#388053 (Common Lisp) No.391 CODING WAR

提出ソース

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 22:47:15
言語	Common Lisp (sbcl 2.5.0)
結果	AC
実行時間	138 ms / 2,000 ms
コード長	5,573 bytes
コンパイル時間	1,446 ms
コンパイル使用メモリ	41,984 KB
実行使用メモリ	27,136 KB
最終ジャッジ日時	2024-11-07 19:53:01
合計ジャッジ時間	2,753 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

このコードへのチャレンジ
（要ログイン）

ファイルパターン	結果
sample	AC * 4
other	AC * 16

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 07 NOV 2024 07:52:57 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.

;     (POWER-MOD (- M I) N +MOD+)
; --> BLOCK LABELS RECUR THE PROGN BLOCK COND IF IF RECUR MOD 
; ==>
;   1
; 
; note: forced to do */UNSIGNED=>INTEGER (cost 10)
;       unable to do inline fixnum arithmetic (cost 2) because:
;       The result is a (VALUES (MOD 21267647932558653957237540927630737410)
;                               &OPTIONAL), not a (VALUES FIXNUM &OPTIONAL).
;       unable to do inline (signed-byte 64) arithmetic (cost 4) because:
;       The result is a (VALUES (MOD 21267647932558653957237540927630737410)
;                               &OPTIONAL), not a (VALUES (SIGNED-BYTE 64)
;                                                         &OPTIONAL).

; --> BLOCK LABELS RECUR THE PROGN BLOCK COND IF IF THE MOD

ソースコード

raw source code

;; -*- 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 ((integer 0 #.most-positive-fixnum) x p)
                      (values (integer 0 #.most-positive-fixnum)))
             (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 n m))
    (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)

yukicoder

結果

コンパイルメッセージ

ソースコード