转自:http://blog.csdn.net/itachi85/article/details/6918761

一:什么是ANR

ANR:Application Not Responding,即应用无响应

二:ANR的类型

ANR一般有三种类型:

1:KeyDispatchTimeout(5 seconds) --主要类型

按键或触摸事件在特定时间内无响应

2:BroadcastTimeout(10 seconds)

BroadcastReceiver在特定时间内无法处理完成

3:ServiceTimeout(20 seconds) --小概率类型

Service在特定的时间内无法处理完成

三:KeyDispatchTimeout

Akey or touch event was not dispatched within the specified time(按键或触摸事件在特定时间内无响应)

具体的超时时间的定义在framework下的

ActivityManagerService.java

//How long we wait until we timeout on key dispatching.

staticfinal int KEY_DISPATCHING_TIMEOUT = 5*1000

四:为什么会超时呢?

超时时间的计数一般是从按键分发给app开始。超时的原因一般有两种:

(1)当前的事件没有机会得到处理(即UI线程正在处理前一个事件,没有及时的完成或者looper被某种原因阻塞住了)

(2)当前的事件正在处理,但没有及时完成

五:如何避免KeyDispatchTimeout

1:UI线程尽量只做跟UI相关的工作

2:耗时的工作(比如数据库操作,I/O,连接网络或者别的有可能阻碍UI线程的操作)把它放入单独的线程处理

3:尽量用Handler来处理UIthread和别的thread之间的交互

六:UI线程

说了那么多的UI线程,那么哪些属于UI线程呢?

UI线程主要包括如下:

    1. Activity:onCreate(), onResume(), onDestroy(), onKeyDown(), onClick(),etc

    2. AsyncTask: onPreExecute(), onProgressUpdate(), onPostExecute(), onCancel,etc

    3. Mainthread handler: handleMessage(), post*(runnable r), etc

      七:如何去分析ANR

      先看个LOG:

      04-01 13:12:11.572 I/InputDispatcher( 220): Application is not responding:Window{2b263310com.Android.email/com.android.email.activity.SplitScreenActivitypaused=false}.  5009.8ms since event, 5009.5ms since waitstarted

      04-0113:12:11.572 I/WindowManager( 220): Input event dispatching timedout sending tocom.android.email/com.android.email.activity.SplitScreenActivity

      04-01 13:12:14.123 I/Process(  220): Sending signal. PID: 21404 SIG: 3---发生ANR的时间和生成trace.txt的时间

      04-01 13:12:14.123 I/dalvikvm(21404):threadid=4: reacting to signal 3

      ……

      04-0113:12:15.872 E/ActivityManager(  220): ANR in com.android.email(com.android.email/.activity.SplitScreenActivity)

      04-0113:12:15.872 E/ActivityManager(  220): Reason:keyDispatchingTimedOut

      04-0113:12:15.872 E/ActivityManager(  220): Load: 8.68 / 8.37 / 8.53

      04-0113:12:15.872 E/ActivityManager(  220): CPUusage from 4361ms to 699ms ago ----CPU在ANR发生前的使用情况

      04-0113:12:15.872 E/ActivityManager(  220):   5.5%21404/com.android.email: 1.3% user + 4.1% kernel / faults: 10 minor

      04-0113:12:15.872 E/ActivityManager(  220):   4.3%220/system_server: 2.7% user + 1.5% kernel / faults: 11 minor 2 major

      04-0113:12:15.872 E/ActivityManager(  220):   0.9%52/spi_qsd.0: 0% user + 0.9% kernel

      04-0113:12:15.872 E/ActivityManager(  220):   0.5%65/irq/170-cyttsp-: 0% user + 0.5% kernel

      04-0113:12:15.872 E/ActivityManager(  220):   0.5%296/com.android.systemui: 0.5% user + 0% kernel

      04-0113:12:15.872 E/ActivityManager(  220): 100%TOTAL: 4.8% user + 7.6% kernel + 87% iowait

      04-0113:12:15.872 E/ActivityManager(  220): CPUusage from 3697ms to 4223ms later:-- ANR后CPU的使用量

      04-0113:12:15.872 E/ActivityManager(  220):   25%21404/com.android.email: 25% user + 0% kernel / faults: 191 minor

