palindromicTips.hs

-- can we have a triply palindromic bill???
-- i.e., a bill where the subtotal, the tip, and the total are all numeric palindromes?

-- (note that we're doing all these calculations in cents)

isPalindrome :: Eq a => [a] -> Bool
isPalindrome x = x == reverse x

numToDigits n = map (\x -> read [x] :: Int) (show n)

numIsPalindrome :: Show a => a -> Bool
numIsPalindrome x = isPalindrome (numToDigits x)

stingyTip = 0.1 -- 10%
generousTip = 0.3 -- 30%

reasonableTips :: Integral a => a -> [Int]
reasonableTips x = map (\z -> fromIntegral z :: Int) (map round [ n * stingyTip .. n * generousTip])
    where n = fromIntegral x
-- stupid number casting crap

triplePalindromes n = [ (sub, tip, tot) | sub <- [1..n],
                                          numIsPalindrome sub,
                                          tip <- reasonableTips sub,
                                          numIsPalindrome tip,
                                          tot <- [sub + tip],
                                          numIsPalindrome tot
                                        ]

-- there are tons and tons!
-- e.g., for bills below $100, and tips between 10 and 30%, we have:
-- length (triplePalindromes 10000)
-- > 488

showCurrency x = "$" ++ show (x `div` 100) ++ "." ++ if (cents < 10) then ("0" ++ show cents) else (show cents)
                                                        where cents = x `mod` 100

showTriplePalindrome (sub,tip,tot) = "subtotal: " ++ showCurrency sub ++ 
                                       "; tip: " ++ showCurrency tip ++ 
                                       "; total: " ++ showCurrency tot

printTriplePalindromesBelowN n = mapM (putStrLn . showTriplePalindrome) (triplePalindromes n)

-- handy reference list:
-- printTriplePalindromesBelowN 10000