;; -*- coding: utf-8 -*- (eval-when (:compile-toplevel :load-toplevel :execute) (sb-int:defconstant-eqx OPT #+swank '(optimize (speed 3) (safety 2)) #-swank '(optimize (speed 3) (safety 0) (debug 0)) #'equal) #+swank (ql:quickload '(:cl-debug-print :fiveam) :silent t) #-swank (set-dispatch-macro-character #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil nil t)))) #+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax) #-swank (disable-debugger) ; for CS Academy ;; BEGIN_INSERTED_CONTENTS (declaim (ftype (function * (values simple-bit-vector &optional)) make-prime-table)) (defun make-prime-table (sup) "Returns a simple-bit-vector of length SUP, whose (0-based) i-th bit is 1 if i is prime and 0 otherwise. Example: (make-prime-table 10) => #*0011010100" (declare (optimize (speed 3) (safety 0))) (check-type sup (integer 2 (#.array-total-size-limit))) (let ((table (make-array sup :element-type 'bit :initial-element 0)) (sup/64 (ceiling sup 64))) ;; special treatment for p = 2 (dotimes (i sup/64) (setf (sb-kernel:%vector-raw-bits table i) #xAAAAAAAAAAAAAAAA)) (setf (sbit table 1) 0 (sbit table 2) 1) ;; p >= 3 (loop for p from 3 to (+ 1 (isqrt (- sup 1))) by 2 when (= 1 (sbit table p)) do (loop for composite from (* p p) below sup by p do (setf (sbit table composite) 0))) table)) ;; FIXME: Currently the element type of the resultant vector is (UNSIGNED-BYTE 62). (defun make-prime-sequence (sup) "Returns the ascending sequence of primes smaller than SUP." (declare (optimize (speed 3) (safety 0))) (check-type sup (integer 2 (#.array-total-size-limit))) (let ((table (make-prime-table sup))) (let* ((length (count 1 table)) (result (make-array length :element-type '(integer 0 #.most-positive-fixnum))) (index 0)) (declare ((integer 0 #.most-positive-fixnum) length)) (loop for x below sup when (= 1 (sbit table x)) do (setf (aref result index) x) (incf index)) (values result table)))) (defstruct (prime-data (:constructor %make-prime-data (seq table))) (seq nil :type (simple-array (integer 0 #.most-positive-fixnum) (*))) (table nil :type simple-bit-vector)) (defun make-prime-data (sup) (multiple-value-call #'%make-prime-data (make-prime-sequence sup))) (declaim (inline factorize) (ftype (function * (values list &optional)) factorize)) (defun factorize (x prime-data) "Returns the associative list of prime factors of X, which is composed of ( . ). E.g. (factorize 100 ) => '((2 . 2) (5 . 5)). - Any numbers beyond the range of PRIME-DATA are regarded as prime. - The returned list is in descending order w.r.t. prime factors." (declare (integer x)) (setq x (abs x)) (when (<= x 1) (return-from factorize nil)) (let ((prime-seq (prime-data-seq prime-data)) result) (loop for prime of-type unsigned-byte across prime-seq do (when (= x 1) (return-from factorize result)) (loop for exponent of-type (integer 0 #.most-positive-fixnum) from 0 do (multiple-value-bind (quot rem) (floor x prime) (if (zerop rem) (setf x quot) (progn (when (> exponent 0) (push (cons prime exponent) result)) (loop-finish)))))) (if (= x 1) result (cons (cons x 1) result)))) (defun make-omega-table (sup prime-data) "Returns the table of prime omega function on {0, 1, ..., SUP-1}." (declare ((integer 0 #.most-positive-fixnum) sup)) ;; (assert (>= (expt (aref prime-seq (- (length prime-seq) 1)) 2) (- sup 1))) (let ((prime-seq (prime-data-seq prime-data)) (table (make-array sup :element-type '(unsigned-byte 32))) (res (make-array sup :element-type '(unsigned-byte 8)))) (dotimes (i (length table)) (setf (aref table i) i)) (loop for p of-type (integer 0 #.most-positive-fixnum) across prime-seq do (loop for i from p below sup by p do (loop (multiple-value-bind (quot rem) (floor (aref table