      04-0113:12:15.872 E/ActivityManager(  220):    16% 21603/__eas(par.hakan: 16% user + 0% kernel

      04-0113:12:15.872 E/ActivityManager(  220):    7.2% 21406/GC: 7.2% user + 0% kernel

      04-0113:12:15.872 E/ActivityManager(  220):    1.8% 21409/Compiler: 1.8% user + 0% kernel

      04-0113:12:15.872 E/ActivityManager(  220):   5.5%220/system_server: 0% user + 5.5% kernel / faults: 1 minor

      04-0113:12:15.872 E/ActivityManager(  220):    5.5% 263/InputDispatcher: 0% user + 5.5% kernel

      04-0113:12:15.872 E/ActivityManager(  220): 32%TOTAL: 28% user + 3.7% kernel

      从LOG可以看出ANR的类型,CPU的使用情况,如果CPU使用量接近100%,说明当前设备很忙,有可能是CPU饥饿导致了ANR

      如果CPU使用量很少,说明主线程被BLOCK了

      如果IOwait很高,说明ANR有可能是主线程在进行I/O操作造成的

      除了看LOG,解决ANR还得需要trace.txt文件,

      如何获取呢?可以用如下命令获取

      1. $chmod 777 /data/anr

      2. $rm /data/anr/traces.txt

      3. $ps

      4. $kill -3 PID

      5. adbpull data/anr/traces.txt ./mytraces.txt

      从trace.txt文件,看到最多的是如下的信息:

      -----pid 21404 at 2011-04-01 13:12:14 -----  
      Cmdline: com.android.email

      DALVIK THREADS:
      (mutexes: tll=0tsl=0 tscl=0 ghl=0 hwl=0 hwll=0)
      "main" prio=5 tid=1NATIVE
        | group="main" sCount=1 dsCount=0obj=0x2aad2248 self=0xcf70
        | sysTid=21404 nice=0 sched=0/0cgrp=[fopen-error:2] handle=1876218976
        atandroid.os.MessageQueue.nativePollOnce(Native Method)
        atandroid.os.MessageQueue.next(MessageQueue.java:119)
        atandroid.os.Looper.loop(Looper.java:110)
       at android.app.ActivityThread.main(ActivityThread.java:3688)
       at java.lang.reflect.Method.invokeNative(Native Method)
        atjava.lang.reflect.Method.invoke(Method.java:507)
        atcom.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:866)
       at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:624)
       at dalvik.system.NativeStart.main(Native Method)

      说明主线程在等待下条消息进入消息队列

      八:Thread状态

      ThreadState (defined at “dalvik/vm/thread.h “)

      THREAD_UNDEFINED = -1, /* makes enum compatible with int32_t */

      THREAD_ZOMBIE = 0, /* TERMINATED */

      THREAD_RUNNING = 1, /* RUNNABLE or running now */

      THREAD_TIMED_WAIT = 2, /* TIMED_WAITING in Object.wait() */

      THREAD_MONITOR = 3, /* BLOCKED on a monitor */

      THREAD_WAIT = 4, /* WAITING in Object.wait() */

      THREAD_INITIALIZING= 5, /* allocated, not yet running */

      THREAD_STARTING = 6, /* started, not yet on thread list */

      THREAD_NATIVE = 7, /* off in a JNI native method */

      THREAD_VMWAIT = 8, /* waiting on a VM resource */

      THREAD_SUSPENDED = 9, /* suspended, usually by GC or debugger */

      九:如何调查并解决ANR

      1:首先分析log

      2: 从trace.txt文件查看调用stack.

      3: 看代码

      4:仔细查看ANR的成因(iowait?block?memoryleak?)

    4. other

      十:案例

      案例1:关键词:ContentResolver in AsyncTask onPostExecute, high iowait

      Process:com.android.email
      Activity:com.android.email/.activity.MessageView
      Subject:keyDispatchingTimedOut
      CPU usage from 2550ms to -2814ms ago:
      5%187/system_server: 3.5% user + 1.4% kernel / faults: 86 minor 20major
      4.4% 1134/com.android.email: 0.7% user + 3.7% kernel /faults: 38 minor 19 major
      4% 372/com.android.eventstream: 0.7%user + 3.3% kernel / faults: 6 minor
      1.1% 272/com.android.phone:0.9% user + 0.1% kernel / faults: 33 minor
      0.9%252/com.android.systemui: 0.9% user + 0% kernel
      0%409/com.android.eventstream.telephonyplugin: 0% user + 0% kernel /faults: 2 minor
      0.1% 632/com.android.devicemonitor: 0.1% user + 0%kernel
      100%TOTAL: 6.9% user + 8.2% kernel + 84%iowait

