Two Palindrome Exercises
October 6, 2017
Many of the people who read my blog are programming students. It is October, about the middle of the Fall Semester at many universities, and my student readers need exercises to cement their understanding of their studies. Here are two exercises about palindromes.
- A number like 123454321 is palindromic; it decimal digits are the same left-to-right as they are right-to-left. Write a program that determines if a given input number is palindromic.
- Given a list of strings, for instance {“a” “bcd” “ef” “g” “f” “ed” “c” “ba”}, write a program to determine if the individual letters of the strings form a palindrome. Note that the letters might be distributed into the individual words differently when read in opposite directions.
Your task is to write two programs that recognize palindromes. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 
We can avoid separate calls to
quotientandremainderby usingfloor/which returns both.With SRFI 13, we can eliminate converting strings to lists and back, and just say:
That said, the successors of SRFI 13 do not support string-reverse, because it is only useful in artificial examples like these. In a Unicode world, “Hägar the Horrible”, when expressed in decomposed form (as here). reverses not to “elbirroH eht ragäH” but to “elibrroH eht rag̈aH”, with the umlaut on the “g” rather than the first “a”.
A Haskell version.
import Data.Bool (bool) import Data.List (unfoldr) import Data.Tuple (swap) import Numeric (showInt) -- Is a number a base-10 palindrome? (We only consider non-negative numbers -- because the showInt library function only supports them.) isNumPalindrome :: Integral a => a -> Bool isNumPalindrome n | n < 0 = False | otherwise = isPalindrome (showInt n "") -- Is the result of concatenating a list of lists a palindrome? isConcatPalindrome :: Eq a => [[a]] -> Bool isConcatPalindrome = isPalindrome . concat -- Is a list a palindrome? isPalindrome :: Eq a => [a] -> Bool isPalindrome xs = xs == reverse xs -------------------------------------------------------------------------------- -- An alternate way of checking whether a number is a palindrome, by explicitly -- converting the number to a list of digits, rather than using the showInt -- library function to convert it to a list of characters. -- The list of a number's digits, in base b. The least significant digits are -- first. The empty list represents 0. toDigits :: Integral a => a -> a -> [a] toDigits b = unfoldr step where step 0 = Nothing step i = Just . swap $ i `quotRem` b -- Is a number a base-10 palindrome? We allow negative numbers: -n is a -- palindrome if n is. isNumPalindrome' :: Integral a => a -> Bool isNumPalindrome' = isPalindrome . toDigits 10 -------------------------------------------------------------------------------- test :: (Eq a, Show a) => (a -> Bool) -> a -> IO () test palFn x = putStrLn $ "Is " ++ show x ++ " a palindrome? " ++ bool "No" "Yes" (palFn x) main :: IO () main = do test isNumPalindrome 0 test isNumPalindrome 123 test isNumPalindrome 12321 test isConcatPalindrome ([] :: [String]) test isConcatPalindrome ["a", "bc"] test isConcatPalindrome ["a", "bcd", "ef", "g", "f", "ed", "c", "ba"] test isNumPalindrome' (-12) test isNumPalindrome' (-121) test isNumPalindrome' 121Klong 20170905 f1::{[a]; a::,/:~x; a=|a} :monad f2::{[a]; a::0;{x>0}{[r]; a::(r::x!10)+a*10; (x-r):%10}:~x; x=a} :monad f1(["a" "bc" "def" "g" "h"]) 0 f1(["a" "bc" "def" "g" "h" "h" "g" "f" "e" "d" "c" "b" "a"]) 1 f1(["a" "bc" "def" "g" "h" "g" "f" "e" "d" "c" "b" "a"]) 1 f2(123) 0 f2(123321) 1 f2(12321) 1(defun palindromic-p (str)
(equal (string-reverse str) str))
(defun palindromic-integer-p (n)
(palindromic-p (int-to-string n)))
(defun palindromic-list-p (list)
(palindromic-p (apply #’concat list)))
;; (palindromic-integer-p 123454321)
;; t
;; (palindromic-integer-p 1234544321)
;; nil
;; (palindromic-list-p ‘(“a” “bcd” “ef” “g” “f” “ed” “c” “ba”))
;; t
;; (palindromic-list-p ‘(“a” “bcd” “ef” “xg” “f” “ed” “c” “ba”))
;; nil