結果
問題 | No.890 移調の限られた旋法 |
ユーザー | sansaqua |
提出日時 | 2019-09-21 18:31:24 |
言語 | Common Lisp (sbcl 2.5.0) |
結果 |
AC
|
実行時間 | 65 ms / 2,000 ms |
コード長 | 11,456 bytes |
コンパイル時間 | 1,317 ms |
コンパイル使用メモリ | 62,464 KB |
実行使用メモリ | 36,096 KB |
最終ジャッジ日時 | 2024-09-19 03:03:05 |
合計ジャッジ時間 | 4,546 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
(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 | 56 ms
35,840 KB |
testcase_01 | AC | 57 ms
36,096 KB |
testcase_02 | AC | 58 ms
35,840 KB |
testcase_03 | AC | 57 ms
35,968 KB |
testcase_04 | AC | 60 ms
35,968 KB |
testcase_05 | AC | 59 ms
35,968 KB |
testcase_06 | AC | 60 ms
35,968 KB |
testcase_07 | AC | 65 ms
35,968 KB |
testcase_08 | AC | 65 ms
35,968 KB |
testcase_09 | AC | 63 ms
35,968 KB |
testcase_10 | AC | 60 ms
35,840 KB |
testcase_11 | AC | 56 ms
35,840 KB |
testcase_12 | AC | 56 ms
35,840 KB |
testcase_13 | AC | 56 ms
35,840 KB |
testcase_14 | AC | 57 ms
35,968 KB |
testcase_15 | AC | 57 ms
35,968 KB |
testcase_16 | AC | 57 ms
35,968 KB |
testcase_17 | AC | 57 ms
35,968 KB |
testcase_18 | AC | 56 ms
35,968 KB |
testcase_19 | AC | 60 ms
36,096 KB |
testcase_20 | AC | 63 ms
35,968 KB |
testcase_21 | AC | 61 ms
35,968 KB |
testcase_22 | AC | 62 ms
35,840 KB |
testcase_23 | AC | 61 ms
35,840 KB |
testcase_24 | AC | 58 ms
35,840 KB |
testcase_25 | AC | 60 ms
35,840 KB |
testcase_26 | AC | 62 ms
35,840 KB |
testcase_27 | AC | 63 ms
35,968 KB |
testcase_28 | AC | 62 ms
35,840 KB |
testcase_29 | AC | 62 ms
35,968 KB |
testcase_30 | AC | 60 ms
35,968 KB |
testcase_31 | AC | 58 ms
35,968 KB |
testcase_32 | AC | 60 ms
35,840 KB |
testcase_33 | AC | 59 ms
35,840 KB |
testcase_34 | AC | 60 ms
35,968 KB |
コンパイルメッセージ
; compiling file "/home/judge/data/code/Main.lisp" (written 19 SEP 2024 03:02:59 AM): ; file: /home/judge/data/code/Main.lisp ; in: DEFUN INITIALIZE-BINOM ; (MOD (* (AREF *INV* I) (AREF *FACT-INV* (- I 1))) +BINOM-MOD+) ; ; note: forced to do inline (unsigned-byte 64) arithmetic (cost 6) ; unable to do inline fixnum arithmetic (cost 1) because: ; The result is a (VALUES ; (OR (INTEGER 1000000007 18446744064127207545) ; (INTEGER 0 0)) ; &OPTIONAL), not a (VALUES FIXNUM &OPTIONAL). ; ; compilation unit finished ; printed 1 note ; wrote /home/judge/data/code/Main.fasl ; compilation finished in 0:00:00.179
ソースコード
;; -*- 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;;;;;; Arithmetic operations with static modulus;;;(defmacro define-mod-operations (&optional (divisor 1000000007))`(progn(defun mod* (&rest args)(reduce (lambda (x y) (mod (* x y) ,divisor)) args))(sb-c:define-source-transform mod* (&rest args)(if (null args)1(reduce (lambda (x y) `(mod (* ,x ,y) ,',divisor)) args)))(defun mod+ (&rest args)(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)))));;;;;; Binomial coefficient with mod;;; build: O(n);;; query: O(1);;;;; TODO: non-global handling(defconstant +binom-size+ 1100000)(defconstant +binom-mod+ #.