      -----pid 1134 at 2010-12-17 17:46:51 -----
      Cmd line:com.android.email

      DALVIK THREADS:
      (mutexes: tll=0 tsl=0tscl=0 ghl=0 hwl=0 hwll=0)
      "main" prio=5 tid=1 WAIT
      |group="main" sCount=1 dsCount=0 obj=0x2aaca180self=0xcf20
      | sysTid=1134 nice=0 sched=0/0 cgrp=[fopen-error:2]handle=1876218976
      at java.lang.Object.wait(Native Method)
      -waiting on <0x2aaca218> (a java.lang.VMThread)
      atjava.lang.Thread.parkFor(Thread.java:1424)
      atjava.lang.LangAccessImpl.parkFor(LangAccessImpl.java:48)
      atsun.misc.Unsafe.park(Unsafe.java:337)
      atjava.util.concurrent.locks.LockSupport.park(LockSupport.java:157)
      atjava.util.concurrent.locks.AbstractQueuedSynchronizer.parkAndCheckInterrupt(AbstractQueuedSynchronizer.java:808)
      atjava.util.concurrent.locks.AbstractQueuedSynchronizer.acquireQueued(AbstractQueuedSynchronizer.java:841)
      atjava.util.concurrent.locks.AbstractQueuedSynchronizer.acquire(AbstractQueuedSynchronizer.java:1171)
      atjava.util.concurrent.locks.ReentrantLock$FairSync.lock(ReentrantLock.java:200)
      atjava.util.concurrent.locks.ReentrantLock.lock(ReentrantLock.java:261)
      atandroid.database.sqlite.SQLiteDatabase.lock(SQLiteDatabase.java:378)
      atandroid.database.sqlite.SQLiteCursor.<init>(SQLiteCursor.java:222)
      atandroid.database.sqlite.SQLiteDirectCursorDriver.query(SQLiteDirectCursorDriver.java:53)
      atandroid.database.sqlite.SQLiteDatabase.rawQueryWithFactory(SQLiteDatabase.java:1356)
      atandroid.database.sqlite.SQLiteDatabase.queryWithFactory(SQLiteDatabase.java:1235)
      atandroid.database.sqlite.SQLiteDatabase.query(SQLiteDatabase.java:1189)
      atandroid.database.sqlite.SQLiteDatabase.query(SQLiteDatabase.java:1271)
      atcom.android.email.provider.EmailProvider.query(EmailProvider.java:1098)
      atandroid.content.ContentProvider$Transport.query(ContentProvider.java:187)
      atandroid.content.ContentResolver.query(ContentResolver.java:268)
      atcom.android.email.provider.EmailContent$Message.restoreMessageWithId(EmailContent.java:648)
      atcom.android.email.Controller.setMessageRead(Controller.java:658)
      atcom.android.email.activity.MessageView.onMarkAsRead(MessageView.java:700)
      atcom.android.email.activity.MessageView.access$2500(MessageView.java:98)
      atcom.android.email.activity.MessageView$LoadBodyTask.onPostExecute(MessageView.java:1290)
      atcom.android.email.activity.MessageView$LoadBodyTask.onPostExecute(MessageView.java:1255)
      atandroid.os.AsyncTask.finish(AsyncTask.java:417)
      atandroid.os.AsyncTask.access$300(AsyncTask.java:127)
      atandroid.os.AsyncTask$InternalHandler.handleMessage(AsyncTask.java:429)
      atandroid.os.Handler.dispatchMessage(Handler.java:99)
      atandroid.os.Looper.loop(Looper.java:123)
      atandroid.app.ActivityThread.main(ActivityThread.java:3652)
      atjava.lang.reflect.Method.invokeNative(Native Method)
      atjava.lang.reflect.Method.invoke(Method.java:507)
      atcom.android.internal.os.ZygoteIn

      原因:IOWait很高,说明当前系统在忙于I/O,因此数据库操作被阻塞

      原来:

      finalMessagemessage =Message.restoreMessageWithId(mProviderContext,messageId);

      if(message==null){

      return;

      }

      Accountaccount =Account.restoreAccountWithId(mProviderContext,message.mAccountKey);

      if(account==null){

      return;//isMessagingController returns false for null, but let's make itclear.

