lisprc

;;;; General things I keep copy-pasting

(defun output (a &rest s) (format t "~a~{ ~a~}~%" a s) a)

(defun range-0 (n)
  (loop for i from 0 to (1- n) collect i))
(defun range-1 (n)
  (loop for i from 1 to n collect i))

;; Number Theory
(defun divides (p n) (if (zerop (mod n p)) p nil))
(defun expt-mod (n k m)
  (cond
    ((= k 0) 1)
    ((evenp k) (mod (expt (expt-mod n (/ k 2) m) 2) m))
    ((oddp k) (mod (* n (expt-mod n (1- k) m)) m))))
(defun get-digit (n i p)
  (mod (truncate n (expt p i)) p))
(defun is-prime (p)
  (if (> p 2) (loop for d from 2 to (isqrt p) never (divides d p))))
(defun is-kth-power (n k)
  (if (< n 0)
    (if (evenp k) nil (is-kth-power (- n) k))
    (let ((a (round (expt n (/ 1 k)))))
    (eql (expt a k) n))))

;; Cartesian Product
(defun mappend (fn the-list)
  (apply #'append (mapcar fn the-list)))
(defun cartesian-product (&rest lists)
  (if (null lists)
      '(())
      (mappend (lambda (x)
                 (mapcar (lambda (lst) (cons x lst))
                         (apply #'cartesian-product (cdr lists))))
               (car lists))))

;; vim: ft=lisp