結果
| 問題 | No.1068 #いろいろな色 / Red and Blue and more various colors (Hard) |
| ユーザー |
 sansaqua
|
| 提出日時 | 2020-07-15 00:06:54 |
| 言語 | Common Lisp (sbcl 2.3.8) |
| 結果 |
AC
|
| 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 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 9 ms
22,656 KB |
| testcase_01 | AC | 9 ms
22,656 KB |
| testcase_02 | AC | 9 ms
22,656 KB |
| testcase_03 | AC | 50 ms
24,960 KB |
| testcase_04 | AC | 32 ms
23,808 KB |
| testcase_05 | AC | 34 ms
24,064 KB |
| testcase_06 | AC | 31 ms
23,808 KB |
| testcase_07 | AC | 30 ms
23,808 KB |
| testcase_08 | AC | 34 ms
24,064 KB |
| testcase_09 | AC | 35 ms
23,808 KB |
| testcase_10 | AC | 20 ms
23,296 KB |
| testcase_11 | AC | 30 ms
23,808 KB |
| testcase_12 | AC | 19 ms
23,168 KB |
| testcase_13 | AC | 2,268 ms
96,512 KB |
| testcase_14 | AC | 2,202 ms
96,512 KB |
| testcase_15 | AC | 2,236 ms
96,640 KB |
| testcase_16 | AC | 2,235 ms
96,640 KB |
| testcase_17 | AC | 2,237 ms
96,644 KB |
| testcase_18 | AC | 2,252 ms
96,640 KB |
| testcase_19 | AC | 2,225 ms
96,512 KB |
| testcase_20 | AC | 2,234 ms
96,640 KB |
| testcase_21 | AC | 2,402 ms
96,640 KB |
| testcase_22 | AC | 2,263 ms
96,512 KB |
| testcase_23 | AC | 2,235 ms
96,640 KB |
| testcase_24 | AC | 2,236 ms
96,512 KB |
| testcase_25 | AC | 2,238 ms
96,640 KB |
| testcase_26 | AC | 2,251 ms
96,512 KB |
| testcase_27 | AC | 2,249 ms
96,512 KB |
| testcase_28 | AC | 1,984 ms
96,640 KB |
| testcase_29 | AC | 1,947 ms
96,512 KB |
| testcase_30 | AC | 1,964 ms
96,384 KB |
| testcase_31 | AC | 12 ms
26,796 KB |
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 = 1
for k of-type ntt-int = 0
do (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 = 1
for k of-type ntt-int = 0
do (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 fixed
len1
(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 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 "3 4
3 4 5
0 1 2 3
"
"24
26
9
1
"))
(it.bese.fiveam:is
(common-lisp-user::io-equal "4 3
1 3 3 3
3 1 4
"
"6
8
1
"))
(it.bese.fiveam:is
(common-lisp-user::io-equal "3 2
5 7 5
1 3
"
"64
1
")))