      }

      if(isMessagingController(account)){

      newThread(){

      @Override

      publicvoidrun(){

      mLegacyController.processPendingActions(message.mAccountKey);

      }

      }.start();

      }

      解决后:

      newThread() {

      finalMessagemessage =Message.restoreMessageWithId(mProviderContext,messageId);

      if(message==null){

      return;

      }

      Accountaccount =Account.restoreAccountWithId(mProviderContext,message.mAccountKey);

      if(account==null){

      return;//isMessagingController returns false for null, but let's make itclear.

      }

      if(isMessagingController(account)) {

      mLegacyController.processPendingActions(message.mAccountKey);

      }

      }.start();

      关于AsyncTask:http://developer.android.com/reference/android/os/AsyncTask.html

      案例2:关键词:在UI线程进行网络数据的读写

      ANRin process: com.android.mediascape:PhotoViewer (last incom.android.mediascape:PhotoViewer)
      Annotation:keyDispatchingTimedOut
      CPU usage:
      Load: 6.74 / 6.89 / 6.12
      CPUusage from 8254ms to 3224ms ago:
      ovider.webmedia: 4% = 4% user +0% kernel / faults: 68 minor
      system_server: 2% = 1% user + 0%kernel / faults: 18 minor
      re-initialized>: 0% = 0% user + 0%kernel / faults: 50 minor
      events/0: 0% = 0% user + 0%kernel
      TOTAL:7% = 6% user + 1% kernel

      DALVIKTHREADS:
      ""main"" prio=5 tid=3 NATIVE
      |group=""main"" sCount=1 dsCount=0 s=Yobj=0x4001b240 self=0xbda8
      | sysTid=2579 nice=0 sched=0/0cgrp=unknown handle=-1343993184
      atorg.apache.harmony.luni.platform.OSNetworkSystem.receiveStreamImpl(NativeMethod)
      atorg.apache.harmony.luni.platform.OSNetworkSystem.receiveStream(OSNetworkSystem.java:478)
      atorg.apache.harmony.luni.net.PlainSocketImpl.read(PlainSocketImpl.java:565)
      atorg.apache.harmony.luni.net.SocketInputStream.read(SocketInputStream.java:87)
      atorg.apache.harmony.luni.internal.net.www.protocol.http.HttpURLConnection$LimitedInputStream.read(HttpURLConnection.java:303)
      atjava.io.InputStream.read(InputStream.java:133)
      atjava.io.BufferedInputStream.fillbuf(BufferedInputStream.java:157)
      atjava.io.BufferedInputStream.read(BufferedInputStream.java:346)
      atandroid.graphics.BitmapFactory.nativeDecodeStream(Native Method)
      atandroid.graphics.BitmapFactory.decodeStream(BitmapFactory.java:459)
      atcom.android.mediascape.activity.PhotoViewerActivity.getPreviewImage(PhotoViewerActivity.java:4465)
      atcom.android.mediascape.activity.PhotoViewerActivity.dispPreview(PhotoViewerActivity.java:4406)
      atcom.android.mediascape.activity.PhotoViewerActivity.access$6500(PhotoViewerActivity.java:125)
      atcom.android.mediascape.activity.PhotoViewerActivity$33$1.run(PhotoViewerActivity.java:4558)
      atandroid.os.Handler.handleCallback(Handler.java:587)
      atandroid.os.Handler.dispatchMessage(Handler.java:92)
      atandroid.os.Looper.loop(Looper.java:123)
      atandroid.app.ActivityThread.main(ActivityThread.java:4370)
      atjava.lang.reflect.Method.invokeNative(Native Method)
      atjava.lang.reflect.Method.invoke(Method.java:521)
      atcom.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:868)
      atcom.android.internal.os.ZygoteInit.main(ZygoteInit.java:626)
      atdalvik.system.NativeStart.main(Native Method)

