結果
| 問題 | No.875 Range Mindex Query |
| ユーザー |
 sansaqua
|
| 提出日時 | 2019-09-17 17:51:21 |
| 言語 | Common Lisp (sbcl 2.3.8) |
| 結果 |
AC
|
| 実行時間 | 197 ms / 2,000 ms |
| コード長 | 21,117 bytes |
| コンパイル時間 | 1,644 ms |
| コンパイル使用メモリ | 74,604 KB |
| 実行使用メモリ | 32,128 KB |
| 最終ジャッジ日時 | 2024-07-07 13:19:20 |
| 合計ジャッジ時間 | 4,285 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
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 | 10 ms
23,936 KB |
| testcase_01 | AC | 10 ms
23,936 KB |
| testcase_02 | AC | 11 ms
23,936 KB |
| testcase_03 | AC | 10 ms
23,936 KB |
| testcase_04 | AC | 10 ms
23,936 KB |
| testcase_05 | AC | 10 ms
24,192 KB |
| testcase_06 | AC | 10 ms
23,936 KB |
| testcase_07 | AC | 11 ms
24,064 KB |
| testcase_08 | AC | 12 ms
23,936 KB |
| testcase_09 | AC | 10 ms
23,936 KB |
| testcase_10 | AC | 10 ms
24,064 KB |
| testcase_11 | AC | 177 ms
29,824 KB |
| testcase_12 | AC | 141 ms
28,288 KB |
| testcase_13 | AC | 134 ms
30,848 KB |
| testcase_14 | AC | 129 ms
30,464 KB |
| testcase_15 | AC | 171 ms
31,104 KB |
| testcase_16 | AC | 180 ms
31,616 KB |
| testcase_17 | AC | 197 ms
31,872 KB |
| testcase_18 | AC | 191 ms
32,128 KB |
コンパイルメッセージ
; compiling file "/home/judge/data/code/Main.lisp" (written 07 JUL 2024 01:19:15 PM): ; file: /home/judge/data/code/Main.lisp ; in: DEFUN MAIN ; (+ 1 (ITREAP-RANGE-BISECT-LEFT DP MIN #'> L)) ; ; note: doing unsigned word to integer coercion (cost 20), for: ; the first result of inline (unsigned-byte 64) arithmetic ; ; compilation unit finished ; printed 1 note ; wrote /home/judge/data/code/Main.fasl ; compilation finished in 0:00:00.210
ソースコード
;; -*- 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
;; Should we do this with UNWIND-PROTECT?
(defmacro with-buffered-stdout (&body body)
"Buffers all outputs to *STANDARD-OUTPUT* in BODY and flushes them to
*STANDARD-OUTPUT* after BODY has been done (without error). Note that only
BASE-CHAR is allowed."
(let ((out (gensym)))
`(let ((,out (make-string-output-stream :element-type 'base-char)))
(let ((*standard-output* ,out))
,@body)
(write-string (get-output-stream-string ,out)))))
(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
(declare #.OPT)
(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 #\-))
(setf 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))))))))
;;;
;;; Implicit treap
;;; (treap with implicit key)
;;;
;; Note:
;; - An empty treap is NIL.
;; value . index
(declaim (inline op))
(defun op (a b)
(declare (fixnum a b))
"Is a binary operator comprising a monoid."
(min a b))
(sb-int:defconstant-eqx +op-identity+ most-positive-fixnum
#'eql
"identity element w.r.t. OP")
(defstruct (itreap (:constructor %make-itreap (value priority &key left right (count 1) (accumulator value)))
(:copier nil)
(:conc-name %itreap-))
(value +op-identity+ :type fixnum)
(accumulator +op-identity+ :type fixnum)
(priority 0 :type (integer 0 #.most-positive-fixnum))
(count 1 :type (integer 0 #.most-positive-fixnum)) ; size of (sub)treap
(left nil :type (or null itreap))
(right nil :type (or null itreap)))
(declaim (inline itreap-count))
(defun itreap-count (itreap)
"Returns the number of the elements."
(declare ((or null itreap) itreap))
(if itreap
(%itreap-count itreap)
0))
(declaim (inline itreap-accumulator))
(defun itreap-accumulator (itreap)
"Returns the sum (w.r.t. OP) of the whole ITREAP:
ITREAP[0]+ITREAP[1]+...+ITREAP[SIZE-1]."
