結果
| 問題 |
No.391 CODING WAR
|
| コンテスト | |
| ユーザー |
 sansaqua
|
| 提出日時 | 2019-10-08 22:49:20 |
| 言語 | Common Lisp (sbcl 2.5.0) |
| 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 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 16 |
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
;; -*- 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)))