;; -*- 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 (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) ;;; ;;; Disjoint set by Union-Find algorithm ;;; (defstruct (disjoint-set (:constructor make-disjoint-set (size &aux (data (make-array size :element-type 'int32 :initial-element -1)))) (:conc-name ds-)) (data nil :type (simple-array int32 (*)))) (declaim (ftype (function * (values (mod #.array-total-size-limit) &optional)) ds-root)) (defun ds-root (x disjoint-set) "Returns the root of X." (declare #.OPT ((mod #.array-total-size-limit) x)) (let ((data (ds-data disjoint-set))) (if (< (aref data x) 0) x (setf (aref data x) (ds-root (aref data x) disjoint-set))))) (declaim (inline ds-unite!)) (defun ds-unite! (x1 x2 disjoint-set) "Destructively unites X1 and X2 and returns true iff X1 and X2 become connected for the first time." (let ((root1 (ds-root x1 disjoint-set)) (root2 (ds-root x2 disjoint-set))) (unless (= root1 root2) (let ((data (ds-data disjoint-set))) ;; ensure the size of root1 >= the size of root2 (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 (x1 x2 disjoint-set) "Returns true iff X1 and X2 have the same root." (= (ds-root x1 disjoint-set) (ds-root x2 disjoint-set))) (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)))))))) ;;; ;;; Strongly connected components of directed graph ;;; (defstruct (scc (:constructor %make-scc (graph revgraph posts components sizes count))) (graph nil :type (simple-array list (*))) ;; reversed graph (revgraph nil :type (simple-array list (*))) ;; vertices by post-order DFS posts ;; components[i] := strongly connected component of the i-th vertex (components nil :type (simple-array (unsigned-byte 32) (*))) ;; sizes[k] := size of the k-th strongly connected component (sizes nil :type (simple-array (unsigned-byte 32) (*))) ;; the total number of strongly connected components (count 0 :type (unsigned-byte 32))) (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)) (defun make-scc (graph &optional revgraph) "GRAPH := vector of adjacency lists REVGRAPH := NIL | reversed graph of GRAPH" (declare #.OPT ((simple-array list (*)) graph) ((or null (simple-array list (*))) 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 '(unsigned-byte 32))) (components (make-array n :element-type '(unsigned-byte 32))) (sizes (make-array n :element-type '(unsigned-byte 32) :initial-element 0)) (pointer 0) (ord 0) ; ordinal number for a strongly connected component ) (declare ((unsigned-byte 32) 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)))) (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)))) (defconstant +mod+ 1000000007) ;;; ;;; Body ;;; (defun main () (declare #.OPT) (let* ((n (read)) (m (read)) (dset (make-disjoint-set (+ n n m))) (graph (make-array (* 4 n) :element-type 'list :initial-element nil))) (declare (uint16 n m)) (dotimes (i n) (let* ((l (read-fixnum)) (r (read-fixnum))) (loop for j from l to r do (ds-unite! i (+ j (* 2 n)) dset)) (loop for j from (- m r 1) to (- m l 1) do (ds-unite! (+ i n) (+ j (* 2 n)) dset)))) (labels ((negate (x) (declare (uint16 x)) (mod (+ x (* 2 n)) (* 4 n))) (add-clause! (literal1 literal2 bool1 bool2) (unless bool1 (setq literal1 (negate literal1))) (unless bool2 (setq literal2 (negate literal2))) (push literal2 (aref graph (negate literal1))) (push literal1 (aref graph (negate literal2))))) (gc :full t) (dotimes (x (* 2 n)) (loop for y from (+ x 1) below (* 2 n) do (when (ds-connected-p x y dset) (add-clause! x y nil nil)))) (dotimes (x n) (add-clause! x (+ x n) t t) (add-clause! x (+ x n) nil nil)) (let* ((scc (make-scc graph)) (comps (scc-components scc))) (write-line (if (loop for x below (* 2 n) thereis (= (aref comps x) (aref comps (+ x (* 2 n))))) "NO" "YES")))))) #-swank (main)