#450261 (Common Lisp) No.40 多項式の割り算

提出ソース

結果

問題	No.40 多項式の割り算
ユーザー	sansaqua
提出日時	2020-03-28 06:10:22
言語	Common Lisp (sbcl 2.3.8)
結果	AC
実行時間	15 ms / 5,000 ms
コード長	10,932 bytes
コンパイル時間	416 ms
コンパイル使用メモリ	54,196 KB
実行使用メモリ	27,328 KB
最終ジャッジ日時	2023-08-30 17:20:55
合計ジャッジ時間	2,104 ms
ジャッジサーバーID （参考情報）	judge15 / judge12

このコードへのチャレンジ
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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	9 ms 23,532 KB
testcase_01	AC	8 ms 25,528 KB
testcase_02	AC	8 ms 23,416 KB
testcase_03	AC	8 ms 23,392 KB
testcase_04	AC	13 ms 25,896 KB
testcase_05	AC	14 ms 27,328 KB
testcase_06	AC	15 ms 23,556 KB
testcase_07	AC	15 ms 25,664 KB
testcase_08	AC	8 ms 23,396 KB
testcase_09	AC	13 ms 23,592 KB
testcase_10	AC	15 ms 23,544 KB
testcase_11	AC	12 ms 25,860 KB
testcase_12	AC	10 ms 23,604 KB
testcase_13	AC	15 ms 25,608 KB
testcase_14	AC	12 ms 23,528 KB
testcase_15	AC	12 ms 25,544 KB
testcase_16	AC	15 ms 25,580 KB
testcase_17	AC	9 ms 23,500 KB
testcase_18	AC	13 ms 23,540 KB
testcase_19	AC	14 ms 23,580 KB
testcase_20	AC	11 ms 23,572 KB
testcase_21	AC	9 ms 23,604 KB
testcase_22	AC	10 ms 23,512 KB
testcase_23	AC	11 ms 23,604 KB
testcase_24	AC	14 ms 23,632 KB
testcase_25	AC	9 ms 23,396 KB
testcase_26	AC	8 ms 23,460 KB
testcase_27	AC	10 ms 23,532 KB
testcase_28	AC	8 ms 23,456 KB
testcase_29	AC	7 ms 23,540 KB
testcase_30	AC	7 ms 23,460 KB
testcase_31	AC	8 ms 23,416 KB
testcase_32	AC	9 ms 23,400 KB
testcase_33	AC	9 ms 23,372 KB
testcase_34	AC	7 ms 23,384 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 30 AUG 2023 05:20:52 PM):
; processing (SB-INT:DEFCONSTANT-EQX OPT ...)
; processing (SET-DISPATCH-MACRO-CHARACTER #\# ...)
; processing (DISABLE-DEBUGGER)
; processing (DECLAIM (INLINE PRINTLN-SEQUENCE))
; processing (DEFUN PRINTLN-SEQUENCE ...)
; processing (DECLAIM (INLINE POLY-VALUE))
; processing (DEFUN POLY-VALUE ...)
; processing (DECLAIM (INLINE POLY-MULT))
; processing (DEFUN POLY-MULT ...)
; processing (DECLAIM (FTYPE # ...))
; processing (DEFUN %MOD-INVERSE ...)
; processing (DECLAIM (INLINE POLY-FLOOR!))
; processing (DEFUN POLY-FLOOR! ...)
; processing (DEFUN POLY-MOD! ...)
; processing (DEFUN POLY-POWER ...)
; processing (DEFMACRO DBG ...)
; processing (DEFMACRO DEFINE-INT-TYPES ...)
; processing (DEFINE-INT-TYPES 2 ...)
; processing (DECLAIM (INLINE PRINTLN))
; processing (DEFUN PRINTLN ...)
; processing (DEFCONSTANT +MOD+ ...)
; processing (DEFUN MAIN ...)
; processing (MAIN)

; wrote /home/judge/data/code/Main.fasl
; compilation finished in 0:00:00.077

ソースコード

raw source code

(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 (inline println-sequence))
(defun println-sequence (sequence &key (out *standard-output*) (key #'identity))
  (let ((init t))
    (sequence:dosequence (x sequence)
      (if init
          (setq init nil)
          (write-char #\  out))
      (princ (funcall key x) out))
    (terpri out)))

;; NOTE: These are poor man's utilities for polynomial arithmetic. NOT
;; sufficiently equipped in all senses.

