結果
問題 | No.1068 #いろいろな色 / Red and Blue and more various colors (Hard) |
ユーザー |
|
提出日時 | 2020-07-15 00:06:54 |
言語 | Common Lisp (sbcl 2.5.0) |
結果 |
AC
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実行時間 | 2,402 ms / 3,500 ms |
コード長 | 13,796 bytes |
コンパイル時間 | 1,478 ms |
コンパイル使用メモリ | 52,352 KB |
実行使用メモリ | 96,644 KB |
最終ジャッジ日時 | 2024-11-19 06:31:38 |
合計ジャッジ時間 | 44,636 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 29 |
コンパイルメッセージ
; compiling file "/home/judge/data/code/Main.lisp" (written 19 NOV 2024 06:30:52 AM): ; file: /home/judge/data/code/Main.lisp ; in: DEFUN NTT! ; (COERCE VECTOR 'NTT-VECTOR) ; ; note: unable to ; optimize ; due to type uncertainty: ; The second argument is a (AND VECTOR ; (NOT ; (SIMPLE-ARRAY (UNSIGNED-BYTE 31) ; (*)))), not a (SIMPLE-ARRAY * (*)). ; in: DEFUN INVERSE-NTT! ; (COERCE VECTOR 'NTT-VECTOR) ; ; note: unable to ; optimize ; due to type uncertainty: ; The second argument is a (AND VECTOR ; (NOT ; (SIMPLE-ARRAY (UNSIGNED-BYTE 31) ; (*)))), not a (SIMPLE-ARRAY * (*)). ; in: DEFUN MAIN ; (MAKE-ARRAY N2 :ELEMENT-TYPE '(SIMPLE-ARRAY UINT31 (*))) ; ; caught STYLE-WARNING: ; The default initial element 0 is not a (SIMPLE-ARRAY UINT31 (*)). ; See also: ; The ANSI Standard, Function MAKE-ARRAY ; The ANSI Standard, Function UPGRADED-ARRAY-ELEMENT-TYPE ; file: /home/judge/data/code/Main.lisp ; in: DEFUN NTT! ; (BASE *NTT-BASE*) ; ; caught WARNING: ; undefined variable: COMMON-LISP-USER::*NTT-BASE* ; in: DEFUN INVERSE-NTT! ; (BASE *NTT-INV-BASE*) ; ; caught WARNING: ; undefined variable: COMMON-LISP-USER::*NTT-INV-BASE* ; ; compilation unit finished ; Undefined variables: ; *NTT-BASE* *NTT-INV-BASE* ; caught 2 WARNING conditions ; caught 1 STYLE-WARNING condition ; printed 2 notes ; wrote /home/judge/data/code/Main.fasl ; compilation finished in 0:00:00.130
ソースコード
(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;;;;;; Fast Number Theoretic Transform;;; Reference: https://github.com/ei1333/library/blob/master/math/fft/number-theoretic-transform-friendly-mod-int.cpp;;;(defconstant +ntt-mod+ 998244353)(defconstant +ntt-root+ 3)(deftype ntt-int () '(unsigned-byte 31))(deftype ntt-vector () '(simple-array ntt-int (*)))(eval-when (:compile-toplevel :load-toplevel :execute)(assert (typep +ntt-mod+ 'ntt-int)))(declaim (inline %tzcount))(defun %tzcount (x)(- (integer-length (logand x (- x))) 1))(declaim (inline %mod-power))(defun %mod-power (base exp)(declare (ntt-int base)((integer 0 #.most-positive-fixnum) exp))(let ((res 1))(declare (ntt-int res))(loop while (> exp 0)when (oddp exp)do (setq res (mod (* res base) +ntt-mod+))do (setq base (mod (* base base) +ntt-mod+)exp (ash exp -1)))res))(defun check-ntt-vector (vector)(declare (optimize (speed 3))(vector vector))(let ((len (length vector)))(assert (zerop (logand len (- len 1)))) ;; power of two(check-type len ntt-int)))(defun make-ntt-base ()(labels ((mod-inverse (x) (%mod-power x (- +ntt-mod+ 2))))(let* ((base-size (%tzcount (- +ntt-mod+ 