import papaya.*;

PFont myfont;
PFont myboldfont;

JakeSlider samplepropslider, confidenceslider, largesampleslider;
JakeButton leftarrow, rightarrow;

PImage CIpeqn;
PImage smallleft;
PImage smallup;
PImage smalldown;
PImage smallright;

String[] names = {
  "Neo", "Batman", "Mr. Anderson", "Lisa Simpson", "Bart Simpson", "Homer Simpson", "Ted Mosby", "Robin Scherbatsky", "Spiderman", "Felicia", "Carol", "Samantha", "Nathan", "Morpheus"
};
String[] gender = {
  "He", "He", "He", "She", "He", "He", "He", "She", "He", "She", "She", "She", "He", "He"
};
String[] obj = {
  "smartphone", "tablet", "desktop computer", "laptop", "blu-ray player", "dvd player", "wii", "ps3", "xbox 360", "high definition TV", "Roomba", "quadrocopter", "Roku box", "5.1 surrond sound system", "photo printer", "ipad", "Kindle Fire"
}; 

int[] samplesize = {60, 70, 80, 90, 100};
int[] confidence = {80, 90, 95, 99};
float[] Zvalues = { 0.8997, .9505, .9750, .9951};
float[] Zrow = {1.2, 1.6, 1.6, 2.5};
float[] Zcolumn = { .08, .05, .06, .08};
float[] zvalues;
float leftCI = 0, rightCI = 0;

int samplesizeslidervalue;
int confidenceslidervalue;
float samplepropslidervalue;

int page = 1;
int numtemplates = 2;
String[] problemText = new String[numtemplates];

int namerand;
int objrand;
int sizerand;
int confidencerand;
int numrand;
String numrandstr;
String pagetext;
String propstr;
int temprand;

void setup()
{
  size(700, 500);
  smooth();

  myfont = loadFont("ArialMT-24.vlw");
  myboldfont = loadFont("Arial-BoldMT-24.vlw");

  CIpeqn = loadImage("CIp.gif");
  smallleft = loadImage("leftbluesmall.jpg");
  smallup = loadImage("bluesmallup.jpg");
  smalldown = loadImage("smalldown.jpg");
  smallright = loadImage("rightbluesmall.jpg");
  
  PImage[] lefts = {loadImage("leftblue.jpg"), loadImage("leftpurple.jpg")};
  leftarrow = new JakeButton(30,415,lefts[1],lefts[0],lefts[0]);

  PImage[] rights = {loadImage("rightblue.jpg"), loadImage("rightpurple.jpg")};
  rightarrow = new JakeButton(615,415,rights[1],rights[0],rights[0]);

  zvalues = new float[201];
  float xloc = -4;

  for (int i = 0; i < 201; i++)
  {
    zvalues[i] = 1.0/sqrt(2.0*PI)*exp(-1.0*xloc*xloc/2.0);  
    xloc += .04;
  }

  generateRandom();

  samplepropslider = new JakeSlider(390,325,100,30,0.5,0.2,0.8,false,color(71, 145, 255),color(2,52,77),myfont,10,1,2);  
  samplepropslider.setVisible(false);
 
  confidenceslider = new JakeSlider(220,325,100,30,confidence[confidencerand],80,99,true,color(71, 145, 255),color(2,52,77),myfont,10,2,0);
  confidenceslider.setVisible(false);

  largesampleslider = new JakeSlider(50,325,100,30,samplesize[sizerand],60,100,true,color(71, 145, 255),color(2,52,77),myfont,10,2,0);
  largesampleslider.setVisible(false);
}

void generateRandom()
{
  namerand = int(random(names.length));
  objrand = int(random(obj.length));
  sizerand = int(random(samplesize.length));
  confidencerand = int(random(confidence.length));
  numrand = int(random(10.0, samplesize[sizerand]-10.0));
  numrandstr = nf(numrand, 2);
  temprand = int(random(numtemplates));

  samplesizeslidervalue = samplesize[sizerand];
  confidenceslidervalue = confidence[confidencerand];
  float tempfloat = (float)numrand/(float)samplesize[sizerand];
  samplepropslidervalue = 0.5;
  propstr = nf(tempfloat, 1, 2);
}

void draw()
{
  background(255);
  fill(0);

