Euler Project 34

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Note: as 1! = 1 and 2! = 2 are not sums they are not included.

My Solution

(defun factorial(n)

(factorial-iter n 1))

(defun factorial-iter(n result)

(if (> n 0)

(factorial-iter (- n 1) (* n result))

result))

(defun factorialsum(n)

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

(loop for i from 0 to (- (length numberstr) 1)

sum (factorial (parse-integer numberstr :start i :end (+ i 1))))))

(defun Euler34-iter(n)

(loop for i from 3 to n

collect (if (= i (factorialsum i))

i)))

(defun Euler34(n)

(remove-if #'(lambda(x)(null x)) (Euler34-iter n)))

First Solution

(defun digits (num)

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

(defun digit-fact (n)

(aref #(1 1 2 6 24 120 720 5040 40320 362880 3628800) n))

(defun fact-sum (num)

(apply #'+ (mapcar #'digit-fact (digits num))))

(defun euler34 ()

(loop for n from 10 to (* 6 (digit-fact 9))

when (= n (fact-sum n))
collect n))

Second Solution

(defconstant vec #(1 1 2 6 24 120 720 5040 40320 362880))

(defun euler34 ()

(let ((total 0))

(do ((i 3 (+ i 1)))
((> i (upper-bound 2)) total)

(if (= i (sum-factorials-digits (format nil "~A" i)))
(incf total i)))))

(defun upper-bound (n)

(if (> (expt 10 n) (* n (svref vec 9)))
(* n (svref vec 9))
(upper-bound (+ n 1))))

(defun sum-factorials-digits (str)

(if (zerop (length str))
0
(+ (svref vec (- (char-code (elt str 0)) 48))
(sum-factorials-digits (subseq str 1))))))

Third Solution

(defun problem-34 ()

(loop for x from 1 to 999999

when (= x (reduce #'+ (mapcar #'fact-tr (digits x)))) sum x))

(defun fact-tr (n &optional (acc 1))

(if (<= n 1)
acc
(fact-tr (- n 1) (* acc n))))

(defun digits (num)

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