結果

問題 No.1126 SUM
ユーザー sansaquasansaqua
提出日時 2020-07-24 22:16:26
言語 Common Lisp
(sbcl 2.3.8)
結果
AC  
実行時間 769 ms / 1,000 ms
コード長 7,750 bytes
コンパイル時間 113 ms
コンパイル使用メモリ 44,000 KB
実行使用メモリ 140,288 KB
最終ジャッジ日時 2024-06-25 21:45:37
合計ジャッジ時間 20,594 ms
ジャッジサーバーID
(参考情報)
judge5 / judge1
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 741 ms
140,160 KB
testcase_01 AC 759 ms
140,288 KB
testcase_02 AC 734 ms
140,288 KB
testcase_03 AC 713 ms
140,160 KB
testcase_04 AC 769 ms
140,288 KB
testcase_05 AC 743 ms
140,032 KB
testcase_06 AC 709 ms
140,160 KB
testcase_07 AC 748 ms
140,160 KB
testcase_08 AC 759 ms
140,160 KB
testcase_09 AC 740 ms
140,160 KB
testcase_10 AC 748 ms
140,160 KB
testcase_11 AC 726 ms
140,160 KB
testcase_12 AC 723 ms
140,032 KB
testcase_13 AC 740 ms
140,032 KB
testcase_14 AC 724 ms
140,160 KB
testcase_15 AC 719 ms
140,288 KB
testcase_16 AC 704 ms
140,160 KB
testcase_17 AC 695 ms
140,160 KB
testcase_18 AC 702 ms
140,160 KB
testcase_19 AC 728 ms
140,160 KB
testcase_20 AC 685 ms
140,160 KB
testcase_21 AC 694 ms
140,288 KB
testcase_22 AC 707 ms
140,288 KB
testcase_23 AC 739 ms
140,032 KB
testcase_24 AC 728 ms
140,160 KB
testcase_25 AC 688 ms
140,160 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 25 JUN 2024 09:45:12 PM):

; wrote /home/judge/data/code/Main.fasl
; compilation finished in 0:00:00.048

ソースコード

diff #

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

;; TODO: non-global handling

(defconstant +binom-size+ 10000001)
(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")
(declaim (always-bound *fact-inv* *fact* *inv*))

(defun initialize-binom ()
  (declare (optimize (speed 3) (safety 0)))
  (let ((fact *fact*)
        (fact-inv *fact-inv*)
        (inv *inv*))
    (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)))

(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 (loop for i from n to m
                        sum (binom i n) of-type uint62)
                  +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
")))
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