Submission #6722764

---

Source Code Expand

;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (ql:quickload '(:cl-debug-print :fiveam))
  #-swank (set-dispatch-macro-character #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil (values) t))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
;; Treap accessible by index (O(log(n))).
;; Virtually it works like std::set of C++ or TreeSet of Java. 

;; Note:
;; - You shouldn't insert duplicate keys into a treap unless you know what you
;; are doing.
;; - You cannot rely on the side effect when you call any destructive operations
;; on a treap. Always use the returned value.
;; - An empty treap is NIL.

(defstruct (treap (:constructor %make-treap (key priority &key left right (count 1)))
                  (:copier nil)
                  (:conc-name %treap-))
  (key 0 :type fixnum)
  (priority 0 :type (integer 0 #.most-positive-fixnum))
  (count 0 :type (integer 0 #.most-positive-fixnum))
  (left nil :type (or null treap))
  (right nil :type (or null treap)))

(declaim (inline treap-count))
(defun treap-count (treap)
  "Returns the size of the (nullable) TREAP."
  (declare ((or null treap) treap))
  (if (null treap)
      0
      (%treap-count treap)))

(declaim (inline update-count))
(defun update-count (treap)
  (declare (treap treap))
  (setf (%treap-count treap)
        (+ 1
           (treap-count (%treap-left treap))
           (treap-count (%treap-right treap)))))

(declaim (inline treap-bisect-left)
         (ftype (function * (values (integer 0 #.most-positive-fixnum) t &optional)) treap-bisect-left))
(defun treap-bisect-left (value treap &key (order #'<))
  "Returns the smallest index and the corresponding key that satisfies
TREAP[index] >= VALUE. Returns the size of TREAP and VALUE if TREAP[size-1] <
VALUE."
  (declare (function order))
  (labels ((recur (count treap)
             (declare ((integer 0 #.most-positive-fixnum) count))
             (cond ((null treap) (values nil nil))
                   ((funcall order (%treap-key treap) value)
                    (recur count (%treap-right treap)))
                   (t (let ((left-count (- count (treap-count (%treap-right treap)) 1)))
                        (multiple-value-bind (idx key)
                            (recur left-count (%treap-left treap))
                          (if idx
                              (values idx key)
                              (values left-count (%treap-key treap)))))))))
    (declare (ftype (function * (values t t &optional)) recur))
    (multiple-value-bind (idx key)
        (recur (treap-count treap) treap)
      (if idx
          (values idx key)
          (values (treap-count treap) value)))))

(declaim (inline treap-split)
         (ftype (function * (values (or null treap) (or null treap) &optional)) treap-split))
(defun treap-split (key treap &key (order #'<))
  "Destructively splits the TREAP with reference to KEY and returns two treaps,
the smaller sub-treap (< KEY) and the larger one (>= KEY)."
  (declare (function order)
           ((or null treap) treap))
  (labels ((recur (treap)
             (cond ((null treap)
                    (values nil nil))
                   ((funcall order (%treap-key treap) key)
                    (multiple-value-bind (left right) (recur (%treap-right treap))
                      (setf (%treap-right treap) left)
                      (update-count treap)
                      (values treap right)))
                   (t
                    (multiple-value-bind (left right) (recur (%treap-left treap))
                      (setf (%treap-left treap) right)
                      (update-count treap)
                      (values left treap))))))
    (recur treap)))

(declaim (inline treap-insert))
(defun treap-insert (key treap &key (order #'<))
  "Destructively inserts KEY into TREAP and returns the resultant treap."
  (declare ((or null treap) treap)
           (function order))
  (let ((node (%make-treap key (random most-positive-fixnum))))
    (labels ((recur (treap)
               (declare (treap node))
               (cond ((null treap) node)
                     ((> (%treap-priority node) (%treap-priority treap))
                      (setf (values (%treap-left node) (%treap-right node))
                            (treap-split (%treap-key node) treap :order order))
                      (update-count node)
                      node)
                     (t
                      (if (funcall order (%treap-key node) (%treap-key treap))
                          (setf (%treap-left treap)
                                (recur (%treap-left treap)))
                          (setf (%treap-right treap)
                                (recur (%treap-right treap))))
                      (update-count treap)
                      treap))))
      (recur treap))))