(declare ((or null itreap) itreap))
(if itreap
(%itreap-accumulator itreap)
+op-identity+))
(declaim (inline update-count))
(defun update-count (itreap)
(declare (itreap itreap))
(setf (%itreap-count itreap)
(+ 1
(itreap-count (%itreap-left itreap))
(itreap-count (%itreap-right itreap)))))
(declaim (inline update-accumulator))
(defun update-accumulator (itreap)
(declare (itreap itreap))
(setf (%itreap-accumulator itreap)
(if (%itreap-left itreap)
(if (%itreap-right itreap)
(let ((mid (op (%itreap-accumulator (%itreap-left itreap))
(%itreap-value itreap))))
(declare (dynamic-extent mid))
(op mid (%itreap-accumulator (%itreap-right itreap))))
(op (%itreap-accumulator (%itreap-left itreap))
(%itreap-value itreap)))
(if (%itreap-right itreap)
(op (%itreap-value itreap)
(%itreap-accumulator (%itreap-right itreap)))
(%itreap-value itreap)))))
(declaim (inline force-up))
(defun force-up (itreap)
"Propagates up the information from children."
(declare (itreap itreap))
(update-count itreap)
(update-accumulator itreap))
(defun %heapify (top)
"Properly swaps the priorities of the node and its two children."
(declare (optimize (speed 3) (safety 0)))
(when top
(let ((high-priority-node top))
(when (and (%itreap-left top)
(> (%itreap-priority (%itreap-left top))
(%itreap-priority high-priority-node)))
(setq high-priority-node (%itreap-left top)))
(when (and (%itreap-right top)
(> (%itreap-priority (%itreap-right top))
(%itreap-priority high-priority-node)))
(setq high-priority-node (%itreap-right top)))
(unless (eql high-priority-node top)
(rotatef (%itreap-priority high-priority-node)
(%itreap-priority top))
(%heapify high-priority-node)))))
(declaim (inline make-itreap))
(defun make-itreap (size &key initial-contents)
"Makes a treap of SIZE in O(SIZE) time. Its values are filled with the
identity element unless INITIAL-CONTENTS are supplied."
(declare ((or null vector) initial-contents))
(labels ((build (l r)
(declare ((integer 0 #.most-positive-fixnum) l r))
(if (= l r)
nil
(let* ((mid (ash (+ l r) -1))
(node (%make-itreap (if initial-contents
(aref initial-contents mid)
+op-identity+)
(random most-positive-fixnum))))
(setf (%itreap-left node) (build l mid))
(setf (%itreap-right node) (build (+ mid 1) r))
(%heapify node)
(force-up node)
node))))
(build 0 size)))
(define-condition invalid-itreap-index-error (type-error)
((itreap :initarg :itreap :reader invalid-itreap-index-error-itreap)
(index :initarg :index :reader invalid-itreap-index-error-index))
(:report
(lambda (condition stream)
(let ((index (invalid-itreap-index-error-index condition)))
(if (consp index)
(format stream "Invalid range [~W, ~W) for itreap ~W."
(car index)
(cdr index)
(invalid-itreap-index-error-itreap condition))
(format stream "Invalid index ~W for itreap ~W."
index
(invalid-itreap-index-error-itreap condition)))))))
(defun itreap-split (itreap index)
"Destructively splits the ITREAP into two nodes [0, INDEX) and [INDEX, N),
where N is the number of elements of the ITREAP."
(declare (optimize (speed 3))
((integer 0 #.most-positive-fixnum) index))
(unless (<= index (itreap-count itreap))
(error 'invalid-itreap-index-error :index index :itreap itreap))
(labels ((recur (itreap ikey)
(unless itreap
(return-from itreap-split (values nil nil)))
(let ((left-count (itreap-count (%itreap-left itreap))))
(if (<= ikey left-count)
(multiple-value-bind (left right)
(itreap-split (%itreap-left itreap) ikey)
(setf (%itreap-left itreap) right)
(force-up itreap)
(values left itreap))
(multiple-value-bind (left right)
(itreap-split (%itreap-right itreap) (- ikey left-count 1))
(setf (%itreap-right itreap) left)
(force-up itreap)
(values itreap right))))))
(recur itreap index)))
(defun itreap-merge (left right)
"Destructively concatenates two ITREAPs."
(declare (optimize (speed 3))
((or null itreap) left right))
(cond ((null left) (when right (force-up right)) right)
((null right) (when left (force-up left)) left)
(t (if (> (%itreap-priority left) (%itreap-priority right))
(progn
(setf (%itreap-right left)
(itreap-merge (%itreap-right left) right))
(force-up left)
left)
(progn
(setf (%itreap-left right)
(itreap-merge left (%itreap-left right)))
(force-up right)
right)))))
(defun itreap-insert (itreap index obj)
"Destructively inserts OBJ into ITREAP and returns the resultant treap.
