def isPrime(n: Int): Boolean = {
if (n == 1) return false
for (i <- 2 to n/2) {
if (n %i == 0) {
return false
}
}
return true
}
def twoFactors(n: Int): (Int, Int) = {
for (i <- 2 to n/2) {
if (n % i == 0) {
return (i, n / i)
}
}
throw new IllegalStateException("Problemo - twoFactors()!")
}
var Siz = 40.0
val FontSize = 20
def rect(w: Double, h: Double) {
forward(h); right()
forward(w); right()
forward(h); right()
forward(w); right()
}
def square(n: Double) {
rect(n, n)
}
def showNumberHelper(n: Int)(borderMaker: => Unit) {
borderMaker
val ts = textExtent(n.toString, FontSize)
penUp()
forward(ts.height + (Siz - ts.height)/2)
right()
forward((Siz - ts.width)/2)
penDown()
saveStyle()
setPenColor(blue)
write(n.toString)
restoreStyle()
penUp()
back((Siz - ts.width)/2)
left()
back(ts.height + (Siz - ts.height)/2)
penDown()
}
def showNumberInBox(n: Int) {
showNumberHelper(n) {
square(Siz)
}
}
def showNumberInL(n: Int) {
showNumberHelper(n) {
forward(Siz)
back(Siz)
right()
forward(Siz)
back(Siz)
left()
}
}
def showNumber(n: Int) {
showNumberHelper(n) {}
}
def showFactorTree(f: (Int, Int)) {
val (f1, f2) = (f._1, f._2)
// left leg
left(135)
forward(Siz)
// goto box starting position
penUp()
forward(math.sqrt(Siz * Siz * 2))
right(135)
penDown()
// make tree for the first factor
factorTree(f1)
// back to starting point
penUp()
right(45)
forward(math.sqrt(Siz * Siz * 2) + Siz)
left(45)
penDown()
// right leg
right(135)
forward(Siz)
// goto box starting position
penUp()
right(45)
forward(Siz)
right(180)
penDown()
// make tree for the second factor
factorTree(f2)
// go back to the starting point
// this is not strictly necessary for this command because
// (a) the factorTree call above is the last thing that this
// command does, and
// (b) the ealier factorTree call does not recurse (because
// f1 is always a prime)
// be we go back to the starting point anyway - in keeping
// with the convention that a command leaves the turtle
// where it picked it up from
penUp()
forward(Siz)
left(45)
forward(Siz)
right(45)
penDown()
}
def showFactorStairs(f: (Int, Int)) {
val (f1, f2) = (f._1, f._2)
penUp()
left()
forward(Siz)
right()
penDown()
showNumber(f1)
penUp()
right()
forward(Siz)
left()
right(180)
forward(Siz)
left(180)
penDown()
cdiv(f2)
}
def factorTree(n: Int) {
if (isPrime(n)) {
showNumberInBox(n)
}
else {
showNumberInBox(n)
showFactorTree(twoFactors(n))
}
}
def cdiv(n: Int) {
if (isPrime(n)) {
showNumberInL(n)
}
else {
showNumberInL(n)
showFactorStairs(twoFactors(n))
}
}
def title(s: String) {
val ts = textExtent(s, FontSize)
penUp()
forward(100)
left()
forward(ts.width/2)
penDown()
saveStyle()
setPenColor(blue)
setPenThickness(4)
write(s)
restoreStyle()
penUp()
back(ts.width/2)
right()
back(100)
penDown()
}
val pageStyle = "color:white;background:#016491;margin:15px;"
val headerStyle = "text-align:center;font-size:110%;color:yellow;"
def pgHeader(hdr: String) =
<p style={headerStyle}>
{xml.Unparsed(hdr)}
<hr/>
</p>
val pg = Page(
name = "",
body =
<body style={pageStyle}>
{pgHeader("Visualizing Factors and Factorization")}
<p>
Wanna see how you can factorize any number and come
up with its prime factorization?
</p>
<p>
Enter a number below and click <em>Factorize</em>
</p>
</body>,
code = {
clear()
clearOutput()
stAddField("Number", 12)
stAddButton ("Factorize") {
val n = stFieldValue("Number", 12)
val ts = textExtent(n.toString, FontSize)
Siz = if (ts.width > Siz) ts.width + 10 else Siz
clear()
// invisible()
setAnimationDelay(100)
setPenFontSize(FontSize)
penUp()
forward(100)
left()
forward(Siz * 4)
right()
penDown()
title("Factor Tree Method")
factorTree(n)
penUp()
right()
forward(Siz * 8)
left()
penDown()
title("Continuous Division Method")
cdiv(n)
}
}
)
val story = Story(pg)
stClear()
stPlayStory(story)
