Programming Praxis – Galton

In today’s Programming Praxis exercise, our goal is to simulate a Galton board and display the frequencies of the different bins as a histogram. Let’s get started, shall we?

Some imports:

import Control.Applicative
import Control.Monad
import System.Random

When dropping a single marble we simulate a number of coin tosses to see which bin the marble ends up in.

marble :: Int -> IO Int
marble bins = sum . take (bins - 1) . randomRs (0, 1) <$> newStdGen

When dropping multiple marbles we count how often each bucket is hit.

marbles :: Num a => Int -> Int -> IO [a]
marbles n bins = flip fmap (replicateM n $ marble bins) (\results ->
    map (fromIntegral . length . flip filter results . (==)) [0..bins - 1])

Displaying the histogram is a matter of scaling the values and printing the appropriate amount of asterisks. You can choose the horizontal scaling to get more or less detailed results.

histogram :: RealFrac a => a -> [a] -> IO ()
histogram w cols = mapM_ (\n -> 
    putStrLn $ replicate (ceiling $ n * w / maximum cols) '*') cols

The program itself consists of printing the results of the simulation as a histogram.

main :: IO ()
main = histogram 20 =<< marbles 1000 8

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