53 lines
1.1 KiB
Markdown
53 lines
1.1 KiB
Markdown
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# Pi Monte Carlo
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Approximate the value of **pi** using your @boardname@!
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```blocks
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let pir = 0
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let pid = 0
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let y = 0
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let pin = 0
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let x = 0
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let r2 = 0
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let r = 0
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let inside = 0
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let n = 0
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// A simple Monte-Carlo simulation to approximate Pi.
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//
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// number of points
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//
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n = 1000000
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// radius of the circle
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r = 4000
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// radius square
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r2 = r * r
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basic.forever(() => {
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inside = 0
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for (let i = 0; i < n; i++) {
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// generate a point within the square
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x = Math.random(r + 1)
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y = Math.random(r + 1)
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// test if the point is within the circle
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// sqrt(x**2 + y**2) < r ==> x**2 + y**2 < r**2
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if (x * x + y * y < r2) {
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inside += 1
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}
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}
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// surface of a square: 4 * r * r surface of a circle:
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// r * r * pi => inside / n ~= (r*r*pi) / (4*r*r) ~=
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// pi / 4 pi = inside / n * 4
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pin = inside * 4
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// only integer arithmetic here...
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pid = pin / n
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pir = pin % n
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// show results
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basic.showLeds(`
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# # # # #
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. # . # .
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. # . # .
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. # . # .
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. # . . #
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`)
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basic.showString(" " + pid + "." + pir)
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})
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```
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