  problemText[0] = names[namerand] + " has surveyed " + samplesize[sizerand] + " individuals about their " + obj[objrand] + " ownership. In this group, "
    + numrandstr + " said they owned a " + obj[objrand] +". Find the " + confidence[confidencerand] + "% confidence interval for the population proportion who own a " +
    obj[objrand] + ".";  

  problemText[1] = names[namerand] + " is interested in studying the population proportion who own a " + obj[objrand] + ". " + gender[namerand] + " collected a sample of " +
    samplesize[sizerand] + " people and found " + numrandstr + " of them own a " + obj[objrand] + ". Calculate the " + confidence[confidencerand] + "% confidence interval for the population proportion who own a " +
    obj[objrand] + ".";   

  switch(page)
  {
  case 1:
    drawStrings(problemText[temprand], 30, 44, 25);
    pagetext = "Step one: Identify the problem type and formula to use";
    drawStrings(pagetext, 30, 194-25, 25, "bold");
    pagetext = "The type of problem we have here is to find the confidence interval " +
      "for a population proportion. We use the formula: ";
    image(CIpeqn, 350-72, 290-29);
    drawStrings(pagetext, 80, 244-25, 25);

    leftarrow.setVisible(false);
    rightarrow.setVisible(true);
    break;

  case 2:
    drawStrings(problemText[temprand], 30, 44, 25);
    pagetext = "Step two: Identify variables";
    drawStrings(pagetext, 30, 194-25, 25, "bold");
    pagetext = "We want to identify each variable in our formula:";   
    drawStrings(pagetext, 80, 244-25, 25);

    image(CIpeqn, 350-72, 258-25);

    pagetext = " Our sample size is represented by n, which is " + samplesize[sizerand] + "." + 
      " The p with a hat represents our sample proportion. In this problem, the sample proportion is " + propstr + " ("+ numrandstr 
      + " divided by the sample size). We also have the confidence level, given by the variable L, as " 
      + confidence[confidencerand] + "%.";   

    drawStrings(pagetext, 80, 324-25, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 3:
    drawStrings(problemText[temprand], 30, 44, 25);
    pagetext = "Step two continued: ";
    drawStrings(pagetext, 30, 194-25, 25, "bold");

    pagetext = "In our formula: ";
    drawStrings(pagetext, 80, 244-25, 25);

    image(CIpeqn, 350-72, 258-25);

    pagetext = "The Z with the subscript (1 + L)/2 represents (1 + L)/2 percentile of the Z curve. In this case, " +
      "we have L = ." + confidence[confidencerand] + ", so we are looking for the " + 
      (confidence[confidencerand]+100)/2.0 + " percentile of the Z curve. ";

    drawStrings(pagetext, 80, 330-25, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 4:
    drawStrings(problemText[temprand], 30, 44, 25);
    pagetext = "Step three: Find a percentile";
    drawStrings(pagetext, 30, 194-25, 25, "bold");

    float tempfloat = ((float)confidence[confidencerand]/100+1)/2.0;

    pagetext = "Use the table A.3 to the find the percentile of the Z curve. ";
    pagetext += "Scan the entries of the table until you see " + tempfloat + ". The corresponding row and column gives you " +  
      "the " + (confidence[confidencerand]+100)/2.0 + " percentile as " + nf(Zrow[confidencerand]+Zcolumn[confidencerand], 1, 4) + " (ie " +  
      (confidence[confidencerand]+100)/2.0 + "% of the area is to the left of this point).";

    drawStrings(pagetext, 80, 244-25, 25);

    pagetext = nf(Zcolumn[confidencerand], 1, 4);
    drawStrings(pagetext, 230, 294+45-25, 25);
    image(smallup, 245, 294+50-25);

    pagetext = nf(Zrow[confidencerand], 1, 4);
    drawStrings(pagetext, 130, 394-25, 25);
    image(smallleft, 190, 373-25);
    pagetext = nf(Zvalues[confidencerand], 1, 4);
    drawStrings(pagetext, 230, 394-25, 25);

    drawBellcurve(Zrow[confidencerand]+Zcolumn[confidencerand], 400, 308-25, 200, 88);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 5:
    drawStrings(problemText[temprand], 30, 44, 25);

