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 18:32:14 |
| 言語 | Common Lisp (sbcl 2.3.8) |
| 結果 |
AC
|
| 実行時間 | 75 ms / 2,000 ms |
| コード長 | 11,456 bytes |
| コンパイル時間 | 312 ms |
| コンパイル使用メモリ | 62,336 KB |
| 実行使用メモリ | 36,096 KB |
| 最終ジャッジ日時 | 2024-09-19 03:03:16 |
| 合計ジャッジ時間 | 3,780 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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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 | 74 ms
35,840 KB |
| testcase_01 | AC | 72 ms
35,968 KB |
| testcase_02 | AC | 74 ms
35,840 KB |
| testcase_03 | AC | 75 ms
35,840 KB |
| testcase_04 | AC | 58 ms
35,968 KB |
| testcase_05 | AC | 57 ms
35,840 KB |
| testcase_06 | AC | 57 ms
35,968 KB |
| testcase_07 | AC | 60 ms
35,840 KB |
| testcase_08 | AC | 58 ms
35,968 KB |
| testcase_09 | AC | 58 ms
35,968 KB |
| testcase_10 | AC | 57 ms
36,096 KB |
| testcase_11 | AC | 57 ms
35,968 KB |
| testcase_12 | AC | 58 ms
35,840 KB |
| testcase_13 | AC | 57 ms
35,840 KB |
| testcase_14 | AC | 56 ms
35,840 KB |
| testcase_15 | AC | 57 ms
35,968 KB |
| testcase_16 | AC | 56 ms
35,968 KB |
| testcase_17 | AC | 56 ms
35,840 KB |
| testcase_18 | AC | 58 ms
35,840 KB |
| testcase_19 | AC | 60 ms
35,840 KB |
| testcase_20 | AC | 60 ms
35,840 KB |
| testcase_21 | AC | 57 ms
35,968 KB |
| testcase_22 | AC | 57 ms
35,968 KB |
| testcase_23 | AC | 57 ms
35,968 KB |
| testcase_24 | AC | 56 ms
35,840 KB |
| testcase_25 | AC | 56 ms
35,968 KB |
| testcase_26 | AC | 56 ms
35,968 KB |
| testcase_27 | AC | 58 ms
35,968 KB |
| testcase_28 | AC | 58 ms
35,840 KB |
| testcase_29 | AC | 56 ms
35,968 KB |
| testcase_30 | AC | 59 ms
35,968 KB |
| testcase_31 | AC | 63 ms
35,968 KB |
| testcase_32 | AC | 57 ms
35,968 KB |
| testcase_33 | AC | 57 ms
35,840 KB |
| testcase_34 | AC | 57 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 03:03:12 AM): ; wrote /home/judge/data/code/Main.fasl ; compilation finished in 0:00:00.154
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 31) (*)) *fact* *fact-inv* *inv*))
(defparameter *fact* (make-array +binom-size+ :element-type '(unsigned-byte 31))
"table of factorials")
(defparameter *fact-inv* (make-array +binom-size+ :element-type '(unsigned-byte 31))
"table of inverses of factorials")
(defparameter *inv* (make-array +binom-size+ :element-type '(unsigned-byte 31))
"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 than
MOST-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 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 (<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-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
;;;
(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 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)))