結果
| 問題 | No.1102 Remnants |
| ユーザー |
 sansaqua
|
| 提出日時 | 2020-07-03 22:28:11 |
| 言語 | Common Lisp (sbcl 2.3.8) |
| 結果 |
AC
|
| 実行時間 | 89 ms / 2,000 ms |
| コード長 | 10,913 bytes |
| コンパイル時間 | 1,597 ms |
| コンパイル使用メモリ | 56,336 KB |
| 実行使用メモリ | 39,844 KB |
| 最終ジャッジ日時 | 2023-10-17 05:25:58 |
| 合計ジャッジ時間 | 4,293 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge11 |
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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 | 33 ms
37,792 KB |
| testcase_01 | AC | 33 ms
37,792 KB |
| testcase_02 | AC | 33 ms
37,792 KB |
| testcase_03 | AC | 32 ms
37,792 KB |
| testcase_04 | AC | 32 ms
37,792 KB |
| testcase_05 | AC | 64 ms
39,844 KB |
| testcase_06 | AC | 40 ms
37,796 KB |
| testcase_07 | AC | 89 ms
39,844 KB |
| testcase_08 | AC | 33 ms
37,796 KB |
| testcase_09 | AC | 34 ms
37,796 KB |
| testcase_10 | AC | 33 ms
37,804 KB |
| testcase_11 | AC | 34 ms
37,796 KB |
| testcase_12 | AC | 35 ms
37,796 KB |
| testcase_13 | AC | 34 ms
37,796 KB |
| testcase_14 | AC | 55 ms
37,796 KB |
| testcase_15 | AC | 49 ms
37,796 KB |
| testcase_16 | AC | 76 ms
39,844 KB |
| testcase_17 | AC | 73 ms
39,844 KB |
| testcase_18 | AC | 82 ms
39,844 KB |
| testcase_19 | AC | 49 ms
37,796 KB |
| testcase_20 | AC | 38 ms
37,796 KB |
| testcase_21 | AC | 62 ms
39,844 KB |
| testcase_22 | AC | 74 ms
39,844 KB |
| testcase_23 | AC | 65 ms
39,844 KB |
| testcase_24 | AC | 56 ms
37,796 KB |
| testcase_25 | AC | 82 ms
39,844 KB |
| testcase_26 | AC | 35 ms
37,796 KB |
| testcase_27 | AC | 46 ms
37,796 KB |
コンパイルメッセージ
; compiling file "/home/judge/data/code/Main.lisp" (written 16 OCT 2023 08:25:53 PM): ; wrote /home/judge/data/code/Main.fasl ; compilation finished in 0:00:00.121
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)
#-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"
(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 #\-))
(setq 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))))))))
;;;
;;; Arithmetic operations with static modulus
;;;
;; FIXME: Currently MOD* and MOD+ doesn't apply MOD when the number of
;; parameters is one.
(defmacro define-mod-operations (divisor)
`(progn
(defun mod* (&rest args)
(reduce (lambda (x y) (mod (* x y) ,divisor)) args))
(defun mod+ (&rest args)
(reduce (lambda (x y) (mod (+ x y) ,divisor)) args))
#+sbcl
(eval-when (:compile-toplevel :load-toplevel :execute)
(locally (declare (muffle-conditions warning))
(sb-c:define-source-transform mod* (&rest args)
(if (null args)
1
(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)))))
;;;
;;; Binomial coefficient with mod
;;; build: O(n)
;;; query: O(1)
;;;
;; TODO: non-global handling
(defconstant +binom-size+ 510000)
(defconstant +binom-mod+ #.(+ (expt 10 9) 7))
(declaim ((simple-array (unsigned-byte 31) (*)) *fact* *fact-inv* *inv*))
(defparameter *fact* (make-array +binom-size+ :element-type '(unsigned-byte 31))
"table of factorials")
(defparameter *fact-inv* (make-array +binom-size+ :element-type '(unsigned-byte 31))
"table of inverses of factorials")
(defparameter *inv* (make-array +binom-size+ :element-type '(unsigned-byte 31))
"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+)))
(declaim (inline stirling2))
(defun stirling2 (n k)
"Returns the stirling number of the second kind S2(n, k). Time complexity is
O(klog(n))."
(declare ((integer 0 #.most-positive-fixnum) n k))
(labels ((mod-power (base exp)
(declare ((integer 0 #.most-positive-fixnum) base exp))
(loop with res of-type (integer 0 #.most-positive-fixnum) = 1
while (> exp 0)
when (oddp exp)
do (setq res (mod (* res base) +binom-mod+))
do (setq base (mod (* base base) +binom-mod+)
exp (ash exp -1))
finally (return res))))
(loop with result of-type fixnum = 0
for i from 0 to k
for delta = (mod (* (binom k i) (mod-power i n)) +binom-mod+)
when (evenp (- k i))
do (incf result delta)
(when (>= result +binom-mod+)
(decf result +binom-mod+))
else
do (decf result delta)
(when (< result 0)
(incf result +binom-mod+))
finally (return (mod (* result (aref *fact-inv* k)) +binom-mod+)))))
(declaim (inline catalan))
(defun catalan (n)
"Returns the N-th Catalan number."
(declare ((integer 0 #.most-positive-fixnum) n))
(mod (* (aref *fact* (* 2 n))
(mod (* (aref *fact-inv* (+ n 1))
(aref *fact-inv* n))
+binom-mod+))
+binom-mod+))
(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)))
(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 ()
(let* ((n (read))
(k (read))
(as (make-array n :element-type 'uint31 :initial-element 0))
(factors1 (make-array n :element-type 'uint31 :initial-element 0))
(factors2 (make-array n :element-type 'uint31 :initial-element 0))
(res 0))
(declare (uint31 res))
(dotimes (i n)
(setf (aref as i) (read-fixnum)))
(setf (aref factors2 0) 1)
(loop for i from 1 below n
do (setf (aref factors2 i)
(mod* (+ k i) (aref factors2 (- i 1)))))
(setf (aref factors1 (- n 1)) 1)
(loop for i from (- n 2) downto 0
do (setf (aref factors1 i)
(mod* (+ (- n i 1) k) (aref factors1 (+ i 1)))))
;; (dotimes (i n)
;; (incfmod res (mod* (aref as i)
;; (binom (+ (- n i 1) k) k)
;; (binom (+ i k) k))))
(dotimes (i n)
(incfmod res (mod* (aref as i)
(aref factors1 i)
(aref *fact-inv* (- n i 1))
(aref factors2 i)
(aref *fact-inv* i))))
(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 "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 "2 2
3 4
"
"21
"))
(it.bese.fiveam:is
(common-lisp-user::io-equal "4 0
1 2 3 4
"
"10
"))
(it.bese.fiveam:is
(common-lisp-user::io-equal "5 100000000
1000000000 999999999 888888888 777777777 666666666
"
"870870837
")))