結果
| 問題 | No.470 Inverse S+T Problem |
| ユーザー |
 sansaqua
|
| 提出日時 | 2020-02-22 11:11:54 |
| 言語 | Common Lisp (sbcl 2.3.8) |
| 結果 |
AC
|
| 実行時間 | 21 ms / 2,000 ms |
| コード長 | 13,475 bytes |
| コンパイル時間 | 157 ms |
| コンパイル使用メモリ | 64,836 KB |
| 実行使用メモリ | 37,508 KB |
| 最終ジャッジ日時 | 2024-06-01 23:00:23 |
| 合計ジャッジ時間 | 1,916 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
| 外部呼び出し有り |
（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 | 19 ms
31,692 KB |
| testcase_01 | AC | 19 ms
29,484 KB |
| testcase_02 | AC | 19 ms
29,480 KB |
| testcase_03 | AC | 17 ms
29,604 KB |
| testcase_04 | AC | 19 ms
31,560 KB |
| testcase_05 | AC | 18 ms
29,356 KB |
| testcase_06 | AC | 21 ms
37,380 KB |
| testcase_07 | AC | 19 ms
33,320 KB |
| testcase_08 | AC | 19 ms
37,508 KB |
| testcase_09 | AC | 18 ms
32,280 KB |
| testcase_10 | AC | 18 ms
29,480 KB |
| testcase_11 | AC | 20 ms
33,704 KB |
| testcase_12 | AC | 19 ms
32,276 KB |
| testcase_13 | AC | 19 ms
31,564 KB |
| testcase_14 | AC | 18 ms
29,480 KB |
| testcase_15 | AC | 19 ms
29,484 KB |
| testcase_16 | AC | 18 ms
33,596 KB |
| testcase_17 | AC | 18 ms
29,480 KB |
| testcase_18 | AC | 19 ms
30,244 KB |
| testcase_19 | AC | 18 ms
30,140 KB |
| testcase_20 | AC | 17 ms
29,480 KB |
| testcase_21 | AC | 17 ms
29,484 KB |
| testcase_22 | AC | 19 ms
33,704 KB |
| testcase_23 | AC | 19 ms
30,264 KB |
| testcase_24 | AC | 18 ms
29,476 KB |
| testcase_25 | AC | 19 ms
29,476 KB |
| testcase_26 | AC | 19 ms
30,244 KB |
| testcase_27 | AC | 19 ms
31,436 KB |
| testcase_28 | AC | 20 ms
33,724 KB |
| testcase_29 | AC | 18 ms
33,344 KB |
| testcase_30 | AC | 18 ms
30,120 KB |
コンパイルメッセージ
; compiling file "/home/judge/data/code/Main.lisp" (written 01 JUN 2024 11:00:20 PM): ; file: /home/judge/data/code/Main.lisp ; in: DEFUN MAKE-SCC ; (AREF GRAPH V) ; ; note: unable to ; optimize ; because: ; Upgraded element type of array is not known at compile time. ; in: DEFUN MAKE-CONDENSED-GRAPH ; (AREF GRAPH I) ; ; note: unable to ; optimize ; because: ; Upgraded element type of array is not known at compile time. ; ; compilation unit finished ; printed 2 notes ; wrote /home/judge/data/code/Main.fasl ; compilation finished in 0:00:00.095
ソースコード
#-swank
(unless (member :child-sbcl *features*)
(quit
:unix-status
(process-exit-code
(run-program *runtime-pathname*
`("--control-stack-size" "128MB"
"--noinform" "--disable-ldb" "--lose-on-corruption" "--end-runtime-options"
"--eval" "(push :child-sbcl *features*)"
"--script" ,(namestring *load-pathname*))
:output t :error t :input t))))
;; -*- 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
;;;
;;; Strongly connected components of directed graph, 2-SAT
;;;
(defstruct (scc (:constructor %make-scc (graph components sizes count)))
(graph nil :type vector)
;; components[i] := strongly connected component of the i-th vertex
(components nil :type (simple-array (integer 0 #.most-positive-fixnum) (*)))
;; sizes[k] := size of the k-th strongly connected component
(sizes nil :type (simple-array (integer 0 #.most-positive-fixnum) (*)))
;; the total number of strongly connected components
(count 0 :type (integer 0 #.most-positive-fixnum)))
;; (declaim (inline %make-revgraph))
;; (defun %make-revgraph (graph)
;; (let* ((n (length graph))
;; (revgraph (make-array n :element-type 'list :initial-element nil)))
;; (dotimes (i n)
;; (dolist (dest (aref graph i))
;; (push i (aref revgraph dest))))
;; revgraph))
;; Reference: http://www.prefield.com/algorithm/graph/strongly_connected_components.html
;; This is faster than well-known Kosaraju's algorithm because it doesn't
;; generate a reversed graph. I don't know the first person who referred to this
;; algorithm (tmaehara's invention?)