      关于网络连接,再设计的时候可以设置个timeout的时间或者放入独立的线程来处理。

      关于Handler的问题,可以参考:http://developer.android.com/reference/android/os/Handler.html

      案例3

      关键词:Memoryleak/Thread leak

      11-1621:41:42.560 I/ActivityManager( 1190): ANR in process:android.process.acore (last in android.process.acore)
      11-1621:41:42.560 I/ActivityManager( 1190): Annotation:keyDispatchingTimedOut
      11-16 21:41:42.560 I/ActivityManager(1190): CPU usage:
      11-16 21:41:42.560 I/ActivityManager( 1190):Load: 11.5 / 11.1 / 11.09
      11-16 21:41:42.560 I/ActivityManager(1190): CPU usage from 9046ms to 4018ms ago:
      11-16 21:41:42.560I/ActivityManager( 1190): d.process.acore:98%= 97% user + 0% kernel / faults: 1134 minor
      11-16 21:41:42.560I/ActivityManager( 1190): system_server: 0% = 0% user + 0% kernel /faults: 1 minor
      11-16 21:41:42.560 I/ActivityManager( 1190): adbd:0% = 0% user + 0% kernel
      11-16 21:41:42.560 I/ActivityManager(1190): logcat: 0% = 0% user + 0% kernel
      11-16 21:41:42.560I/ActivityManager( 1190): TOTAL:100% = 98% user + 1% kernel

      Cmdline: android.process.acore

      DALVIK THREADS:
      "main"prio=5 tid=3 VMWAIT
      |group="main" sCount=1 dsCount=0 s=N obj=0x40026240self=0xbda8
      | sysTid=1815 nice=0 sched=0/0 cgrp=unknownhandle=-1344001376
      atdalvik.system.VMRuntime.trackExternalAllocation(NativeMethod)
      atandroid.graphics.Bitmap.nativeCreate(Native Method)
      atandroid.graphics.Bitmap.createBitmap(Bitmap.java:468)
      atandroid.view.View.buildDrawingCache(View.java:6324)
      atandroid.view.View.getDrawingCache(View.java:6178)
      atandroid.view.ViewGroup.drawChild(ViewGroup.java:1541)
      ……
      atcom.android.internal.policy.impl.PhoneWindow$DecorView.draw(PhoneWindow.java:1830)
      atandroid.view.ViewRoot.draw(ViewRoot.java:1349)
      atandroid.view.ViewRoot.performTraversals(ViewRoot.java:1114)
      atandroid.view.ViewRoot.handleMessage(ViewRoot.java:1633)
      atandroid.os.Handler.dispatchMessage(Handler.java:99)
      atandroid.os.Looper.loop(Looper.java:123)
      atandroid.app.ActivityThread.main(ActivityThread.java:4370)
      atjava.lang.reflect.Method.invokeNative(Native Method)
      atjava.lang.reflect.Method.invoke(Method.java:521)
      atcom.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:868)
      atcom.android.internal.os.ZygoteInit.main(ZygoteInit.java:626)
      atdalvik.system.NativeStart.main(Native Method)

      "Thread-408"prio=5 tid=329 WAIT 
      |group="main" sCount=1 dsCount=0 s=N obj=0x46910d40self=0xcd0548
      | sysTid=10602 nice=0 sched=0/0 cgrp=unknownhandle=15470792
      at java.lang.Object.wait(Native Method)
      -waiting on <0x468cd420> (a java.lang.Object)
      atjava.lang.Object.wait(Object.java:288)
      atcom.android.dialer.CallLogContentHelper$UiUpdaterExecutor$1.run(CallLogContentHelper.java:289)
      atjava.lang.Thread.run(Thread.java:1096)

      分析:

      atdalvik.system.VMRuntime.trackExternalAllocation(NativeMethod)内存不足导致block在创建bitmap上

      **MEMINFO in pid 1360 [android.process.acore] **
      native dalvik other total
      size: 17036 23111 N/A 40147
      allocated: 16484 20675 N/A 37159
      free: 296 2436 N/A 2732

      解决:如果机器的内存族,可以修改虚拟机的内存为36M或更大,不过最好是复查代码,查看哪些内存没有释放

    5. 实际中,还遇到过空闲内存少导致的anr。可以结合anr文件夹里面的screenshot_xxxx.jpg 和snapshot_xxx.log以及traces.txt_xxx.log分析定位

Android ANR分析(1)的更多相关文章

  1. Android ANR 分析解决方法

    一:什么是ANR ANR:Application Not Responding,即应用无响应 二:ANR的类型 ANR一般有三种类型: 1. KeyDispatchTimeout(5 seconds) ...

