Submission #8339354

---

Source Code Expand

;; -*- 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 (inline relative-error-p))
(defun relative-error<= (x y threshold)
  "Returns true iff the relative error between X and Y is equal to or smaller
than THRESHOLD: i.e. the relative errors of any numbers in the interval [X,
Y] (or [Y, X]) are equal to or smaller than THRESHOLD assuming that the true
value is in the same interval."
  (and (not (zerop x))
       (not (zerop y))
       (<= (abs (/ (- x y) y)) threshold)
       (<= (abs (/ (- x y) x)) threshold)))

(defun error<= (x y threshold)
  "Returns true iff the relative or absolute error between X and Y is equal to
or smaller than threshold."
  (or (<= (abs (- x y)) threshold)
      (relative-error<= x y threshold)))

(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))))))))

(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-modify-macro minf (new-value) min)
(define-modify-macro maxf (new-value) max)

(defun feasible-p (xs ys cs threshold)
  (declare #.OPT
           ((simple-array double-float (*)) xs ys cs)
           (double-float threshold))
  (let ((n (length xs))
        (lx most-negative-double-float)
        (rx most-positive-double-float)
        (ly most-negative-double-float)
        (ry most-positive-double-float))
    (declare (double-float lx rx ly ry))
    (dotimes (i n)
      (let ((x (aref xs i))
            (y (aref ys i))
            (c (aref cs i)))
        (maxf lx (- x (* c threshold)))
        (minf rx (+ x (* c threshold)))
        (maxf ly (- y (* c threshold)))
        (minf ry (+ y (* c threshold)))))
    (and (<= lx rx) (<= ly ry))))

(defun main ()
  (let* ((n (read))
         (xs (make-array n :element-type 'double-float))
         (ys (make-array n :element-type 'double-float))
         (cs (make-array n :element-type 'double-float)))
    (dotimes (i n)
      (setf (aref xs i) (float (read-fixnum) 1d0)
            (aref ys i) (float (read-fixnum) 1d0)
            (aref cs i) (/ (float (read-fixnum) 1d0))))
    (sb-int:named-let bisect ((ng 1d-5) (ok 1d9))
      (if (relative-error<= ok ng 1d-6)
          (println ok)
          (let ((mid (* 0.5d0 (+ ng ok))))
            (if (feasible-p xs ys cs mid)
                (bisect ng mid)
                (bisect mid ok)))))))

#-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)))

;; To run: (5am:run! :sample)
#+swank
(it.bese.fiveam:test :sample
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "2
0 0 1
10 10 1
"
    "5.000000000000000
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "2
0 0 1
10 10 2
"
    "6.666666666666667
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "10
-27 -67 10
59 13 10
14 -15 9
-29 -84 7
-75 -2 2
-12 -74 5
77 31 9
40 64 8
-81 32 1
81 26 5
"
    "582.222222222222222
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "8
-81739 73917 446
42230 30484 911
79354 -50126 200
33440 -47087 651
-73 84114 905
79222 -53608 713
65194 -46284 685
81145 40933 47
"
    "54924095.383189122374461
")))

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