結果
問題 | No.1207 グラフX |
ユーザー |
|
提出日時 | 2020-08-30 13:35:15 |
言語 | Common Lisp (sbcl 2.5.0) |
結果 |
AC
|
実行時間 | 387 ms / 2,000 ms |
コード長 | 19,652 bytes |
コンパイル時間 | 1,811 ms |
コンパイル使用メモリ | 89,612 KB |
実行使用メモリ | 89,856 KB |
最終ジャッジ日時 | 2024-11-15 06:51:05 |
合計ジャッジ時間 | 14,698 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge4 |
外部呼び出し有り |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 46 |
コンパイルメッセージ
; compiling file "/home/judge/data/code/Main.lisp" (written 15 NOV 2024 06:50:48 AM): ; wrote /home/judge/data/code/Main.fasl ; compilation finished in 0:00:00.323
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))))(in-package :cl-user)(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)(defconstant +mod+ 1000000007)(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))));; BEGIN_INSERTED_CONTENTS;;;;;; Minimum spanning tree (Boruvka's algorithm, O(ElogV));;;;;; Reference:;;; Ahuja, Magnanti, Orlin. Network Flows: Theory, Algorithms, and Applications.;;;(defpackage :cp/boruvka(:use :cl)(:export #:find-mst))(in-package :cp/boruvka)(defconstant +inf-cost+ most-positive-fixnum);; Here I express each connected component as a cycle with singly-linked list,;; though Ahuja's book adopts doubly-linked list. I learned about this technique;; in noshi91's article: http://noshi91.hatenablog.com/entry/2019/07/19/180606;; (Japanese)(declaim (inline find-mst)(ftype (function * (values (simple-array fixnum (*))(simple-array fixnum (*))(simple-array fixnum (*))&optional))find-mst))(defun find-mst (graph &key (vertex-key #'car) (cost-key #'cdr) maximize)"Computes an MST by Boruvka's algorithm. Returns three values: a vector thatstores each cost of the edges, two vectors that store each end of the edges. IfGRAPH is not connected, this function computes MST for each connected component.GRAPH := vector of adjacency listsMAXIMIZE := if true, solve maximization problem instead"(declare (vector graph))(let* ((n (length graph))(roots (make-array n :element-type 'fixnum));; next node in a connected component(nexts (make-array n :element-type 'fixnum))(min-costs (make-array n :element-type 'fixnum))(min-srcs (make-array n :element-type 'fixnum))(min-dests (make-array n :element-type 'fixnum))(edge-count 0)(res-costs (make-array (max 0 (- n 1)) :element-type 'fixnum))(res-srcs (make-array (max 0 (- n 1)) :element-type 'fixnum))(res-dests (make-array (max 0 (- n 1)) :element-type 'fixnum)))(dotimes (i n)(setf (aref roots i) i(aref nexts i) i))(labels ((%add (src dest cost)"Adds a new edge to the (unfinished) MST."(declare (fixnum src dest cost))(when (> src dest) (rotatef src dest))(setf (aref res-srcs edge-count) src(aref res-dests edge-count) dest(aref res-costs edge-count) (if maximize (- cost) cost)edge-count (+ edge-count 1)))(%merge (root1 root2)"Merges ROOT2 into ROOT1."(loop for v = (aref nexts root2) then (aref nexts v)until (= v root2)do (setf (aref roots v) root1)finally (setf (aref roots v) root1));; meld two cycles(rotatef (aref nexts root1) (aref nexts root2))))(loop for updated = nilwhile (< edge-count (- n 1))do (fill min-costs +inf-cost+);; detect minimum cost edge starting from each connected component(dotimes (u n)(let ((root (aref roots u)))(dolist (edge (aref graph u))(let ((v (funcall vertex-key edge))(cost (funcall cost-key edge)))(declare (fixnum v cost))(when maximize (setq cost (- cost)))(when (and (/= root (aref roots v))(<= cost (aref min-costs root)))(setf (aref min-costs root) cost(aref min-srcs root) u(aref min-dests root) v))))));; merge all the pairs of connected components linked with above;; enumerated edges(dotimes (v n)(let* ((root (aref roots v))(src (aref min-srcs root))(dest (aref min-dests root))(cost (aref min-costs root)))(unless (= cost +inf-cost+) ; can be true if GRAPH is not connected(loop for root2 = (aref roots dest)until (= root root2)do (setq updated t)(%add src dest cost)(%merge root root2)(setq src (aref min-srcs root2)dest (aref min-dests root2)cost (aref min-costs root2))))))while updated)(values (adjust-array res-costs