結果
| 問題 |
No.1126 SUM
|
| ユーザー |
 sansaqua
|
| 提出日時 | 2020-07-24 22:27:10 |
| 言語 | Common Lisp (sbcl 2.5.0) |
| 結果 |
AC
|
| 実行時間 | 12 ms / 1,000 ms |
| コード長 | 7,229 bytes |
| コンパイル時間 | 1,267 ms |
| コンパイル使用メモリ | 38,272 KB |
| 実行使用メモリ | 22,656 KB |
| 最終ジャッジ日時 | 2024-06-25 21:55:06 |
| 合計ジャッジ時間 | 1,802 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 26 |
コンパイルメッセージ
; compiling file "/home/judge/data/code/Main.lisp" (written 25 JUN 2024 09:55:03 PM): ; file: /home/judge/data/code/Main.lisp ; in: DEFUN MOD-INVERSE ; (+ U MODULUS) ; ; note: deleting unreachable code ; ; compilation unit finished ; printed 1 note ; wrote /home/judge/data/code/Main.fasl ; compilation finished in 0:00:00.092
ソースコード
(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)) `(values ,(read s nil nil t)))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
(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)
;; BEGIN_INSERTED_CONTENTS
;; Blankinship algorithm
;; Reference: https://topcoder-g-hatena-ne-jp.jag-icpc.org/spaghetti_source/20130126/ (Japanese)
(declaim (ftype (function * (values fixnum fixnum &optional)) %ext-gcd))
(defun %ext-gcd (a b)
(declare (optimize (speed 3) (safety 0))
(fixnum a b))
(let ((y 1)
(x 0)
(u 1)
(v 0))
(declare (fixnum y x u v))
(loop (when (zerop a)
(return (values x y)))
(let ((q (floor b a)))
(decf x (the fixnum (* q u)))
(rotatef x u)
(decf y (the fixnum (* q v)))
(rotatef y v)
(decf b (the fixnum (* q a)))
(rotatef b a)))))
;; Simple recursive version. A bit slower but more comprehensible.
;; https://cp-algorithms.com/algebra/extended-euclid-algorithm.html (English)
;; https://drken1215.hatenablog.com/entry/2018/06/08/210000 (Japanese)
;; (defun %ext-gcd (a b)
;; (declare (optimize (speed 3) (safety 0))
;; (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) (%ext-gcd b q)
;; (declare (fixnum u v))
;; (values u (the fixnum (- v (the fixnum (* p u)))))))))
;; TODO: deal with bignums
(declaim (inline ext-gcd))
(defun ext-gcd (a b)
"Returns two integers X and Y which satisfy AX + BY = gcd(A, B)."
(declare ((integer #.(- most-positive-fixnum) #.most-positive-fixnum) a b))
(if (>= a 0)
(if (>= b 0)
(%ext-gcd a b)
(multiple-value-bind (x y) (%ext-gcd a (- b))
(declare (fixnum x y))
(values x (- y))))
(if (>= b 0)
(multiple-value-bind (x y) (%ext-gcd (- a) b)
(declare (fixnum x y))
(values (- x) y))
(multiple-value-bind (x y) (%ext-gcd (- a) (- b))
(declare (fixnum x y))
(values (- x) (- y))))))
(declaim (inline mod-inverse)
(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 (integer a)
;; ((integer 1 #.most-positive-fixnum) modulus))
;; (mod (%ext-gcd (mod a modulus) modulus) modulus))
;; FIXME: Perhaps no advantage in efficiency? Then I should use the above simple
;; code.
(defun mod-inverse (a modulus)
"Solves ax ≡ 1 mod m. A and M must be coprime."
(declare ((integer 1 #.most-positive-fixnum) modulus))
(let ((a (mod a modulus))
(b modulus)
(u 1)
(v 0))
(declare (fixnum a b u v))
(loop until (zerop b)
for quot = (floor a b)
do (decf a (the fixnum (* quot b)))
(rotatef a b)
(decf u (the fixnum (* quot v)))
(rotatef u v))
(setq u (mod u modulus))
(if (< u 0)
(+ u modulus)
u)))
;; not tested
;; TODO: move to another file
(declaim (inline mod-binomial))
(defun mod-binomial (n k modulus)
(declare (uint31 n k modulus))
(if (or (< n k) (< n 0) (< k 0))
0
(let ((k (if (< k (- n k)) k (- n k)))
(num 1)
(denom 1))
(declare (uint31 k num denom))
(loop for x of-type uint31 from n above (- n k)
do (setq num (mod (* num x) modulus)))
(loop for x of-type uint31 from 1 to k
do (setq denom (mod (* denom x) modulus)))
(mod (* num (mod-inverse denom modulus)) modulus))))
(in-package :cl-user)
(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)))
(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 ()
(declare #.opt)
(let* ((n (read))
(m (read)))
(declare (uint31 n m))
(println (mod-binomial (+ m 1) (+ n 1) +mod+))))
#-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)
#+os-windows (run-program "powershell.exe" '("-Command" "Get-Clipboard") :output out :search t)
#+os-unix (run-program "xsel" '("-b" "-o") :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 "0 3
"
"4
"))
(it.bese.fiveam:is
(common-lisp-user::io-equal "12 20
"
"203490
"))
(it.bese.fiveam:is
(common-lisp-user::io-equal "100 200
"
"256185103
")))