    pagetext = "Step four: Plug in values and interpret result";
    drawStrings(pagetext, 30, 194-25, 25, "bold");

    pagetext = "Now, plug in your values for the variables into: ";
    drawStrings(pagetext, 80, 244-25, 25);

    image(CIpeqn, 350-72, 258-27);

    pagetext = "Plugging in, we get " + propstr + " plus or minus the square root of (" + propstr + "*(1-"+propstr+")/"+samplesize[sizerand] + ") times " +
      nf(Zrow[confidencerand]+Zcolumn[confidencerand], 1, 4)+".";

    tempfloat = Float.parseFloat(propstr); 
    leftCI = tempfloat - sqrt(tempfloat*(1.0-tempfloat)/(float)samplesize[sizerand]) *(Zrow[confidencerand]+Zcolumn[confidencerand]);
    rightCI = tempfloat + sqrt(tempfloat*(1.0-tempfloat)/(float)samplesize[sizerand]) *(Zrow[confidencerand]+Zcolumn[confidencerand]);
    pagetext += " This gives us the interval (" + nf(leftCI, 1, 2) + ", " + nf(rightCI, 1, 2)+ "). " + names[namerand] + " is " + 
      confidence[confidencerand] + "% confident that the population proportion owning a " + obj[objrand] + " will be between " + nf(leftCI, 1, 2)  +
      " and " + nf(rightCI, 1, 2) + ".";

    drawStrings(pagetext, 80, 319-25, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 6:
    drawStrings(problemText[temprand], 30, 44, 25);

    pagetext = "Step five: State your assumptions";
    drawStrings(pagetext, 30, 194-25, 25, "bold");

    pagetext = "In creating our confidence interval, we have assumed a Bin(n,p) model and that the " +
      "sample size is large. You need to check the conditions: ";

    drawStrings(pagetext, 80, 244-25, 25);

    pagetext = "Y >= 10 and n - Y >= 10.";
    drawStrings(pagetext, 80, 244+25*2-25, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 7:
    drawStrings(problemText[temprand], 30, 44, 25); 
    pagetext = "Exploring the confidence interval: ";
    drawStrings(pagetext, 30, 194-25, 25, "bold"); 

    pagetext = "What is the effect of the sample proportion on the confidence interval? What are the effects of the confidence level and sample size? ";
    drawStrings(pagetext, 50, 244-25, 25); 

    pagetext = "Sample size";
    drawStrings(pagetext, 50, 294+25-25, 25); 

    pagetext = "Confidence Level";
    drawStrings(pagetext, 205, 294+25-25, 25); 

    pagetext = "Sample proportion";
    drawStrings(pagetext, 385, 294+25-25, 25); 

    pagetext = "Your interval:";
    drawStrings(pagetext, 540, 294+25-25, 25); 

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);

    confidenceslider.setVisible(true);
    samplepropslider.setVisible(true);

    float leftedge, rightedge;
    tempfloat = Float.parseFloat(propstr);

    largesampleslider.setVisible(true);
    float percentile = (float)Probability.norminv((1.0 + (float)confidenceslidervalue/100.0)/2.0);
    leftCI = samplepropslidervalue - sqrt(samplepropslidervalue*(1.0-samplepropslidervalue)/(float)samplesizeslidervalue)*percentile;
    rightCI = samplepropslidervalue + sqrt(samplepropslidervalue*(1.0-samplepropslidervalue)/(float)samplesizeslidervalue)*percentile;
    leftedge = map(leftCI, 0.2-sqrt(.25/60.0)*2.58, 0.8+sqrt(.25/60.0)*2.58, 540, 640);
    rightedge = map(rightCI, 0.2-sqrt(.25/60.0)*2.58, 0.8+sqrt(.25/60.0)*2.58, 540, 640);

    pagetext = "("+nf(leftCI, 1, 2)+", "+nf(rightCI, 1, 2)+")";
    drawStrings(pagetext, 540, 294+100-5-25, 25); 

    fill(71, 145, 255);
    rect(leftedge, 294+57-25, rightedge-leftedge, 4);

    // fill(255,0,0);

