recursion - Common Lisp: Using (let) for evaluating recursive function -

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so wrote returns maximal subset sum given list of positive integers. however, use (let) make code more efficient. know if or how possible.

(defun subset-sum1 (numbers capacity)   (subset-sum numbers capacity 0))  (defun subset-sum (numbers capacity counter)    (cond ((null numbers) counter)         ((= counter capacity) counter) ;; return if counter 'hits' capacity         ((< capacity (+ (car numbers) counter))          (subset-sum (cdr numbers) capacity counter)) ;; cdr if car branch exceeds capacity         ((<= (subset-sum (cdr numbers) capacity counter)              (subset-sum (cdr numbers) capacity (+ (car numbers) counter)))          (subset-sum (cdr numbers) capacity (+ (car numbers) counter))) ;; choose car         (t (subset-sum (cdr numbers) capacity counter)))) ;; choose cdr

the above code works fine in common lisp. but, below, because feel using let make code better. wrote goes infinite loop :( assignment introductory ai class... out novice please!

(defun subset-sum (numbers capacity counter)   (let ((exclude (subset-sum (cdr numbers) capacity counter))    (include (subset-sum (cdr numbers) capacity (+ (car numbers) counter))))      (cond ((null numbers) counter)        ((= counter capacity) counter)        ((< capacity (+ (car numbers) counter)) exclude)        ((<= exclude include) include)        (t (exclude)))))

you infinite loop because of these lines:

(defun subset-sum (numbers capacity counter)   (let ((exclude (subset-sum (cdr numbers) capacity counter))

you keep calling subset-sum recursively, , never terminates. when end of list, , numbers (), keep going, because (cdr '()) '(). handled in original checking (null numbers) (though might more idiomatic use (endp numbers)). can like:

(defun subset-sum (numbers capacity counter)   (if (endp numbers)     counter     (let ((exclude (subset-sum (cdr numbers) capacity counter))           ;...          )       (cond ; ...           ))))

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