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to Luhn in the Common Lisp Track

Published at Feb 22 2020 · 0 comments
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Given a number determine whether or not it is valid per the Luhn formula.

The Luhn algorithm is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers and Canadian Social Insurance Numbers.

The task is to check if a given string is valid.

Validating a Number

Strings of length 1 or less are not valid. Spaces are allowed in the input, but they should be stripped before checking. All other non-digit characters are disallowed.

Example 1: valid credit card number

4539 1488 0343 6467

The first step of the Luhn algorithm is to double every second digit, starting from the right. We will be doubling

4_3_ 1_8_ 0_4_ 6_6_

If doubling the number results in a number greater than 9 then subtract 9 from the product. The results of our doubling:

8569 2478 0383 3437

Then sum all of the digits:

8+5+6+9+2+4+7+8+0+3+8+3+3+4+3+7 = 80

If the sum is evenly divisible by 10, then the number is valid. This number is valid!

Example 2: invalid credit card number

8273 1232 7352 0569

Double the second digits, starting from the right

7253 2262 5312 0539

Sum the digits

7+2+5+3+2+2+6+2+5+3+1+2+0+5+3+9 = 57

57 is not evenly divisible by 10, so this number is not valid.


Check out Installing Common Lisp for instructions to get started or take a look at the guides available in the track's side bar.


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One suggested add-on for Emacs and Common Lisp is SLIME which offers tight integration with the REPL; making iterative coding and testing very easy.


The Luhn Algorithm on Wikipedia http://en.wikipedia.org/wiki/Luhn_algorithm

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.


(ql:quickload "lisp-unit")
#-xlisp-test (load "luhn")

(defpackage #:luhn-test
  (:use #:cl #:lisp-unit))

(in-package #:luhn-test)

(define-test single-digit-strings-can-not-be-valid
  (assert-false (luhn:is-valid "1")))

(define-test a-single-zero-is-invalid
  (assert-false (luhn:is-valid "0")))

(define-test a-simple-valid-sin-that-remains-valid-if-reversed
  (assert-true (luhn:is-valid "059")))

(define-test a-simple-valid-sin-that-becomes-invalid-if-reversed
  (assert-true (luhn:is-valid "59")))

(define-test a-valid-canadian-sin
  (assert-true (luhn:is-valid "055 444 285")))

(define-test invalid-canadian-sin
  (assert-false (luhn:is-valid "055 444 286")))

(define-test invalid-credit-card
  (assert-false (luhn:is-valid "8273 1232 7352 0569")))

(define-test valid-strings-with-a-non-digit-included-become-invalid
  (assert-false (luhn:is-valid "055a 444 285")))

(define-test valid-strings-with-punctuation-included-become-invalid
  (assert-false (luhn:is-valid "055-444-285")))

(define-test valid-strings-with-symbols-included-become-invalid
  (assert-false (luhn:is-valid "055£ 444$ 285")))

(define-test single-zero-with-space-is-invalid
  (assert-false (luhn:is-valid " 0")))

(define-test more-than-a-single-zero-is-valid
  (assert-true (luhn:is-valid "0000 0")))

(define-test input-digit-9-is-correctly-converted-to-output-digit-9
  (assert-true (luhn:is-valid "091")))

(define-test strings-with-non-digits-is-invalid
  (assert-false (luhn:is-valid ":9")))

(let ((*print-errors* t)
      (*print-failures* t))
  (run-tests :all :luhn-test))
(in-package #:cl-user)
(defpackage #:luhn
  (:use #:cl)
  (:export #:is-valid))

(in-package #:luhn)

(defun is-valid (input)
  (let ((numbers
         (loop for x across input
            when (char<= #\0 x #\9)
            collect (- (char-code x) 48)
            when (not (find x " 0123456789"))
            return nil)))
    (if (<= (length numbers) 1)
        (let ((processed
          (loop for x in (reverse numbers)
             for counter from 0
             if (oddp counter)
             collect (if (> x 4) (- (* x 2) 9) (* x 2))
             collect x)))
          (zerop (mod (apply #'+ processed) 10))))))

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