Euler Project 4

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 99.

Find the largest palindrome made from the product of two 3-digit numbers.

My Solution

(defun palindrome(n)

(let ((numberstr (format nil "~a" n)))

(string= numberstr (reverse numberstr))))

(defun Euler4()

(loop for i from 100 to 999

do(loop for j from 100 to 999

do(if (and (palindrome (* i j))

(zerop (rem (* i j) i))

(zerop (rem (* i j) j)))

(print (* i j))))))

Others' Solution

First Solution

(defun digits (num)
(map 'list
#'(lambda (char) (read-from-string (string char)))
(prin1-to-string num)))

(defun palindromep (lst)
(or (< (length lst) 2)
(and (equal (car lst) (car (last lst)))
(palindromep (cdr (butlast lst))))))

(defun prod-list (min max j)
(loop for i from min to max collecting (* i j)))

(defun all-prods (min max)
(loop for j from min to max appending (prod-list min j j)))

(defun euler4 ()
(apply #'max (remove-if-not
#'(lambda (n) (palindromep (digits n)))
(all-prods 100 999))))

Second Solution

(defun digits (n)

"extract base 10 digits from a number into a sequence"

(loop for input = n then (truncate (/ input 10))
until (= input 0)
for digit = (mod input 10)
collecting digit into digits
finally (return (reverse digits))))

(defun palindrome? (seq)
"returns t if a sequence is a palindrome"
(equal seq (reverse seq)))

(defun problem-4 ()

(loop for n1 from 100 to 999

maximizing (loop for n2 from 100 to 999

and p = (* n1 n2)
maximizing

(if (palindrome? (digits p)) p 0))))

Third Solution

(defun euler4 (&optional (n 999))

(let ((largest 0))

(do ((i 1 (+ i 1))) ((> i n) largest)

(do ((j 1 (+ j 1))) ((> j n) 'done)

(if (and (> (* i j) largest)

(string= (format nil "~A" (* i j))
(reverse (format nil "~A" (* i j)))))

(setf largest (* i j)))))))