(defun make-scc (graph)
(declare (optimize (speed 3))
(vector graph))
(let* ((n (length graph))
(ord 0)
(ords (make-array n :element-type 'fixnum :initial-element -1)) ; in-order
;; store the lowest in-order number as the representative element of a
;; strongly connected component
(lowests (make-array n :element-type 'fixnum))
(components (make-array n :element-type '(integer 0 #.most-positive-fixnum)))
(comp-index 0) ; index number of component
(sizes (make-array n :element-type '(integer 0 #.most-positive-fixnum)
:initial-element 0))
(stack (make-array n :element-type '(integer 0 #.most-positive-fixnum)))
(end 0) ; stack pointer
(in-stack (make-array n :element-type 'bit :initial-element 0)))
(declare ((integer 0 #.most-positive-fixnum) ord end comp-index))
(labels ((%push (v)
(setf (aref stack end) v
(aref in-stack v) 1)
(incf end))
(%pop ()
(decf end)
(let ((v (aref stack end)))
(setf (aref in-stack v) 0)
v))
(visit (v)
(setf (aref ords v) ord
(aref lowests v) ord)
(incf ord)
(%push v)
(dolist (next (aref graph v))
(cond ((= -1 (aref ords next))
(visit next)
(setf (aref lowests v)
(min (aref lowests v) (aref lowests next))))
((= 1 (aref in-stack next))
(setf (aref lowests v)
(min (aref lowests v) (aref ords next))))))
(when (= (aref lowests v) (aref ords v))
(loop for size of-type (integer 0 #.most-positive-fixnum) from 1
for w = (%pop)
do (setf (aref components w) comp-index)
until (= v w)
finally (setf (aref sizes comp-index) size)
(incf comp-index)))))
(dotimes (v n)
(when (= -1 (aref ords v))
(visit v)))
(%make-scc graph components sizes comp-index))))
;; (defun make-scc (graph &optional revgraph)
;; "GRAPH := vector of adjacency lists
;; REVGRAPH := NIL | reversed graph of GRAPH"
;; (declare (optimize (speed 3))
;; (vector graph)
;; ((or null vector) revgraph))
;; (let* ((revgraph (or revgraph (%make-revgraph graph)))
;; (n (length graph))
;; (visited (make-array n :element-type 'bit :initial-element 0))
;; (posts (make-array n :element-type '(integer 0 #.most-positive-fixnum)))
;; (components (make-array n :element-type '(integer 0 #.most-positive-fixnum)))
;; (sizes (make-array n :element-type '(integer 0 #.most-positive-fixnum)
;; :initial-element 0))
;; (pointer 0)
;; (ord 0) ; ordinal number for a strongly connected component
;; )
;; (declare ((integer 0 #.most-positive-fixnum) pointer ord))
;; (assert (= n (length revgraph)))
;; (labels ((dfs (v)
;; (setf (aref visited v) 1)
;; (dolist (neighbor (aref graph v))
;; (when (zerop (aref visited neighbor))
;; (dfs neighbor)))
;; (setf (aref posts pointer) v)
;; (incf pointer))
;; (reversed-dfs (v ord)
;; (setf (aref visited v) 1
;; (aref components v) ord)
;; (incf (aref sizes ord))
;; (dolist (neighbor (aref revgraph v))
;; (when (zerop (aref visited neighbor))
;; (reversed-dfs neighbor ord)))))
;; (dotimes (v n)
;; (when (zerop (aref visited v))
;; (dfs v)))
;; (fill visited 0)
;; (loop for i from (- n 1) downto 0
;; for v = (aref posts i)
;; when (zerop (aref visited v))
;; do (reversed-dfs v ord)
;; (incf ord))
;; (%make-scc graph revgraph posts components sizes ord))))
(declaim (ftype (function * (values (simple-array t (*)) &optional)) make-condensed-graph))
(defun make-condensed-graph (scc)
"Does graph condensation.
