Two Palindrome Exercises
October 6, 2017
We’ve done the first task previously. One approach converts the number to a string, then compares, but it’s easy to strip off the digits of the number, one by one, comparing at the end:
(define (number-palindrome? n)
(let loop ((x n) (z 0))
(if (zero? x) (= n z)
(let ((q (quotient x 10)) (r (remainder x 10)))
(loop q (+ (* z 10) r))))))
And here are some examples:
> (number-palindrome? 123454321) #t > (number-palindrome? 123456789) #f
For the second task, we convert the input strings to a list of characters and compare the list to its reverse; mappend is like map, but uses append instead of cons to assemble its output, thereby splitting multi-letter words into their individual letters:
(define (string-palindrome? xs)
(let ((chars (mappend string->list xs)))
(equal? chars (reverse chars))))
And here are some examples:
> (define x ‘(“a” “bcd” “ef” “g” “f” “ed” “c” “ba”))
> (string-palindrome? x)
#t
> (string-palindrome? (cdr x))
#f
You can run the program at https://ideone.com/9VdOBA.
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