結果

問題 No.890 移調の限られた旋法
ユーザー sansaquasansaqua
提出日時 2019-09-21 18:28:27
言語 Common Lisp
(sbcl 2.3.8)
結果
AC  
実行時間 78 ms / 2,000 ms
コード長 11,447 bytes
コンパイル時間 1,091 ms
コンパイル使用メモリ 58,516 KB
実行使用メモリ 43,892 KB
最終ジャッジ日時 2023-10-19 06:42:06
合計ジャッジ時間 5,391 ms
ジャッジサーバーID
(参考情報)
judge13 / judge15
このコードへのチャレンジ(β)

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 69 ms
43,892 KB
testcase_01 AC 70 ms
43,892 KB
testcase_02 AC 70 ms
43,892 KB
testcase_03 AC 68 ms
43,892 KB
testcase_04 AC 67 ms
43,892 KB
testcase_05 AC 69 ms
43,892 KB
testcase_06 AC 70 ms
43,892 KB
testcase_07 AC 67 ms
43,892 KB
testcase_08 AC 69 ms
43,892 KB
testcase_09 AC 66 ms
43,892 KB
testcase_10 AC 68 ms
43,892 KB
testcase_11 AC 66 ms
43,892 KB
testcase_12 AC 65 ms
43,892 KB
testcase_13 AC 69 ms
43,892 KB
testcase_14 AC 67 ms
43,892 KB
testcase_15 AC 69 ms
43,892 KB
testcase_16 AC 68 ms
43,892 KB
testcase_17 AC 75 ms
43,892 KB
testcase_18 AC 76 ms
43,892 KB
testcase_19 AC 70 ms
43,892 KB
testcase_20 AC 71 ms
43,892 KB
testcase_21 AC 73 ms
43,892 KB
testcase_22 AC 74 ms
43,892 KB
testcase_23 AC 70 ms
43,892 KB
testcase_24 AC 71 ms
43,892 KB
testcase_25 AC 67 ms
43,892 KB
testcase_26 AC 67 ms
43,892 KB
testcase_27 AC 72 ms
43,892 KB
testcase_28 AC 74 ms
43,892 KB
testcase_29 AC 70 ms
43,892 KB
testcase_30 AC 70 ms
43,892 KB
testcase_31 AC 72 ms
43,892 KB
testcase_32 AC 78 ms
43,892 KB
testcase_33 AC 73 ms
43,892 KB
testcase_34 AC 76 ms
43,892 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
; compiling file "/home/judge/data/code/Main.lisp" (written 18 OCT 2023 09:42:00 PM):

; 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 (MOD 18446744064127207546) &OPTIONAL), not a (VALUES
;                                                                             FIXNUM
;                                                                             &OPTIONAL).
; 
; compilation unit finished
;   printed 1 note


; wrote /home/judge/data/code/Main.fasl
; compilation finished in 0:00:00.122

ソースコード

diff #

;; -*- 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 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 10000))
         (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)
                (decfmod res 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)))
0