You cannot rely on the side effect. Use the returned value."
(declare (optimize (speed 3))
((or null itreap) itreap)
((integer 0 #.most-positive-fixnum) index))
(unless (<= index (itreap-count itreap))
(error 'invalid-itreap-index-error :itreap itreap :index index))
(let ((node (%make-itreap obj (random most-positive-fixnum))))
(labels ((recur (itreap ikey)
(declare ((integer 0 #.most-positive-fixnum) ikey))
(unless itreap (return-from recur node))
(if (> (%itreap-priority node) (%itreap-priority itreap))
(progn
(setf (values (%itreap-left node) (%itreap-right node))
(itreap-split itreap ikey))
(force-up node)
node)
(let ((left-count (itreap-count (%itreap-left itreap))))
(if (<= ikey left-count)
(setf (%itreap-left itreap)
(recur (%itreap-left itreap) ikey))
(setf (%itreap-right itreap)
(recur (%itreap-right itreap) (- ikey left-count 1))))
(force-up itreap)
itreap))))
(recur itreap index))))
(defun itreap-delete (itreap index)
"Destructively deletes the object at INDEX in ITREAP.
You cannot rely on the side effect. Use the returned value."
(declare (optimize (speed 3))
((integer 0 #.most-positive-fixnum) index))
(unless (< index (itreap-count itreap))
(error 'invalid-itreap-index-error :itreap itreap :index index))
(labels ((recur (itreap ikey)
(declare ((integer 0 #.most-positive-fixnum) ikey))
(let ((left-count (itreap-count (%itreap-left itreap))))
(cond ((< ikey left-count)
(setf (%itreap-left itreap)
(recur (%itreap-left itreap) ikey))
(force-up itreap)
itreap)
((> ikey left-count)
(setf (%itreap-right itreap)
(recur (%itreap-right itreap) (- ikey left-count 1)))
(force-up itreap)
itreap)
(t
(itreap-merge (%itreap-left itreap) (%itreap-right itreap)))))))
(recur itreap index)))
(defmacro itreap-push (obj itreap pos)
"Pushes OBJ to ITREAP at POS."
`(setf ,itreap (itreap-insert ,itreap ,pos ,obj)))
(defmacro itreap-pop (itreap pos)
"Returns the object at POS and deletes it."
(let ((p (gensym)))
`(let ((,p ,pos))
(prog1 (itreap-ref ,itreap ,p)
(setf ,itreap (itreap-delete ,itreap ,p))))))
(declaim (inline itreap-map))
(defun itreap-map (function itreap)
"Successively applies FUNCTION to ITREAP[0], ..., ITREAP[SIZE-1]."
(declare (function function))
(labels ((recur (node)
(when node
(recur (%itreap-left node))
(funcall function (%itreap-value node))
(recur (%itreap-right node))
(force-up node))))
(recur itreap)))
(defmethod print-object ((object itreap) stream)
(print-unreadable-object (object stream :type t)
(let ((init t))
(itreap-map (lambda (x)
(if init
(setq init nil)
(write-char #\ stream))
(write x :stream stream))
object))))
(defmacro do-itreap ((var itreap &optional result) &body body)
"Successively binds ITREAP[0], ..., ITREAP[SIZE-1] to VAR and executes BODY
each time."
`(block nil
(itreap-map (lambda (,var) ,@body) ,itreap)
,result))
(defun itreap (&rest args)
;; NOTE: It takes O(nlog(n)). Use MAKE-ITREAP for efficiency.
(labels ((recur (list position itreap)
(declare ((integer 0 #.most-positive-fixnum) position))
(if (null list)
itreap
(recur (cdr list)
(1+ position)
(itreap-insert itreap position (car list))))))
(recur args 0 nil)))
(declaim (inline itreap-ref))
(defun itreap-ref (itreap index)
"Returns the element ITREAP[INDEX]."
(declare ((integer 0 #.most-positive-fixnum) index))
(labels ((%ref (itreap index)
(declare ((integer 0 #.most-positive-fixnum) index))
(prog1
(let ((left-count (itreap-count (%itreap-left itreap))))
(cond ((< index left-count)
(%ref (%itreap-left itreap) index))
((> index left-count)
(%ref (%itreap-right itreap) (- index left-count 1)))
(t (%itreap-value itreap))))
(force-up itreap))))
(%ref itreap index)))
(declaim (inline (setf itreap-ref)))
(defun (setf itreap-ref) (new-value itreap index)
"Sets ITREAP[INDEX] to the given value."