edge-count)(adjust-array res-srcs edge-count)(adjust-array res-dests edge-count)))))(defpackage :cp/mod-power(:use :cl)(:export #:mod-power))(in-package :cp/mod-power)(declaim (inline mod-power))(defun mod-power (base power modulus)"Returns BASE^POWER mod MODULUS. Note: 0^0 = 1.BASE := integerPOWER, MODULUS := non-negative fixnum"(declare ((integer 0 #.most-positive-fixnum) modulus power)(integer base))(let ((base (mod base modulus))(res (mod 1 modulus)))(declare ((integer 0 #.most-positive-fixnum) base res))(loop while (> power 0)when (oddp power)do (setq res (mod (* res base) modulus))do (setq base (mod (* base base) modulus)power (ash power -1)))res));;;;;; Arithmetic operations with static modulus;;;(defpackage :cp/mod-operations(:use :cl)(:export #:define-mod-operations))(in-package :cp/mod-operations);; NOTE: Currently MOD* and MOD+ doesn't apply MOD when the number of;; parameters is one. For simplicity I won't fix it for now.(defmacro define-mod-operations (divisor)(let ((mod* (intern "MOD*"))(mod+ (intern "MOD+"))(incfmod (intern "INCFMOD"))(decfmod (intern "DECFMOD"))(mulfmod (intern "MULFMOD")))`(progn(defun ,mod* (&rest args)(reduce (lambda (x y) (mod (* x y) ,divisor)) args))(defun ,mod+ (&rest args)(reduce (lambda (x y) (mod (+ x y) ,divisor)) args))#+sbcl(eval-when (:compile-toplevel :load-toplevel :execute)(locally (declare (sb-ext:muffle-conditions warning))(sb-c:define-source-transform ,mod* (&rest args)(if (null args)1(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))))))(defpackage :cp/read-fixnum(:use :cl)(:export #:read-fixnum))(in-package :cp/read-fixnum)(declaim (ftype (function * (values fixnum &optional)) read-fixnum))(defun read-fixnum (&optional (in *standard-input*))"NOTE: cannot read -2^62"(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 #\-))(setq 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))))))));;;;;; Disjoint set (union by size & path compression);;;(defpackage :cp/disjoint-set(:use :cl)(:export #:disjoint-set #:make-disjoint-set #:ds-data#:ds-root #:ds-unite! #:ds-connected-p #:ds-size))(in-package :cp/disjoint-set)(defstruct (disjoint-set(:constructor make-disjoint-set(size &aux (data (make-array size :element-type 'fixnum :initial-element -1))))(:conc-name ds-)(:predicate nil)(:copier nil))(data nil :type (simple-array fixnum (*))))(declaim (inline ds-root))(defun ds-root (disjoint-set x)"Returns the root of X."(declare ((mod #.array-total-size-limit) x))(let ((data (ds-data disjoint-set)))(labels ((recur (x)(if (< (aref data x) 0)x(setf (aref data x)(recur (aref data x))))))(recur x))))(declaim (inline ds-unite!))(defun ds-unite! (disjoint-set x1 x2)"Destructively unites X1 and X2 and returns true iff X1 and X2 becomeconnected for the first time."(let ((root1 (ds-root disjoint-set x1))(root2 (ds-root disjoint-set x2)))(unless (= root1 root2)(let ((data (ds-data disjoint-set)));; NOTE: If you want X1 to always be root, just delete this form. (Time;; complexity becomes worse, however.)(when (> (aref data root1) (aref data root2))(rotatef root1 root2))(incf (aref data root1) (aref data root2))(setf (aref data root2) root1)))))(declaim (inline ds-connected-p))(defun ds-connected-p (disjoint-set x1 x2)"Returns true iff X1 and X2 have the same root."(= (ds-root disjoint-set x1) (ds-root disjoint-set x2)))(declaim (inline ds-size))(defun ds-size (disjoint-set x)"Returns the size of the connected component to which X belongs."(- (aref (ds-data disjoint-set)(ds-root disjoint-set x))));;;;;; Sort multiple vectors;;;(defpackage :cp/parallel-sort(:use :cl)(:export #:parallel-sort!))