(declaim (inline poly-value))
(defun poly-value (poly x modulus)
  "Returns the value f(x)."
  (declare (vector poly))
  (let ((x^i 1)
        (res 0))
    (declare (fixnum x^i res))
    (dotimes (i (length poly))
      (setq res (mod (+ res (* x^i (aref poly i))) modulus))
      (setq x^i (mod (* x^i x) modulus)))
    res))

;; naive multiplication in O(n^2)
(declaim (inline poly-mult))
(defun poly-mult (u v modulus &optional result-vector)
  "Multiplies u(x) and v(x) over Z/nZ in O(deg(u)deg(v)) time.

The result is stored in RESULT-VECTOR if it is given, otherwise a new vector is
created."
  (declare (vector u v)
           ((or null vector) result-vector)
           ((integer 1 #.most-positive-fixnum) modulus))
  (let* ((deg1 (loop for i from (- (length u) 1) downto 0
                     while (zerop (aref u i))
                     finally (return i)))
         (deg2 (loop for i from (- (length v) 1) downto 0
                     while (zerop (aref v i))
                     finally (return i)))
         (len (max 0 (+ deg1 deg2 1)))
         (res (or result-vector (make-array len :element-type (array-element-type u)))))
    (declare ((integer -1 (#.array-total-size-limit)) deg1 deg2 len))
    (dotimes (d len res)
      ;; 0 <= i <= deg1, 0 <= j <= deg2
      (loop with coef of-type (integer 0 #.most-positive-fixnum) = 0
            for i from (max 0 (- d deg2)) to (min d deg1)
            for j = (- d i)
            do (setq coef (mod (+ coef (* (aref u i) (aref v j)))
                               modulus))
            finally (setf (aref res d) coef)))))

(declaim (ftype (function * (values (mod #.most-positive-fixnum) &optional)) %mod-inverse))
(defun %mod-inverse (a modulus)
  "Solves ax ≡ 1 mod m. A and M must be coprime."
  (declare (optimize (speed 3))
           (integer a)
           ((integer 1 #.most-positive-fixnum) modulus))
  (labels ((%gcd (a b)
             (declare (optimize (safety 0))
                      ((integer 0 #.most-positive-fixnum) a b))
             (if (zerop b)
                 (values 1 0)
                 (multiple-value-bind (p q) (floor a b) ; a = pb + q
                   (multiple-value-bind (v u) (%gcd b q)
                     (declare (fixnum u v))
                     (values u (the fixnum (- v (the fixnum (* p u))))))))))
    (mod (%gcd (mod a modulus) modulus) modulus)))

;; naive division in O(n^2)
;; Reference: http://web.cs.iastate.edu/~cs577/handouts/polydivide.pdf
(declaim (inline poly-floor!))
(defun poly-floor! (u v modulus &optional quotient)
  "Returns the quotient q(x) and the remainder r(x) over Z/nZ: u(x) = q(x)v(x) +
r(x), deg(r) < deg(v). This function destructively modifies U. The time
complexity is O((deg(u)-deg(v))deg(v)).

The quotient is stored in QUOTIENT if it is given, otherwise a new vector is
created.

