euler4.el

;; 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.
;;

(defun array-reverse (array)
  "Reverse the ARRAY."
  (let ((reversed-array (copy-sequence array))
	(array-length (length array))
	(i 0))
    (while (< i array-length)
      (aset reversed-array i (aref array (- array-length 1 i)))
      (setq i (1+ i)))
    reversed-array))

(defun palindrome-p (num)
  "Is the number a palindrome?"
  (let* ((num-string (number-to-string num))
	 (num-length (length num-string)))
    (if (= 0 (% num-length 2)) ;; length is even
	(progn
	  (let* ((num-centre (/ num-length 2))
		 (first-half (substring num-string 0 num-centre))
		 (second-half (substring num-string num-centre num-length)))
	    (string= first-half (array-reverse second-half))))
      nil)))

(defun build-number-pair-permutations (limit)
  "Build a list of the permutations of the numbers."
  (let ((list '())
	(num1 limit)
	(num2 limit))
    (while (> num2 0)
      (while (> num1 0)
	(setq list (cons (list num1 num2) list))
	(setq num1 (1- num1)))
      (setq num1 limit)
      (setq num2 (1- num2)))
    list))

(defun product-is-palindrome (pair)
  "Is the product of the pair of numbers a palindrome?"
  (let ((product (* (car pair) (cadr pair))))
    (if (palindrome-p product)
	product)))

(defun find-palindromes (permutations)
  "Find the palindromes from the products of the given permutations."
  (mapcar 'product-is-palindrome permutations))

(defun euler-4 (limit)
  "Solution to Project Euler 4."
  (let* ((permutations (build-number-pair-permutations limit))
	 (palindromes (find-palindromes permutations)))
    (setq palindromes (remove nil palindromes))
    (car (sort palindromes '>))))

(euler-4 999) ;; 906609