    // pagetext = "Warning: assumptions violated. Y needs to be ";
    // drawStrings(pagetext, 150, 425, 25, "bold"); 
    // pagetext = " between 10 and (samplesize-10).";
    // drawStrings(pagetext, 150, 450, 25, "bold"); 

    break;
  case 8:
    drawStrings(problemText[temprand], 30, 44, 25); 
    pagetext = "Exploring the confidence interval continued: ";
    drawStrings(pagetext, 30, 194-25, 25, "bold"); 

    pagetext = "The sample proportion is the midpoint/center of the confidence interval. Varying it will move the confidence interval left and right. The sample size " +
      "alters the width of the confidence interval. As you increase your sample size, the width gets smaller. Lastly, if you increase your level of confidence, " +
      "the width of the confidence interval will increase. ";
    drawStrings(pagetext, 30, 194+50-25, 25); 

    pagetext = "To try another problem, click the right arrow.";
    drawStrings(pagetext, 30, 194+200-25, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  }

  samplepropslider.updateSlider();
  samplepropslider.drawSlider();
  samplepropslidervalue = samplepropslider.getValue();
  samplepropslidervalue = round(samplepropslidervalue*100.0)/100.0;

  confidenceslider.updateSlider();
  confidenceslider.drawSlider();
  confidenceslidervalue = (int)confidenceslider.getValue();
  
  largesampleslider.updateSlider();
  largesampleslider.drawSlider();
  samplesizeslidervalue = (int)largesampleslider.getValue();  

  leftarrow.updateButton();
  leftarrow.drawButton();

  if (leftarrow.clicked)
  {
    largesampleslider.setVisible(false);
    confidenceslider.setVisible(false);
    samplepropslider.setVisible(false);
    page--;
  }
  
  rightarrow.updateButton();
  rightarrow.drawButton();
  
  if(rightarrow.clicked)
  {
    largesampleslider.setVisible(false);
    confidenceslider.setVisible(false);
    samplepropslider.setVisible(false);

    if (page == 8) 
    {
      page = 0; 
      generateRandom();
      float tempfloat = Float.parseFloat(propstr);
      confidenceslider.setValue(confidenceslidervalue);
      samplepropslider.setValue(0.5);
    }
    if (page != 8) page++;
  }
}

void drawStrings(String astring, int startx, int starty, int yspacing)
{
  drawStrings(astring, startx, starty, yspacing, "plain");
}

void drawStrings(String astring, int startx, int starty, int yspacing, String boldtype)
{
  String[] theTokens = splitTokens(astring, " ");
  int x = startx;
  int y = starty;

  if (boldtype.equals("plain"))
    textFont(myfont, 18);
  else
    textFont(myboldfont, 18);

  for (int words = 0; words < theTokens.length; words++)
  {
    String currentword = theTokens[words];
    float wordwidth = textWidth(currentword + " ");
    if (x + wordwidth > 675)
    { 
      x = startx;
      y += yspacing;
    }
    text(currentword, x, y);
    x += wordwidth;
  }
}

void drawBellcurve(float loc, int xstart, int ystart, int bwidth, int bheight)
{
  int index = round(map(loc, -4, 4, 0, 200));
  float xscreen, yscreen;
  float xloc = -4.0;

  fill(255, 0, 0);
  beginShape();
  for (int i = 10; i <= index; i++)
  {
    xscreen = map(xloc, -4, 4, xstart, xstart+bwidth);
    yscreen = map(zvalues[i], 0, 0.5, ystart+bheight, ystart);
    vertex(xscreen, yscreen);
    xloc += .04;
  }
  xloc-=.04;
  xscreen = map(xloc, -4, 4, xstart, xstart+bwidth);
  yscreen = map(zvalues[0], 0, 0.5, ystart+bheight, ystart);
  vertex(xscreen, yscreen);
  endShape(CLOSE);

  float saveloc = xloc;

  fill(255, 255, 255);
  beginShape();
  for (int i = index; i < 191; i++)
  {
    xscreen = map(xloc, -4, 4, xstart, xstart+bwidth);
    yscreen = map(zvalues[i], 0, 0.5, ystart+bheight, ystart);
    vertex(xscreen, yscreen);
    xloc += .04;
  }
  xscreen = map(saveloc, -4, 4, xstart, xstart+bwidth);
  yscreen = map(zvalues[0], 0, 0.5, ystart+bheight, ystart);
  vertex(xscreen, yscreen);
  endShape(CLOSE);
}