This function is non-destructive. The resultant graph doesn't contain self-loops
even if the given graph does."
(declare (optimize (speed 3)))
(let* ((graph (scc-graph scc))
(n (length graph))
(comp-n (scc-count scc))
(components (scc-components scc))
(condensed (make-array comp-n :element-type t)))
(dotimes (i comp-n)
(setf (aref condensed i) (make-hash-table :test #'eql)))
(dotimes (i n)
(let ((i-comp (aref components i)))
(dolist (neighbor (aref graph i))
(let ((neighbor-comp (aref components neighbor)))
(unless (= i-comp neighbor-comp)
(setf (gethash neighbor-comp (aref condensed i-comp)) t))))))
(dotimes (i comp-n)
(setf (aref condensed i)
(loop for x being each hash-key of (aref condensed i) collect x)))
condensed))
;;;
;;; 2-SAT
;;;
(defstruct (2sat (:constructor make-2sat
(size
&aux
(graph (make-array (* 2 size) :element-type 'list :initial-element nil)))))
(size 0 :type (integer 0 #.most-positive-fixnum))
(graph nil :type (simple-array list (*)))
(scc nil :type (or null scc)))
(declaim (inline negate))
(defun negate (p)
(- -1 p))
(declaim (inline add-implication))
(defun add-implication (2sat p q)
"Adds `P => Q' to 2SAT."
(declare (fixnum p q))
(let ((size (2sat-size 2sat))
(graph (2sat-graph 2sat)))
(when (< p 0)
(setq p (+ size (- -1 p))))
(when (< q 0)
(setq q (+ size (- -1 q))))
(push q (aref graph p))
2sat))
(declaim (inline add-disjunction))
(defun add-disjunction (2sat p q)
"Adds `P or Q' to 2SAT."
(declare (fixnum p q))
(add-implication 2sat (negate p) q)
(add-implication 2sat (negate q) p)
2sat)
(declaim (inline 2sat-solve))
(defun 2sat-solve (2sat)
"Solves 2-SAT and returns a simple bit vector expressing the boolean of each
variable if it is feasible, otherwise returns NIL."
(let* ((size (2sat-size 2sat))
(graph (2sat-graph 2sat))
(scc (make-scc graph))
(components (scc-components scc))
(result (make-array size :element-type 'bit :initial-element 0)))
(setf (2sat-scc 2sat) scc)
(loop for v below size
for v-comp = (aref components v)
for neg-comp = (aref components (+ v size))
do (cond ((< v-comp neg-comp)
(setf (sbit result v) 1))
((= v-comp neg-comp)
(return-from 2sat-solve nil))))
result))
;; NOTE: not enclosed with (BLOCK NIL)
(defmacro dopairs ((var1 var2 list &optional result) &body body)
"Iterates BODY for each subset of LIST containing two elements."
(let ((suffix (gensym))
(_list (gensym)))
`(let ((,_list ,list))
(loop for ,suffix on ,_list
for ,var1 = (car ,suffix)
do (dolist (,var2 (cdr ,suffix))
,@body))
,result)))
(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 ()
(let* ((n (read))
(us (make-array n :element-type 'simple-string))
(table (make-hash-table :test #'equal))
(2sat (make-2sat n)))
(when (> n 52)
(write-line "Impossible")
(return-from main))
(dotimes (i n)
(let* ((u (read-line))
(pre1 (subseq u 0 1))
(suf2 (subseq u 1 3))
(pre2 (subseq u 0 2))
(suf1 (subseq u 2 3)))
(declare (simple-string u))
(push i (gethash pre1 table))
(push i (gethash suf2 table))
(push (negate i) (gethash pre2 table))
(push (negate i) (gethash suf1 table))
(setf (aref us i) u)))
(loop for set being each hash-value of table
do (dopairs (i j set)
(declare (fixnum i j))
;; cannot be true simultaneously
(add-disjunction 2sat (negate i) (negate j))))
(let ((result (2sat-solve 2sat)))
(if (null result)
(write-line "Impossible")
(dotimes (i n)
(let ((u (aref us i)))
(if (= 1 (sbit result i))
(format t "~A ~A~A~%" (aref u 0) (aref u 1) (aref u 2))
(format t "~A~A ~A~%" (aref u 0) (aref u 1) (aref u 2)))))))))
#-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)))