1)))(base (make-array base-size :element-type 'ntt-int))(inv-base (make-array base-size :element-type 'ntt-int)))(dotimes (i base-size)(setf (aref base i)(mod (- (%mod-power +ntt-root+ (ash (- +ntt-mod+ 1) (- (+ i 2)))))+ntt-mod+)(aref inv-base i)(mod-inverse (aref base i))))(values base inv-base))))(multiple-value-bind (base inv-base) (make-ntt-base)(defparameter *ntt-base* base)(defparameter *ntt-inv-base* inv-base));; FIXME: Here I resort to SBCL's behaviour. Actually ADJUST-ARRAY isn't;; guaranteed to preserve the given VECTOR.(declaim (ftype (function * (values ntt-vector &optional)) %adjust-array))(defun %adjust-array (vector length)(declare (vector vector))(let ((vector (coerce vector 'ntt-vector)))(if (= (length vector) length)(copy-seq vector)(adjust-array vector length :initial-element 0))))(declaim (ftype (function * (values ntt-vector &optional)) ntt!))(defun ntt! (vector)(declare #.OPT(vector vector))(check-ntt-vector vector)(labels ((mod* (x y) (mod (* x y) +ntt-mod+))(mod+ (x y)(let ((res (+ x y)))(if (>= res +ntt-mod+)(- res +ntt-mod+)res)))(mod- (x y) (mod+ x (- +ntt-mod+ y))))(declare (inline mod* mod+ mod-))(let* ((vector (coerce vector 'ntt-vector))(len (length vector))(base *ntt-base*))(declare ((simple-array ntt-int (*)) vector base)(ntt-int len))(when (<= len 1)(return-from ntt! vector))(loop for m of-type ntt-int = (ash len -1) then (ash m -1)while (> m 0)for w of-type ntt-int = 1for k of-type ntt-int = 0do (loop for s of-type ntt-int from 0 below len by (* 2 m)do (loop for i from s below (+ s m)for j from (+ s m)for x = (aref vector i)for y = (mod* (aref vector j) w)do (setf (aref vector i) (mod+ x y)(aref vector j) (mod- x y)))(incf k)(setq w (mod* w (aref base (%tzcount k))))))vector)))(defun inverse-ntt! (vector &optional inverse)(declare #.OPT(vector vector))(check-ntt-vector vector)(labels ((mod* (x y)(declare (ntt-int x y))(mod (* x y) +ntt-mod+))(mod+ (x y)(declare (ntt-int x y))(let ((res (+ x y)))(if (>= res +ntt-mod+)(- res +ntt-mod+)res)))(mod- (x y)(declare (ntt-int x y))(mod+ x (- +ntt-mod+ y))))(declare (inline mod* mod+ mod-))(let* ((vector (coerce vector 'ntt-vector))(len (length vector))(base *ntt-inv-base*))(declare ((simple-array ntt-int (*)) vector base)(ntt-int len))(when (<= len 1)(return-from inverse-ntt! vector))(loop for m of-type ntt-int = 1 then (ash m 1)while (< m len)for w of-type ntt-int = 1for k of-type ntt-int = 0do (loop for s of-type ntt-int from 0 below len by (* 2 m)do (loop for i from s below (+ s m)for j from (+ s m)for x = (aref vector i)for y = (aref vector j)do (setf (aref vector i) (mod+ x y)(aref vector j) (mod* (mod- x y) w)))(incf k)(setq w (mod* w (aref base (%tzcount k))))))(when inverse(let ((inv-len (%mod-power len (- +ntt-mod+ 2))))(dotimes (i len)(setf (aref vector i) (mod* inv-len (aref vector i))))))vector)))(declaim (ftype (function * (values ntt-vector &optional)) ntt-convolute!))