提出 #9890003

---

ソースコード 拡げる

(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
           ;; enclose the form with VALUES to avoid being captured by LOOP macro
           #\# #\> (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
(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (declare #.OPT)
  (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 #\-))
                                  (setf 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))))))))

;;;
;;; Calculate a^n on any monoids in O(log(n)) time
;;;

;; (declaim (inline power))
;; (defun power (base exponent op identity)
;;   "OP := binary operation (comprising a monoid)
;; IDENTITY := identity element w.r.t. OP"
;;   (declare ((integer 0) exponent))
;;   (labels ((recur (x p)
;;              (declare ((integer 0 #.most-positive-fixnum) p))
;;              (cond ((zerop p) identity)
;;                    ((evenp p) (recur (funcall op x x) (ash p -1)))
;;                    (t (nth-value 0 (funcall op x (recur x (- p 1)))))))
;;            (recur-big (x p)
;;              (declare ((integer 0) p))
;;              (cond ((zerop p) identity)
;;                    ((evenp p) (recur-big (funcall op x x) (ash p -1)))
;;                    (t (nth-value 0 (funcall op x (recur-big x (- p 1))))))))
;;     (typecase exponent
;;       (fixnum (recur base exponent))
;;       (otherwise (recur-big base exponent)))))

(declaim (inline decompose-to-cycles))
(defun decompose-to-cycles (permutation)
  "Returns the list of all the cyclic permutations in a given permutation of {0,
1, ..., N-1}"
  (declare (vector permutation))
  (let* ((n (length permutation))
         result
         (visited (make-array n :element-type 'bit :initial-element 0)))
    (dotimes (init n)
      (when (zerop (sbit visited init))
        (push (loop for x = init then (aref permutation x)
                    until (= (sbit visited x) 1)
                    collect x
                    do (setf (sbit visited x) 1))
              result)))
    result))

(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
;;;

;; (defun perm* (perm1 perm2)
;;   (let* ((n (length perm1))
;;          (res (make-array n :element-type 'uint31)))
;;     (dotimes (i n)
;;       (setf (aref res i) (aref perm2 (aref perm1 i))))
;;     res))

;; (defun perm-power (perm exp)
;;   (let ((iden (make-array (length perm) :element-type 'uint31)))
;;     (dotimes (i (length perm))
;;       (setf (aref iden i) i))
;;     (power perm exp #'perm* iden)))

(declaim (inline lastcar))
(defun lastcar (list)
  (car (last list)))

(defun main ()
  (let* ((n (read))
         (k (read))
         (as (make-array n :element-type 'uint31))
         (res (make-array n :element-type 'uint31)))
    (declare (uint16 n k))
    (dotimes (i n)
      (setf (aref as i) (- (read-fixnum) 1)))
    (let ((cycles (decompose-to-cycles as))
          (cycle-table (make-array (+ n 1) :element-type 'list :initial-element nil))
          (num-table (make-array (+ n 1) :element-type 'uint31 :initial-element 0)))
      (dolist (cycle cycles)
        (let ((len (length (the list cycle))))
          (incf (aref num-table len))
          (push cycle (aref cycle-table len))))
      (labels ((no () (println 0) (return-from main))
               (render-cycle (len num)
                 (let* ((total (* len num))
                        (large-perm (make-array total :element-type 'uint31)))
                   (dbg len num total)
                   #>large-perm
                   (let ((index 0))
                     (declare (uint31 index))
                     (dotimes (_ num)
                       (let ((cycle (pop (aref cycle-table len))))
                         #>cycle
                         (dotimes (_ len)
                           (let ((v (pop cycle)))
                             (setf (aref large-perm index) v)
                             (setq index (mod (+ index k) total))))
                         (setq index (mod (+ index 1) total)))))
                   #>large-perm
                   (dotimes (i (- total 1))
                     (setf (aref res (aref large-perm i))
                           (aref large-perm (+ i 1))))
                   (setf (aref res (aref large-perm (- total 1)))
                         (aref large-perm 0))
                   #>res)))
        (loop for l from 1 to n
              for l-num = (aref num-table l)
              for perimtr-set = (make-array 0 :fill-pointer 0 :element-type 'uint31)
              unless (zerop l-num)
              do (loop for length from 1 to (* l l-num)
                       when (= length (* (gcd length k) l))
                       do (vector-push-extend length perimtr-set))
                 ;; perimtr-setの中の周長Lを使うとgcd(L, k)個の巡回置換が消費で
                 ;; きる。重複を許して自由にこれらの長さを使ってl-num個の巡回置
                 ;; 換をちょうど消費したい（重複あり部分和問題）
                 (let* ((set-size (length perimtr-set))
                        (dp (make-array (list (+ 1 set-size) (+ l-num 1))
                                        :element-type 'bit
                                        :initial-element 0)))
                   (setf (aref dp 0 0) 1)
                   (loop for x from 1 to set-size
                         for perimeter = (aref perimtr-set (- x 1))
                         for consum = (gcd perimeter k)
                         do (loop for y from 0 to l-num
                                  do (setf (aref dp x y)
                                           (logior (if (< y consum)
                                                       0
                                                       (aref dp x (- y consum)))
                                                   (aref dp (- x 1) y)))))
                   (when (zerop (aref dp set-size l-num))
                     (no))
                   (sb-int:named-let recur ((x set-size) (y l-num))
                     (declare (uint31 x y))
                     (unless (and (zerop x) (zerop y))
                       (if (and (> x 0)
                                (= 1 (aref dp (- x 1) y)))
                           (recur (- x 1) y)
                           (let* ((perimeter (aref perimtr-set (- x 1)))
                                  (consum (gcd perimeter k)))
                             (declare (uint31 perimeter consum))
                             (assert (= 1 (aref dp x (- y consum))))
                             (render-cycle l consum)
                             (recur x (- y consum))))))))))
    (loop for x across res
          do (println (+ x 1)))))

#-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
  (5am:is (io-equal "3 5
3
1
2
"
                    "2
3
1
"))
  (5am:is (io-eqaul "4 4
2
1
4
3
"
                    "0
")))

提出情報

ジャッジ結果