(in-package :cp/parallel-sort);; TODO: throw an error if there are two ore more identical vectors in the given;; vectors(declaim (inline %median3))(defun %median3 (x y z order)(if (funcall order x y)(if (funcall order y z)y(if (funcall order z x)xz))(if (funcall order z y)y(if (funcall order x z)xz))))(defun parallel-sort! (vector order &rest vectors)"Destructively sorts VECTOR w.r.t. ORDER and applies the same permutation toall the vectors in VECTORS.Note: not randomized; shuffle the inputs if necessary"(declare (vector vector))(labels((recur (left right)(when (< left right)(let* ((l left)(r right)(pivot (%median3 (aref vector l)(aref vector (ash (+ l r) -1))(aref vector r)order)))(declare ((integer 0 #.most-positive-fixnum) l r))(loop (loop while (funcall order (aref vector l) pivot)do (incf l 1))(loop while (funcall order pivot (aref vector r))do (decf r 1))(when (>= l r)(return))(rotatef (aref vector l) (aref vector r))(dolist (v vectors)(rotatef (aref v l) (aref v r)))(incf l 1)(decf r 1))(recur left (- l 1))(recur (+ r 1) right)))))(recur 0 (- (length vector) 1))vector))#+sbcl(eval-when (:compile-toplevel :load-toplevel :execute)(locally (declare (sb-ext:muffle-conditions warning))(sb-c:define-source-transform parallel-sort! (vector order &rest vectors)(let ((vec (gensym))(vecs (loop for _ in vectors collect (gensym))))`(let ((,vec ,vector),@(loop for v in vectorsfor sym in vecscollect `(,sym ,v)))(labels((recur (left right)(when (< left right)(let* ((l left)(r right)(pivot (%median3 (aref ,vec l)(aref ,vec (ash (+ l r) -1))(aref ,vec r),order)))(declare ((integer 0 #.most-positive-fixnum) l r))(loop (loop while (funcall ,order (aref ,vec l) pivot)do (incf l 1))(loop while (funcall ,order pivot (aref ,vec r))do (decf r 1))(when (>= l r)(return))(rotatef (aref ,vec l) (aref ,vec r)),@(loop for sym in vecscollect `(rotatef (aref ,sym l) (aref ,sym r)))(incf l 1)(decf r 1))(recur left (- l 1))(recur (+ r 1) right)))))(recur 0 (- (length ,vec) 1)),vec))))));; BEGIN_USE_PACKAGE(eval-when (:compile-toplevel :load-toplevel :execute)(use-package :cp/parallel-sort :cl-user))(eval-when (:compile-toplevel :load-toplevel :execute)(use-package :cp/disjoint-set :cl-user))(eval-when (:compile-toplevel :load-toplevel :execute)(use-package :cp/read-fixnum :cl-user))(eval-when (:compile-toplevel :load-toplevel :execute)(use-package :cp/mod-operations :cl-user))(eval-when (:compile-toplevel :load-toplevel :execute)(use-package :cp/mod-power :cl-user))(eval-when (:compile-toplevel :load-toplevel :execute)(use-package :cp/boruvka :cl-user))(in-package :cl-user);;;;;; Body;;;(define-mod-operations +mod+)(defun main ()(let* ((n (read))(m (read))(x (read))(us (make-array m :element-type 'uint31 :initial-element 0))(vs (make-array m :element-type 'uint31 :initial-element 0))(zs (make-array m :element-type 'uint31 :initial-element 0))(res 0))(declare (uint31 n m x res))(dotimes (i m)(let ((x (- (read-fixnum) 1))(y (- (read-fixnum) 1))(z (read-fixnum)))(setf (aref us i) x(aref vs i) y(aref zs i) z)))(parallel-sort! zs #'< us vs)(let ((dset (make-disjoint-set n))(graph (make-array n :element-type 'list :initial-element nil))(sizes (make-array n :element-type 'uint31 :initial-element 0)))(loop for u across usfor v across vsfor z across zsfor cost = (mod-power x z +mod+)when (ds-unite! dset u v)do (push (cons u cost) (aref graph v))(push (cons v cost) (aref graph u)))(sb-int:named-let dfs ((v 0) (parent -1))(let ((value 1))(loop for (child . cost) in (aref graph v)unless (= child parent)do (dfs child v)(incf value (aref sizes child)))(setf (aref sizes v) value)))#>sizes(sb-int:named-let dfs ((v 0) (parent -1))(loop for (child . cost) of-type (uint31 . uint31) in (aref graph v)for size1 = (aref sizes child)for size2 of-type uint31 = (- n size1)unless (= child parent)do (incfmod res (mod* cost size1 size2))(dfs child v))))(println res)))#-swank (main);;;;;; Test and benchmark;;;#+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 | pathnamenull: 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* (or out (make-string-output-stream)))(res (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))))))(if out res (get-output-stream-string *standard-output*))))#+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(equal "8"(run "3 2 31 2 02 3 1" nil)))(it.bese.fiveam:is(equal "2660500"(run "5 5 51 4 32 4 43 5 72 3 82 3 10" nil)))(it.bese.fiveam:is(equal "524978526"(run "6 8 10000002 6 103 5 114 6 231 3 261 6 305 6 483 5 883 6 100" nil))))