結果

問題 No.391 CODING WAR
ユーザー sansaquasansaqua
提出日時 2019-10-08 22:49:20
言語 Common Lisp
(sbcl 2.3.8)
結果
AC  
実行時間 53 ms / 2,000 ms
コード長 7,513 bytes
コンパイル時間 380 ms
コンパイル使用メモリ 42,368 KB
実行使用メモリ 27,136 KB
最終ジャッジ日時 2024-11-07 19:55:50
合計ジャッジ時間 1,443 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 14 ms
23,808 KB
testcase_01 AC 15 ms
23,936 KB
testcase_02 AC 15 ms
23,936 KB
testcase_03 AC 15 ms
23,936 KB
testcase_04 AC 15 ms
23,936 KB
testcase_05 AC 14 ms
23,936 KB
testcase_06 AC 14 ms
23,808 KB
testcase_07 AC 14 ms
23,936 KB
testcase_08 AC 14 ms
23,936 KB
testcase_09 AC 53 ms
27,008 KB
testcase_10 AC 46 ms
27,008 KB
testcase_11 AC 39 ms
27,136 KB
testcase_12 AC 14 ms
23,936 KB
testcase_13 AC 49 ms
27,008 KB
testcase_14 AC 45 ms
26,240 KB
testcase_15 AC 49 ms
26,624 KB
testcase_16 AC 35 ms
25,344 KB
testcase_17 AC 38 ms
25,728 KB
testcase_18 AC 31 ms
25,088 KB
testcase_19 AC 31 ms
25,088 KB
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コンパイルメッセージ
; compiling file "/home/judge/data/code/Main.lisp" (written 07 NOV 2024 07:55:48 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
;                        (OR (INTEGER 1000000007 18446744064127207545)
;                            (INTEGER 0 0))
;                        &OPTIONAL), not a (VALUES FIXNUM &OPTIONAL).

; in: DEFUN MAIN
;     (INCFMOD RES
;              (IF (EVENP I)
;                  DELTA
;                  (- +MOD+ DELTA)))
; --> SETQ THE (LAMBDA (X Y) (MOD (+ X Y) +MOD+)) SB-C::%FUNCALL MOD 
; ==>
;   1
; 
; note: unable to
;   optimize
; due to type uncertainty:
;   The first argument is a REAL, not a SINGLE-FLOAT.
; 
; note: unable to
;   optimize
; due to type uncertainty:
;   The first argument is a REAL, not a DOUBLE-FLOAT.
; 
; note: unable to
;   optimize
; due to type uncertainty:
;   The first argument is a REAL, not a INTEGER.
; 
; note: unable to
;   convert division by 2^k to shift
; due to type uncertainty:
;   The first argument is a REAL, not a INTEGER.

;     (BINOM M I)
; --> BLOCK IF MOD 
; ==>
;   1
; 
; 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).

;     (- +MOD+ DELTA)
; 
; note: forced to do GENERIC-- (cost 10)
;       unable to do inline fixnum arithmetic (cost 2) because:
;       The second argument is a NUMBER, not a FIXNUM.
;       The result is a (VALUES NUMBER &OPTIONAL), not a (VALUES FIXNUM &OPTIONAL).
;       unable to do inline (unsigned-byte 64) arithmetic (cost 4) b

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
;;;
;;; Binomial coefficient with mod
;;; build: O(n)
;;; query: O(1)
;;;

;; TODO: non-global handling

(defconstant +binom-size+ 110000)
(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+)))

;;;
;;; Arithmetic operations with static modulus
;;;

(defmacro define-mod-operations (divisor)
  `(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)))))

(declaim (inline power-mod))
(defun power-mod (base power modulus)
  "BASE := integer
POWER, MODULUS := non-negative fixnum"
  (declare ((integer 0 #.most-positive-fixnum) modulus power)
           (integer base))
  (labels ((recur (x p)
             (declare ((unsigned-byte 31) x)
                      ((integer 0 #.most-positive-fixnum) p)
                      (values (unsigned-byte 31)))
             (cond ((zerop p) 1)
                   ((evenp p) (recur (mod (* x x) modulus) (ash p -1)))
                   (t (mod (* x (recur x (- p 1))) modulus)))))
    (recur (mod base modulus) power)))

(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 ()
  (declare #.OPT)
  (let* ((n (read))
         (m (read))
         (res 0))
    (declare (uint31 res m)
             (uint62 n))
    (dotimes (i (+ m 1))
      (let ((delta (mod* (binom m i)
                         (power-mod (- m i) n +mod+))))
        (incfmod res
                 (if (evenp i)
                     delta
                     (- +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)))
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