10,40);
/*s=String.valueOf(buttonStatus);
g.drawString("buttonStatus="+s,10,60);
s=String.valueOf(drawAnswer);
g.drawString("drawAnswer="+s,10,80);
s=String.valueOf(doneDrawing);
g.drawString("doneDrawing="+s,10,100);
*/

      }

    private synchronized void done() {
      busy = false;
      notifyAll();
    }
  }
}


//in future -  don't allow guess AFTER true value
//  interpolate away long segments