(defun treap-map (function treap)
  "Successively applies FUNCTION to TREAP[0], ..., TREAP[SIZE-1]. FUNCTION must
take one argument."
  (declare (function function))
  (when treap
    (treap-map function (%treap-left treap))
    (funcall function (%treap-key treap))
    (treap-map function (%treap-right treap))))

(defmethod print-object ((object treap) stream)
  (print-unreadable-object (object stream :type t)
    (let ((init t))
      (treap-map (lambda (key)
                   (if init
                       (setq init nil)
                       (write-char #\  stream))
                   (write key :stream stream))
                 object))))

(define-condition invalid-treap-index-error (type-error)
  ((treap :initarg :treap :reader invalid-treap-index-error-treap)
   (index :initarg :index :reader invalid-treap-index-error-index))
  (:report
   (lambda (condition stream)
     (format stream "Invalid index ~W for treap ~W."
             (invalid-treap-index-error-index condition)
             (invalid-treap-index-error-treap condition)))))

(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))))))))

(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+ 998244353)

;; Body
;;;
;;; Arithmetic operations with static modulus
;;;

(defmacro define-mod-operations (&optional (divisor 1000000007))
  `(progn
     (defun mod* (&rest args)
       (reduce (lambda (x y) (mod (* x y) ,divisor)) args))

     (sb-c:define-source-transform mod* (&rest args)
       (if (null args)
           1
           (reduce (lambda (x y) `(mod (* ,x ,y) ,',divisor)) args)))

     (defun mod+ (&rest args)
       (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 divisor)
       (lambda (x y divisor) (mod (+ x y) divisor)))

     (define-modify-macro decfmod (delta divisor)
       (lambda (x y divisor) (mod (- x y) divisor)))))

(define-mod-operations 998244353)

(defun main ()
  (declare #.OPT
           (inline sort))
  (let* ((n (read))
         (xs (make-array n :element-type 'int32))
         (ys (make-array n :element-type 'int32))
         (powers (make-array 200001 :element-type 'uint32))
         (ord-xs (make-array n :element-type 'uint32))
         (res 0))
    (declare (uint32 n res)
             ((simple-array uint32 (*)) ord-xs))
    ;; construct table of 2^n
    (setf (aref powers 0) 1)
    (loop for i from 1 below (length powers)
          do (setf (aref powers i)
                   (mod* 2 (aref powers (- i 1)))))
    (dotimes (i n)
      (setf (aref xs i) (read-fixnum)
            (aref ys i) (read-fixnum)))
    (dotimes (i n)
      (setf (aref ord-xs i) i))
    (setf ord-xs (sort ord-xs (lambda (i j) (< (aref xs i) (aref xs j)))))
    ;; L R U D
    (incfmod res (mod* (- n 4) (- (aref powers n) 1)) +mod+)
    ;; LU LD
    (let (treap)
      (loop for i from 0 below n
            do (let* ((ord (aref ord-xs i))
                      (y (aref ys ord))
                      (ld (treap-bisect-left y treap))
                      (lu (- (treap-count treap) ld)))
                 (incfmod res (aref powers ld) +mod+)
                 (incfmod res (aref powers lu) +mod+)
                 (setq treap (treap-insert y treap)))))
    ;; RU RD
    (let (treap)
      (loop for i from (- n 1) downto 0
            do (let* ((ord (aref ord-xs i))
                      (y (aref ys ord))
                      (rd (treap-bisect-left y treap))
                      (ru (- (treap-count treap) rd)))
                 (incfmod res (aref powers rd) +mod+)
                 (incfmod res (aref powers ru) +mod+)
                 (setq treap (treap-insert y treap)))))
    (println res)))

#-swank (main)

Submission Info

Judge Result