Note that MODULUS and V[deg(V)] must be coprime."
  (declare (vector u v)
           ((integer 1 #.most-positive-fixnum) modulus))
  ;; m := deg(u), n := deg(v)
  (let* ((m (loop for i from (- (length u) 1) downto 0
                  while (zerop (aref u i))
                  finally (return i)))
         (n (loop for i from (- (length v) 1) downto 0
                  unless (zerop (aref v i))
                  do (return i)
                  finally (error 'division-by-zero
                                 :operation #'poly-floor!
                                 :operands (list u v))))
         (quot (or quotient
                   (make-array (max 0 (+ 1 (- m n)))
                               :element-type (array-element-type u))))
         ;; FIXME: Is it better to signal an error in non-coprime case?
         (inv (%mod-inverse (aref v n) modulus)))
    (declare ((integer -1 (#.array-total-size-limit)) m n))
    (loop for k from (- m n) downto 0
          do (setf (aref quot k)
                   (mod (* (aref u (+ n k)) inv) modulus))
             (loop for j from (+ n k -1) downto k
                   do (setf (aref u j)
                            (mod (- (aref u j)
                                    (* (aref quot k) (aref v (- j k))))
                                 modulus))))
    (loop for i from (- (length u) 1) downto n
          do (setf (aref u i) 0)
          finally (return (values quot u)))))

;; naive division in O(n^2)
(defun poly-mod! (poly divisor modulus)
  "Returns the remainder of POLY divided by DIVISOR over Z/nZ. This function
destructively modifies POLY."
  (declare (vector poly divisor)
           ((integer 1 #.most-positive-fixnum) modulus))
  (let* ((m (loop for i from (- (length poly) 1) downto 0
                  while (zerop (aref poly i))
                  finally (return i)))
         (n (loop for i from (- (length divisor) 1) downto 0
                  unless (zerop (aref divisor i))
                  do (return i)
                  finally (error 'division-by-zero
                                 :operation #'poly-mod!
                                 :operands (list poly divisor))))
         (inv (%mod-inverse (aref divisor n) modulus)))
    (declare ((integer -1 (#.array-total-size-limit)) m n))
    (loop for pivot-deg from m downto n
          for factor of-type (integer 0 #.most-positive-fixnum)
             = (mod (* (aref poly pivot-deg) inv) modulus)
          do (loop for delta from 0 to n
                   do (setf (aref poly (- pivot-deg delta))
                            (mod (- (aref poly (- pivot-deg delta))
                                    (* factor (aref divisor (- n delta))))
                                 modulus))))
    poly))

(defun poly-power (poly exponent divisor modulus)
  "Returns POLY to the power of EXPONENT modulo DIVISOR over Z/nZ."
  (declare (vector poly divisor)
           ((integer 0 #.most-positive-fixnum) exponent)
           ((integer 1 #.most-positive-fixnum) modulus))
  (labels
      ((recur (power)
         (declare ((integer 0 #.most-positive-fixnum) power))
         (cond ((zerop power)
                (make-array 1 :element-type (array-element-type poly) :initial-element 1))
               ((oddp power)
                (poly-mod! (poly-mult poly (recur (- power 1)) modulus)
                           divisor modulus))
               ((let ((res (recur (floor power 2))))
                  (poly-mod! (poly-mult res res modulus)
                             divisor modulus))))))
    (recur exponent)))

(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 main ()
  (let* ((d (read))
         (as (make-array (+ d 1) :element-type 'int32)))
    (dotimes (i (+ d 1))
      (setf (aref as i) (read)))
    (let* ((res (poly-mod! as #(0 -1 0 1) +mod+))
           (max-d (position 0 res :from-end t :test-not #'=)))
      (if max-d
          (progn
            (println max-d)
            (println-sequence (subseq res 0 (+ max-d 1))
                              :key (lambda (x) (if (> x 500000000) (- x +mod+) x))))
          (format t "0~%0~%")))))

#-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 "5
1 1 1 0 0 1
"
    "2
1 2 1
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "8
0 -5 0 4 0 1 -1 0 1
"
    "0
0
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "5
-5 0 -1 1 1 1
"
    "1
-5 2
")))

yukicoder

結果

テストケース

コンパイルメッセージ

ソースコード