(+ (expt 10 9) 7))(declaim ((simple-array (unsigned-byte 32) (*)) *fact* *fact-inv* *inv*))(defparameter *fact* (make-array +binom-size+ :element-type '(unsigned-byte 32))"table of factorials")(defparameter *fact-inv* (make-array +binom-size+ :element-type '(unsigned-byte 32))"table of inverses of factorials")(defparameter *inv* (make-array +binom-size+ :element-type '(unsigned-byte 32))"table of inverses of non-negative integers")(defun initialize-binom ()(declare (optimize (speed 3) (safety 0)))(setf (aref *fact* 0) 1(aref *fact* 1) 1(aref *fact-inv* 0) 1(aref *fact-inv* 1) 1(aref *inv* 1) 1)(loop for i from 2 below +binom-size+do (setf (aref *fact* i) (mod (* i (aref *fact* (- i 1))) +binom-mod+)(aref *inv* i) (- +binom-mod+(mod (* (aref *inv* (rem +binom-mod+ i))(floor +binom-mod+ i))+binom-mod+))(aref *fact-inv* i) (mod (* (aref *inv* i)(aref *fact-inv* (- i 1)))+binom-mod+))))(initialize-binom)(declaim (inline binom))(defun binom (n k)"Returns nCk."(if (or (< n k) (< n 0) (< k 0))0(mod (* (aref *fact* n)(mod (* (aref *fact-inv* k) (aref *fact-inv* (- n k))) +binom-mod+))+binom-mod+)))(declaim (inline perm))(defun perm (n k)"Returns nPk."(if (or (< n k) (< n 0) (< k 0))0(mod (* (aref *fact* n) (aref *fact-inv* (- n k))) +binom-mod+)));; TODO: compiler macro or source-transform(declaim (inline multinomial))(defun multinomial (&rest ks)"Returns the multinomial coefficient K!/k_1!k_2!...k_n! for K = k_1 + k_2 +... + k_n. K must be equal to or smaller thanMOST-POSITIVE-FIXNUM. (multinomial) returns 1."(let ((sum 0)(result 1))(declare ((integer 0 #.most-positive-fixnum) result sum))(dolist (k ks)(incf sum k)(setq result(mod (* result (aref *fact-inv* k)) +binom-mod+)))(mod (* result (aref *fact* sum)) +binom-mod+)))(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 iis 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 2when (= 1 (sbit table p))do (loop for composite from (* p p) below sup by pdo (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 supwhen (= 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 composedof (<prime> . <exponent>). E.g. (factorize 100 <prime-table>) => '((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-seqdo (when (= x 1)(return-from factorize result))(loop for exponent of-type (integer 0 #.most-positive-fixnum) from 0do (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-seqdo (loop for i from p below sup by pdo (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 supunless (= 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;;;(define-mod-operations +mod+)(defun main ()(let* ((pdata (make-prime-data 1000))(n (read))(k (read))(pfactors (factorize n pdata))(ps (map '(simple-array uint32 (*)) #'car pfactors))(size (length pfactors))(res 0))(declare (uint31 n k res)((integer 0 10) size))(dotimes (bits (expt 2 size))(let ((freq 1))(declare (uint31 freq))(dotimes (pos size)(when (logbitp pos bits)(setq freq (* freq (aref ps pos)))))(when (and (/= freq 1)(zerop (mod k freq)))(let ((delta (binom (floor n freq) (floor k freq))))(if (oddp (logcount bits))(incfmod res delta)(incfmod res (- +mod+ delta)))))))(println 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 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 "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 | 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)))