(declare ((integer 0 #.most-positive-fixnum) index))
(labels ((%set (itreap index)
(declare ((integer 0 #.most-positive-fixnum) index))
(prog1
(let ((left-count (itreap-count (%itreap-left itreap))))
(cond ((< index left-count)
(%set (%itreap-left itreap) index))
((> index left-count)
(%set (%itreap-right itreap) (- index left-count 1)))
(t (setf (%itreap-value itreap) new-value))))
(force-up itreap))))
(%set itreap index)
new-value))
(declaim (inline itreap-query))
(defun itreap-query (itreap l r)
"Queries the `sum' (w.r.t. OP) of the interval [L, R)."
(declare ((integer 0 #.most-positive-fixnum) l r))
(labels
((recur (itreap l r)
(declare ((integer 0 #.most-positive-fixnum) l r))
(unless itreap
(return-from recur +op-identity+))
(if (and (zerop l) (= r (%itreap-count itreap)))
(itreap-accumulator itreap)
(let ((left-count (itreap-count (%itreap-left itreap))))
(if (<= l left-count)
(if (< left-count r)
;; LEFT-COUNT is in [L, R)
(op (op (recur (%itreap-left itreap) l (min r left-count))
(%itreap-value itreap))
(recur (%itreap-right itreap) 0 (- r left-count 1)))
;; LEFT-COUNT is in [R, END)
(recur (%itreap-left itreap) l (min r left-count)))
;; LEFT-COUNT is in [0, L)
(recur (%itreap-right itreap) (- l left-count 1) (- r left-count 1)))))))
(recur itreap l r)))
;; FIXME: might be problematic when two priorities collide and START is not
;; zero.
(declaim (inline itreap-range-bisect-left))
(defun itreap-range-bisect-left (itreap value order &optional (start 0))
"Returns the smallest index that satisfies ITREAP[START]+ ITREAP[START+1] +
... + ITREAP[index] >= VALUE (if ORDER is #'<).
Note:
- This function handles a **closed** interval.
- This function returns the length of ITREAP instead if ITREAP[START]+
... +ITREAP[length-1] < VALUE.
- The prefix sums of ITREAP, (ITREAP[START], ITREAP[START]+ITREAP[START+1], ...)
must be monotone w.r.t. ORDER.
- ORDER must be strict order"
(declare ((integer 0 #.most-positive-fixnum) start))
(multiple-value-bind (itreap-prefix itreap)
(if (zerop start)
(values nil itreap)
(itreap-split itreap start))
(labels
((recur (itreap offset prev-sum)
(declare ((integer 0 #.most-positive-fixnum) offset)
#+sbcl (values (integer 0 #.most-positive-fixnum)))
(unless itreap
(return-from recur offset))
(let ((sum prev-sum))
(prog1
(cond ((not (funcall order
(setq sum (op sum (itreap-accumulator (%itreap-left itreap))))
value))
(recur (%itreap-left itreap) offset prev-sum))
((not (funcall order
(setq sum (op sum (%itreap-value itreap)))
value))
(+ offset (itreap-count (%itreap-left itreap))))
(t
(recur (%itreap-right itreap)
(+ offset (itreap-count (%itreap-left itreap)) 1)
sum)))
(force-up itreap)))))
(prog1 (+ start (recur itreap 0 +op-identity+))
(itreap-merge itreap-prefix itreap)))))
(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
;;;
(defun main ()
(declare #.OPT)
(let* ((n (read))
(q (read))
(as (make-array n :element-type 'uint62)))
(declare (uint32 n q))
(dotimes (i n)
(setf (aref as i) (read-fixnum)))
(let ((dp (make-itreap n :initial-contents as)))
(with-buffered-stdout
(dotimes (_ q)
(let* ((kind (read-fixnum))
(l (- (read-fixnum) 1))
(r (- (read-fixnum) 1)))
(if (= kind 1)
(rotatef (itreap-ref dp l) (itreap-ref dp r))
(let ((min (itreap-query dp l (+ r 1))))
(println (+ 1 (itreap-range-bisect-left dp min #'> l)))))))))))
#-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 "C:/msys64/usr/bin/cat.exe" '("/dev/clipboard") :output out)))
#+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)))