scalar-product

;; Enter your code here. Read input from STDIN. Print output to STDOUT
;;; (pgroup '(1 2 3 4)) => ((1 2) (3 4))
(defun pgroup (s)
  "Do pairs of elements of a given list."
  (cond ((null s) s)
    ((null (cdr s)) s)
    (t (cons (list (car s) (cadr s))
         (pgroup (cddr s))))))

;;; (gen 5 0 '(4 0)) => ((4 3) (2 0) (2 2))
(defun gen (n i s &optional (m 5))
  "Gen algorirthm from hackerrank."
  (cond ((> i n) (pgroup (cddr (reverse s))))
    (t (gen n (1+ i) (cons (mod (+ (car s) (cadr s)) m) s)))))

;;; (dot-product '(4) '(5)) => 20
(defun dot-product (a b)
  "Compute the mathematical dot product of two vectors."
  (apply #'+ (mapcar #'* a b)))

(defparameter *ps* '())

;;; (comb 2 '(1 2 3) #'print) =>
;;; (3 2)
;;; (3 1)
;;; (2 1)
(defun comb (m list fn)
  "Find all possible combinations of a given list."
  (labels ((comb1 (l c m)
         (when (>= (length l) m)
           (if (zerop m) (return-from comb1 (funcall fn c)))
           (comb1 (cdr l) c m)
           (comb1 (cdr l) (cons (first l) c) (1- m)))))
    (comb1 list nil m)))

;;; (explanation '(4 0) 5 3) => (8 14 4)
(defun explanation (c m n)
  "Explanation algorithm from hackerrank."
  (setf *ps* '())
  (comb 2 (gen (+ 2 n) 0 c m)
    (lambda (s) (push (dot-product (car s) (cadr s)) *ps*))))

;;; (diff (loop :for x in *ps* :collect (mod x 5)) => (3 4)
(defun diff (s)
  "Remove duplicated atoms of a list."
  (cond ((null s) s)
    ((member (car s) (cdr s))
     (diff (cdr s)))
    (t (cons (car s) (diff (cdr s))))))

;;; hackerrank I/O
(setq *ps* (explanation (list (read) 0) (read) (read)))

(format t "~a" (length (diff (loop :for x in *ps* :collect (mod x (third *ps*))))))