Posts Tagged ‘coins’

Programming Praxis – MindCipher

May 10, 2013

In today’s Programming Praxis exercise, our goal is to solve two exercises from the MindCipher website (technically three, but the third one can be solved without programming). Let’s get started, shall we?

import Control.Monad
import Data.List
import System.Random

The first exercise is to see which pattern, on average, takes longer to come up when flipping a coin: heads, tails, heads or heads, tails, tails. First, we define a function to simulate single series of flips, counting the number of flips before the desired pattern is produced. Heads and tails are represented as booleans for the sake of convenience.

flipUntil :: [Bool] -> IO Int
flipUntil pattern = fmap (length . takeWhile (not . isPrefixOf pattern) .
                    tails . randomRs (False, True)) newStdGen

Next, we simulate an entire day by repeating this process 10000 times and taking the average.

day :: [Bool] -> IO Double
day pattern = fmap (\cs -> fromIntegral (sum cs) / fromIntegral (length cs)) .
              replicateM 10000 $ flipUntil pattern

For the second exercise, we need to find the first year for which the sum of both groups of two digits is equal to the middle two digits. This is easily achieved via a simple brute-force search.

sumDay :: Maybe Integer
sumDay = find (\d -> div d 100 + mod d 100 == div (mod d 1000) 10) [1979..]

Running our two algorithms shows that monday’s pattern takes longer on average and that the first year that satisfies the criteria is 2307.

main :: IO ()
main = do print =<< liftM2 compare (day [False, True, False])
                                   (day [False, True, True])
          print sumDay

Programming Praxis – Floupia

February 22, 2013

In today’s Programming Praxis exercise, our goal is to calculate the minimum total amount of coins involved in a payment (including change) for a currency with a given set of coin denominations. Let’s get started, shall we?

import Data.List
import Math.Combinat

First we search all transactions involving one coin, then all transactions involving two coins, etc. We exclude all options where the payment and the change include the same coin, since that would make both coins useless. We return the first option for which the change equals the difference between the payment and the amount required.

pay :: (Eq a, Num a) => a -> [a] -> ([a], [a])
pay total coins = head
    [(p,c) | n <- [1..], pc <- [1..n], p <- combine pc coins
           , c <- combine (n - pc) (coins \\ p), sum p - total == sum c]

Some tests to see if everything is working properly:

main :: IO ()
main = do print $ pay 17 [1,3,7,31,153] == ([31], [7,7])
          print $ pay 18 [1,10]         == ([10,10],[1,1])