i) p) (if (zerop rem) (progn (incf (aref res i)) (setf (aref table i) quot)) (return)))))) (loop for i below sup unless (= 1 (aref table i)) do (incf (aref res i))) res)) (defmacro dbg (&rest forms) #+swank (if (= (length forms) 1) `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms)) `(format *error-output* "~A => ~A~%" ',forms `(,,@forms))) #-swank (declare (ignore forms))) (defmacro define-int-types (&rest bits) `(progn ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits) ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits))) (define-int-types 2 4 7 8 15 16 31 32 62 63 64) (declaim (inline println)) (defun println (obj &optional (stream *standard-output*)) (let ((*read-default-float-format* 'double-float)) (prog1 (princ obj stream) (terpri stream)))) (defconstant +mod+ 1000000007) ;;; ;;; Body ;;; (defun main () (let* ((pdata (make-prime-data 10001)) (n (read)) (as (make-array n :element-type 'uint31)) (pfactor-table (make-hash-table))) (dotimes (i n) (let ((a (read))) (setf (aref as i) a) (dolist (node (factorize a pdata)) (setf (gethash (car node) pfactor-table) t)))) (let* ((count (hash-table-count pfactor-table)) (ps (make-array count :element-type 'uint31)) (pos 0) (res 0)) (sb-int:dohash ((p _) pfactor-table) (setf (aref ps pos) p) (incf pos)) (labels ((recur (pos parity divisor) (declare (uint31 pos parity) (uint62 divisor)) (cond ((= pos count) (let* ((num (loop for a across as count (zerop (mod a divisor)) of-type uint31)) (value (- (expt 2 num) 1))) (declare ((integer 0 50) num)) (if (oddp parity) (decf res value) (incf res value)))) ((<= (* divisor (aref ps pos)) 100000000) (recur (+ pos 1) (+ parity 1) (* divisor (aref ps pos))) (recur (+ pos 1) parity divisor)) (t (recur (+ pos 1) parity divisor))))) (println (recur 0 0 1)) pfactor-table)))) #-swank (main) ;;; ;;; Test and benchmark ;;; #+swank (defun io-equal (in-string out-string &key (function #'main) (test #'equal)) "Passes IN-STRING to *STANDARD-INPUT*, executes FUNCTION, and returns true if the string output to *STANDARD-OUTPUT* is equal to OUT-STRING." (labels ((ensure-last-lf (s) (if (eql (uiop:last-char s) #\Linefeed) s (uiop:strcat s uiop:+lf+)))) (funcall test (ensure-last-lf out-string) (with-output-to-string (out) (let ((*standard-output* out)) (with-input-from-string (*standard-input* (ensure-last-lf in-string)) (funcall function))))))) #+swank (defun get-clipbrd () (with-output-to-string (out) (run-program "C:/msys64/usr/bin/cat.exe" '("/dev/clipboard") :output out))) #+swank (defparameter *this-pathname* (uiop:current-lisp-file-pathname)) #+swank (defparameter *dat-pathname* (uiop:merge-pathnames* "test.dat" *this-pathname*)) #+swank (defun run (&optional thing (out *standard-output*)) "THING := null | string | symbol | pathname null: run #'MAIN using the text on clipboard as input. string: run #'MAIN using the string as input. symbol: alias of FIVEAM:RUN!. pathname: run #'MAIN using the text file as input." (let ((*standard-output* out)) (etypecase thing (null (with-input-from-string (*standard-input* (delete #\Return (get-clipbrd))) (main))) (string (with-input-from-string (*standard-input* (delete #\Return thing)) (main))) (symbol (5am:run! thing)) (pathname (with-open-file (*standard-input* thing) (main)))))) #+swank (defun gen-dat () (uiop:with-output-file (out *dat-pathname* :if-exists :supersede) (format out ""))) #+swank (defun bench (&optional (out (make-broadcast-stream))) (time (run *dat-pathname* out))) #+swank (5am:test :sample (5am:is (io-equal "3 1 2 3 " "5 ")) (5am:is (io-equal "4 1 1 1 1 " "15 ")) (5am:is (io-equal "4 2 4 8 16 " "0 ")) (5am:is (io-equal "10 801754 703742 332182 68016 914814 8470 937255 293192 313080 501971 " "763 ")))