結果
問題 | No.1126 SUM |
ユーザー | sansaqua |
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 |
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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 |
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
(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 ")))