(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)) `(values ,(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 (inline println-sequence)) (defun println-sequence (sequence &key (out *standard-output*) (key #'identity)) (let ((init t)) (sequence:dosequence (x sequence) (if init (setq init nil) (write-char #\ out)) (princ (funcall key x) out)) (terpri out))) ;; ;; Matrix multiplication over semiring ;; ;; NOTE: These funcions are slow on SBCL version earlier than 1.5.6 as the type ;; propagation of MAKE-ARRAY doesn't work. The following files are required to ;; enable the optimization. ;; version < 1.5.0: array-element-type.lisp, make-array-header.lisp ;; version < 1.5.6: make-array-header.lisp (defun gemm! (a b c &key (op+ #'+) (op* #'*) (identity+ 0)) "Calculates C := A*B. This function destructively modifies C. (OP+, OP*) must comprise a semiring. IDENTITY+ is the identity element w.r.t. OP+." (declare ((simple-array * (* *)) a b c)) (dotimes (row (array-dimension a 0)) (dotimes (col (array-dimension b 1)) (let ((res identity+)) (dotimes (k (array-dimension a 1)) (setf res (funcall op+ (funcall op* (aref a row k) (aref b k col))))) (setf (aref c row col) res)))) c) (declaim (inline gemm)) (defun gemm (a b &key (op+ #'+) (op* #'*) (identity+ 0)) "Calculates A*B. (OP+, OP*) must comprise a semiring. IDENTITY+ is the identity element w.r.t. OP+." (declare ((simple-array * (* *)) a b) (function op+ op*)) (let ((c (make-array (list (array-dimension a 0) (array-dimension b 1)) :element-type (array-element-type a)))) (dotimes (row (array-dimension a 0)) (dotimes (col (array-dimension b 1)) (let ((res identity+)) (dotimes (k (array-dimension a 1)) (setf res (funcall op+ res (funcall op* (aref a row k) (aref b k col))))) (setf (aref c row col) res)))) c)) (declaim (inline matrix-power)) (defun matrix-power (base power &key (op+ #'+) (op* #'*) (identity+ 0) (identity* 1)) (declare ((simple-array * (* *)) base) (function op+ op*) ((integer 0 #.most-positive-fixnum) power)) (let ((size (array-dimension base 0))) (assert (= size (array-dimension base 1))) (let ((iden (make-array (array-dimensions base) :element-type (array-element-type base) :initial-element identity+))) (dotimes (i size) (setf (aref iden i i) identity*)) (labels ((recur (p) (declare ((integer 0 #.most-positive-fixnum) p)) (cond ((zerop p) iden) ((evenp p) (let ((res (recur (ash p -1)))) (gemm res res :op+ op+ :op* op* :identity+ identity+))) (t (gemm base (recur (- p 1)) :op+ op+ :op* op* :identity+ identity+))))) (recur power))))) (declaim (inline gemv)) (defun gemv (a x &key (op+ #'+) (op* #'*) (identity+ 0)) "Calculates A*x for a matrix A and a vector x. (OP+, OP*) must form a semiring. IDENTITY+ is the identity element w.r.t. OP+." (declare ((simple-array * (* *)) a) ((simple-array * (*)) x) (function op+ op*)) (let ((y (make-array (array-dimension a 0) :element-type (array-element-type x)))) (dotimes (i (length y)) (let ((res identity+)) (dotimes (j (length x)) (setf res (funcall op+ res (funcall op* (aref a i j) (aref x j))))) (setf (aref y i) res))) y)) ;;; ;;; Arithmetic operations with static modulus ;;; ;; FIXME: Currently MOD* and MOD+ doesn't apply MOD when the number of ;; parameters is one. (defmacro define-mod-operations (divisor) `(progn (defun mod* (&rest args) (reduce (lambda (x y) (mod (* x y) ,divisor)) args)) (defun mod+ (&rest args) (reduce (lambda (x y) (mod (+ x y) ,divisor)) args)) #+sbcl (eval-when (:compile-toplevel :load-toplevel :execute) (locally (declare (muffle-conditions warning)) (sb-c:define-source-transform mod* (&rest args) (if (null args) 1 (reduce (lambda (x y) `(mod (* ,x ,y) ,',divisor)) args))) (sb-c:define-source-transform mod+ (&rest args) (if (null args) 0 (reduce (lambda (x y) `(mod (+ ,x ,y) ,',divisor)) args))))) (define-modify-macro incfmod (delta) (lambda (x y) (mod (+ x y) ,divisor))) (define-modify-macro decfmod (delta) (lambda (x y) (mod (- x y) ,divisor))) (define-modify-macro mulfmod (multiplier) (lambda (x y) (mod (* x y) ,divisor))))) (in-package :cl-user) (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* ((n (read)) (a1 (read)) (b1 (read)) (c1 (read)) (mat (make-array '(3 3) :element-type 'uint31 :initial-element 0)) (vec (make-array 3 :element-type 'uint31 :initial-contents (list a1 b1 c1)))) (setf (aref mat 0 0) 1 (aref mat 0 1) (- +mod+ 1) (aref mat 1 1) 1 (aref mat 1 2) (- +mod+ 1) (aref mat 2 0) (- +mod+ 1) (aref mat 2 2) 1) (let ((res (gemv (matrix-power mat (- n 1) :op+ #'mod+ :op* #'mod*) vec :op+ #'mod+ :op* #'mod*))) (println-sequence res)))) #-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 "powershell.exe" '("-Command" "Get-Clipboard") :output out :search t))) #+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))) ;; To run: (5am:run! :sample) #+swank (it.bese.fiveam:test :sample (it.bese.fiveam:is (common-lisp-user::io-equal "2 1 2 3 " "1000000006 1000000006 2 ")) (it.bese.fiveam:is (common-lisp-user::io-equal "3 0 0 0 " "0 0 0 ")) (it.bese.fiveam:is (common-lisp-user::io-equal "10 1000000000 998244353 924844033 " "945425885 912366722 142207407 ")))