  2. Android ANR分析(2)

    转自:http://blog.csdn.net/ruingman/article/details/53118202   定义 主线程在特定的时间内没有做完特定的事情 常见的场景 A.input事件超过 ...

  3. android anr分析方法

    目录(?)[+] 案例1关键词ContentResolver in AsyncTask onPostExecute high iowait 案例2关键词在UI线程进行网络数据的读写   一:什么是AN ...

  4. Android ANR分析及解决方案

    一:什么是ANR ANR:Application Not Responding,即应用无响应. ANR定义:在Android上,如果你的应用程序有一段时间响应不够灵敏,系统会向用户显示一个对话框,这个 ...

  5. [转]Android ANR 分析解决方法

    一:什么是ANR ANR:Application Not Responding,即应用无响应 二:ANR的类型 ANR一般有三种类型: 1. KeyDispatchTimeout(5 seconds) ...

  6. android ANR 分析定位问题

    ANR ? android 规定,Activity如果5秒钟之内无法响应屏幕触摸事件或者键盘输入事件,BroadcastReceiver 如果10s中之内还未执行完操作就会出现ANR 定位ANR问题 ...

  7. Android ANR分析(三)

    http://www.jianshu.com/p/8964812972be http://stackoverflow.com/questions/704311/android-how-do-i-inv ...

  8. Android ANR 分析

    首先贴一下trace 文件 Process: com.oppo.reader PID: 20358 Time: 2933175644_1545041895232 Flags: 0x38d83e44 P ...

  9. Android ANR分析

    1.发生anr时手机会生产traces文件 拉取trace文件:adb pull data/anr/traces.txt ./mytraces.txt 保存路径 参考

随机推荐

  1. Android中的“再按一次返回键退出程序”实现

    用户退出应用前给出一个提示是很有必要的,因为可能是用户并不真的想退出,而只是一不小心按下了返回键,大部分应用的做法是在应用退出去前给出一个Dialog,我觉得这样不太友好,用户还得移动手指去按dial ...

  2. PHPExcel类的使用讲解

    下面是总结的几个使用方法 include 'PHPExcel.php'; include 'PHPExcel/Writer/Excel2007.php'; //或者include 'PHPExcel/ ...

  3. 解决vi/vim中粘贴会在行首多很多缩进和空格的问题

    解决vi/vim中粘贴会在行首多很多缩进和空格的问题 secureCRT会将你原来的文本原封不动的按照字符串的样式发送给服务器.所以当你的服务器上的vim设置为autoindent的话,在i模式下,那 ...

  4. 深入理解学习Git工作流

    http://blog.csdn.net/hongchangfirst/article/list/3 //可以看看 http://blog.csdn.net/hongchangfirst/articl ...

  5. HTML精确定位:scrollLeft,scrollWidth,clientWidth,offsetWidth之完全详解

    HTML:scrollLeft,scrollWidth,clientWidth,offsetWidth到底指的哪到哪的距离之完全详解 scrollHeight: 获取对象的滚动高度. scrollLe ...

  6. Leetcode Unique Word Abbreviation

    An abbreviation of a word follows the form <first letter><number><last letter>. Be ...

  7. 【leetcode】Search in Rotated Sorted Array

    Search in Rotated Sorted Array Suppose a sorted array is rotated at some pivot unknown to you before ...

  8. 新建samba配置步骤

    Linux系统默认已经安装了Samba,但是没有安装Samba服务: 1,先查看安装情况:rpm -qa|grep samba 根据系统的安装情况选择下载或者通过光驱安装所缺的rpm包. 我的安装情况 ...

  9. mysql创建用户

    mysql创建用户 创建用于localhost连接的用户并指定密码 mysql> create user 'pcom'@'localhost' identified by 'aaa7B2249' ...

  10. ACM/ICPC 之 分治法入门(画图模拟:POJ 2083)

    题意:大致就是要求画出这个有规律的Fractal图形了= = 例如 1 对应 X 2 对应 X  X   X    X  X 这个题是个理解分治法很典型的例子(详情请参见Code) 分治法:不断缩小规 ...