;; ----------- questao 1
;; versao com dotimes
(defun diag (M)
  (let (a)
    (dotimes (i (min (length M) (length (first M))) (reverse a))
      (push  (elt (pop M)  i) a)
      )))


;versao com loop
(defun diag2 (M)
  (let (linha out (c 0))
    (loop
       (setf linha (first M))
       (setf M (rest M))
       (setf out (append out (list (elt linha c))))
       (setf c (1+ c))
       (if (or (null M) (= c (length linha))) (return out))
       )))


;;------------ questao 2


;; versao com mapcar
(defun centro (l)
  (let ((n (apply #'+ (mapcar #'third l))))
    (list (/ (apply #'+ (mapcar (lambda (x) (* (first x)(third x))) l)) n)
	  (/ (apply #'+ (mapcar (lambda (x) (* (second x) (third x))) l)) n)
	  )))

;; versao com dolist
(defun centro2 (l)
  (let ((xs 0)
	(yx 0)
	(ms 0)
	)
    (dolist (p l)
      (setf xs (+ xs (first p)))
      (setf ys (+ ys (second p)))
      (setf ms (+ ms (third p)))
      )
    (list (/ xs ms) (/ ys ms))
    ))


;;------------ questao 3


;; 3a
(defun subconjn (c n)
  (if (= n 1) (mapcar #'list c)
      (let (out (cc c))
	(dolist (x c out)
	  (pop cc)
	  (setf out 
		(append out (mapcar (lambda (y)  (cons x y) )
				    (subconjn cc (1- n)))))
	  ))
      ))

;; 3a - um versao recursiva

(defun subconj-r (c n)
  (cond
    ((= n 1) (mapcar #'list c))
    ((= n (length c)) (list c))
    (t (append (mapcar (lambda (x) (cons (first c) x))
		       (subconj-r c (- 1 n)))
	       (subconj-r (rest c) n)))
    ))



;; 3b
(defun prodcartn (c n)
  (if (= n 1) (mapcar #'list c)
      (let (out)
      (dolist (x c (reverse out))
	(setf out (append out (mapcar (lambda (y) (cons x y))
				      (prodcartn c (1- n)))))
	))))

;; 3c
(defun subconj2 (c)
  (let (out)
    (dolist (x c)
      (pop c)
      (dolist (y c)
	(push (list x y) out)
	))
    out))



;; 3d
(defun prodcart2 (c)
  (let (out)
    (dolist (x c out)
      (dolist (y c)
	(push (list x y) out)
	)))
  )