#-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 (declaim (ftype (function * (values fixnum &optional)) read-fixnum)) (defun read-fixnum (&optional (in *standard-input*)) (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)))))))) ;;; ;;; Lowest common ancestor of tree (or forest) by binary lifting ;;; build: O(nlog(n)) ;;; query: O(log(n)) ;;; ;; PAY ATTENTION TO THE STACK SIZE! THE CONSTRUCTOR DOES DFS. (deftype lca-vertex-number () '(signed-byte 32)) (defstruct (lca-table (:constructor %make-lca-table (size &aux ;; requires 1 + log_2{size-1} (max-level (+ 1 (integer-length (- size 2)))) (depths (make-array size :element-type 'lca-vertex-number :initial-element -1)) (costs (make-array size :element-type '(unsigned-byte 8))) (parents (make-array (list size max-level) :element-type 'lca-vertex-number)))) (:conc-name lca-)) (max-level nil :type (integer 0 #.most-positive-fixnum)) (depths nil :type (simple-array lca-vertex-number (*))) (costs nil :type (simple-array (unsigned-byte 8) (*))) (parents nil :type (simple-array lca-vertex-number (* *)))) (defun make-lca-table (graph weights &key root (key #'identity)) "GRAPH := vector of adjacency lists ROOT := null | non-negative fixnum If ROOT is null, this function traverses each connected component of GRAPH from an arbitrarily picked vertex. Otherwise this function traverses GRAPH only from ROOT; GRAPH must be tree in the latter case." (declare (optimize (speed 3)) (vector graph weights) (function key) ((or null (integer 0 #.most-positive-fixnum)) root)) (let* ((size (length graph)) (lca-table (%make-lca-table size)) (depths (lca-depths lca-table)) (costs (lca-costs lca-table)) (parents (lca-parents lca-table)) (max-level (lca-max-level lca-table))) (labels ((dfs (v prev-v depth cost) (declare (lca-vertex-number v prev-v) (fixnum cost)) (setf (aref depths v) depth) (setf (aref parents v 0) prev-v) (setf (aref costs v) cost) (dolist (node (aref graph v)) (let ((dest (funcall key node))) (declare (lca-vertex-number dest)) (unless (= dest prev-v) (dfs dest v (+ 1 depth) (+ cost (aref weights dest)))))))) (if root (dfs root -1 0 (aref weights 0)) (dotimes (v size) (when (= (aref depths v) -1) (dfs v -1 0 (aref weights v))))) (dotimes (k (- max-level 1)) (dotimes (v size) (if (= -1 (aref parents v k)) (setf (aref parents v (+ k 1)) -1) (setf (aref parents v (+ k 1)) (aref parents (aref parents v k) k))))) lca-table))) (define-condition two-vertices-disconnected-error (simple-error) ((lca-table :initarg :lca-table :accessor two-vertices-disconnected-error-lca-table) (vertex1 :initarg :vertex1 :accessor two-vertices-disconnected-error-vertex1) (vertex2 :initarg :vertex2 :accessor two-vertices-disconnected-error-vertex2)) (:report (lambda (c s) (format s "~W and ~W are disconnected on lca-table ~W" (two-vertices-disconnected-error-vertex1 c) (two-vertices-disconnected-error-vertex2 c) (two-vertices-disconnected-error-lca-table c))))) (defun get-lca (vertex1 vertex2 lca-table) "Returns the lowest common ancestor of the vertices VERTEX1 and VERTEX2." (declare (optimize (speed 3)) ((and lca-vertex-number (integer 0)) vertex1 vertex2)) (let* ((u vertex1) (v vertex2) (depths (lca-depths lca-table)) (parents (lca-parents lca-table)) (max-level (lca-max-level lca-table))) (declare (lca-vertex-number u v)) ;; Ensures depth[u] <= depth[v] (when (> (aref depths u) (aref depths v)) (rotatef u v)) (dotimes (k max-level) (when (logbitp k (- (aref depths v) (aref depths u))) (setf v (aref parents v k)))) (if (= u v) u (loop for k from (- max-level 1) downto 0 unless (= (aref parents u k) (aref parents v k)) do (setq u (aref parents u k) v (aref parents v k)) finally (if (= (aref parents u 0) -1) (error 'two-vertices-disconnected-error :lca-table lca-table :vertex1 vertex1 :vertex2 vertex2) (return (aref parents u 0))))))) (declaim (inline distance-on-tree)) (defun distance-on-tree (u v lca-table weights) "Returns the distance between two vertices U and V." (declare (optimize (speed 3))) (let ((costs (lca-costs lca-table)) (lca (get-lca u v lca-table))) (+ (- (aref costs u) (aref costs lca)) (- (aref costs v) (aref costs lca)) (aref weights lca)))) (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)) (graph (make-array n :element-type 'list :initial-element nil)) (us (make-array n :element-type 'uint8))) (dotimes (i (- n 1)) (let ((a (read-fixnum)) (b (read-fixnum))) (push a (aref graph b)) (push b (aref graph a)))) (dotimes (i n) (setf (aref us i) (read-fixnum))) (let ((lca-table (make-lca-table graph us)) (m (read)) (res 0)) (dotimes (_ m) (let* ((a (read-fixnum)) (b (read-fixnum)) (c (read-fixnum)) (cost (distance-on-tree a b lca-table us))) (incf res (* cost c)))) (println res)))) #-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)))