(defun ntt-convolute! (vector1 vector2)(declare (ntt-vector vector1 vector2))(let* ((len1 (length vector1))(len2 (length vector2))(mul-len (- (+ len1 len2) 1))(required-len (sb-int:power-of-two-ceiling mul-len))(vector1 (ntt! (adjust-array vector1 required-len)))(vector2 (ntt! (adjust-array vector2 required-len))))(dotimes (i required-len)(setf (aref vector1 i)(mod (* (aref vector1 i) (aref vector2 i)) +ntt-mod+)))(inverse-ntt! vector1 t)));; NOTE: buggy(declaim (ftype (function * (values ntt-vector &optional)) ntt-convolute))(defun ntt-convolute (vector1 vector2 &optional fixed)(declare (optimize (speed 3))(vector vector1 vector2))(let ((len1 (length vector1))(len2 (length vector1)))(when fixed(assert (= len1 len2)))(let* ((mul-len (max 0 (- (+ len1 len2) 1)));; power of two ceiling(required-len (if fixedlen1(ash 1 (integer-length (max 0 (- mul-len 1))))))(vector1 (ntt! (%adjust-array vector1 required-len)))(vector2 (ntt! (%adjust-array vector2 required-len))))(dotimes (i required-len)(setf (aref vector1 i)(mod (* (aref vector1 i) (aref vector2 i)) +ntt-mod+)))(inverse-ntt! vector1))))(declaim (ftype (function * (values fixnum &optional)) read-fixnum))(defun read-fixnum (&optional (in *standard-input*))"NOTE: cannot read -2^62"(macrolet ((%read-byte ()`(the (unsigned-byte 8)#+swank (char-code (read-char in nil #\Nul))#-swank (sb-impl::ansi-stream-read-byte in nil #.(char-code #\Nul) nil))))(let* ((minus nil)(result (loop (let ((byte (%read-byte)))(cond ((<= 48 byte 57)(return (- byte 48)))((zerop byte) ; #\Nul(error "Read EOF or #\Nul."))((= byte #.(char-code #\-))(setq minus t)))))))(declare ((integer 0 #.most-positive-fixnum) result))(loop(let* ((byte (%read-byte)))(if (<= 48 byte 57)(setq result (+ (- byte 48)(* 10 (the (integer 0 #.(floor most-positive-fixnum 10))result))))(return (if minus (- result) result))))))));;;;;; 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+ 998244353);;;;;; Body;;;(define-mod-operations +mod+)(defun main ()(let* ((n (read))(n2 (sb-int:power-of-two-ceiling n))(q (read))(polys (make-array n2 :element-type '(simple-array uint31 (*)))))(declare (uint31 n q))(dotimes (i n2)(if (< i n)(let ((a (read-fixnum))(poly (make-array 2 :element-type 'uint31)))(setf (aref poly 1) (mod (- a 1) +mod+)(aref poly 0) 1)(setf (aref polys i) poly))(let ((poly (make-array 2 :element-type 'uint31)))(setf (aref poly 1) 0(aref poly 0) 1)(setf (aref polys i) poly))))(loop for width = 1 then (ash width 1)while (< width n2)do (loop for i from 0 below n2 by (* width 2)do (setf (aref polys i)(ntt-convolute!(aref polys i)(aref polys (+ i width))))))(let ((poly (aref polys 0)))(dotimes (i q)(let ((b (read-fixnum)))(println (aref poly (- n b))))))))#-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 ifthe 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 | pathnamenull: 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 "3 43 4 50 1 2 3""242691"))(it.bese.fiveam:is(common-lisp-user::io-equal "4 31 3 3 33 1 4""681"))(it.bese.fiveam:is(common-lisp-user::io-equal "3 25 7 51 3""641")))