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5、Prime Ring Problem

Problem Description

A ring is compose of n circles as shown in diagram. Put natural number 1, 2, ..., n into each circle separately, and the sum of numbers in two adjacent circles should be a prime.

Note: the number of first circle should always be 1.

Input

n (0 < n < 20).

Output

The output format is shown as sample below. Each row represents a series of circle numbers in the ring beginning from 1 clockwisely and anticlockwisely. The order of numbers must satisfy the above requirements. Print solutions in lexicographical order.

You are to write a program that completes above process.

Print a blank line after each case.

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有很多与数字相关的题目，主要考察基本的编程能力，如果数学比较好，对于解决这些问题有比较好的帮助。下面的题目是学生收集的题目，我进行了讲解。

1、Self Numbers

Description

In 1949 the Indian mathematician D.R. Kaprekar discovered a class of numbers called self-numbers. For any positive integer n, define d(n) to be n plus the sum of the digits of n. (The d stands for digitadition, a term coined by Kaprekar.) For example, d(75) = 75 + 7 + 5 = 87. Given any positive integer n as a starting point, you can construct the infinite increasing sequence of integers n, d(n), d(d(n)), d(d(d(n))), .... For example, if you start with 33, the next number is 33 + 3 + 3 = 39, the next is 39 + 3 + 9 = 51, the next is 51 + 5 + 1 = 57, and so you generate the sequence 33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141, ... The number n is called a generator of d(n). In the sequence above, 33 is a generator of 39, 39 is a generator of 51, 51 is a generator of 57, and so on. Some numbers have more than one generator: for example, 101 has two generators, 91 and 100. A number with no generators is a self-number. There are thirteen self-numbers less than 100: 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, and 97.

Input

No input for this problem.

Output

Write a program to output all positive self-numbers less than 10000 in increasing order, one per line.

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Java中提供了byte、short、int和long表示整数，float和double来表示浮点数，每种类型都有一定的表示范围，当超过了这个范围之后就不能处理了。为了提供对非常大的整数和浮点数的处理，Java提供了BigDecimal和BigInteger。下面的代码演示了BigDecimal和BigInteger的基本用法：

BigDecimal data1 = new BigDecimal("23232123456789.123456789");
BigDecimal data2 = new BigDecimal("23423423123456789.123456789");
BigDecimal data3 = data1.add(data2);
System.out.println(data3.toString());
BigInteger iData1 = new BigInteger("123123123456456789789123456789");
BigInteger iData2 = new BigInteger("12312312323232456456789789123456789");
BigInteger iData3 = iData1.add(iData2);
System.out.println(iData3.toString());

如果不使用这些类库如何实现大整数和大浮点数的计算呢？下面通过ACM模拟题介绍。

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之前在网上找了很多关于TextView的跑马灯效果实现的例子，实现起来都存在一些问题，例如一种是完全重画一个跑马灯，还有就是只设置TextView的相关属性使其具有跑马灯的效果，总的来说这两种方法都是可行的，但是都有其不足之处，第一种太复杂，实现起来比较麻烦，第二种呢，它只能在TextView获得焦点的时候才有跑马灯的效果，这样有时候并不能达到我们所要求的效果。我通过网上的一些例子自己在做了一些改动，就实现了现在不用获取焦点也能“跑”起来的效果。

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搜集于网络，整理如下：

//调用浏览器
Uri uri = Uri.parse("");
Intent it  = new Intent(Intent.ACTION_VIEW,uri);
startActivity(it);

//显示某个坐标在地图上

Uri uri = Uri.parse("geo:38.899533,-77.036476");
Intent it = new Intent(Intent.Action_VIEW,uri);
startActivity(it);

//显示路径
Uri uri = Uri.parse("http://maps.google.com/maps?f=d&saddr=startLat%20startLng&daddr=endLat%20endLng&hl=en");
Intent it = new Intent(Intent.ACTION_VIEW,URI);
startActivity(it);

//拨打电话
Uri uri = Uri.parse("tel:10086");
Intent it = new Intent(Intent.ACTION_DIAL, uri);
startActivity(it);

Uri uri = Uri.parse("tel.10086");
Intent it =new Intent(Intent.ACTION_CALL,uri);
//需要添加 <uses-permission id="android.permission.CALL_PHONE" /> 这个权限到androidmanifest.xml

//发送短信或彩信
Intent it = new Intent(Intent.ACTION_VIEW);
it.putExtra("sms_body", "The SMS text");
it.setType("vnd.android-dir/mms-sms");
startActivity(it);

//发送短信
Uri uri = Uri.parse("smsto:10086");
Intent it = new Intent(Intent.ACTION_SENDTO, uri);
it.putExtra("sms_body", "cwj");
startActivity(it);

//发送彩信
Uri uri = Uri.parse("content://media/external/images/media/23");
Intent it = new Intent(Intent.ACTION_SEND);
it.putExtra("sms_body", "some text");
it.putExtra(Intent.EXTRA_STREAM, uri);
it.setType("image/png");
startActivity(it);

//发送邮件
Uri uri = Uri.parse("mailto:android123@163.com");
Intent it = new Intent(Intent.ACTION_SENDTO, uri);
startActivity(it);

Intent it = new Intent(Intent.ACTION_SEND);
it.putExtra(Intent.EXTRA_EMAIL, android123@163.com);
it.putExtra(Intent.EXTRA_TEXT, "The email body text");
it.setType("text/plain");
startActivity(Intent.createChooser(it, "Choose Email Client"));

Intent it=new Intent(Intent.ACTION_SEND);
String[] tos={"me@abc.com"};
String[] ccs={"you@abc.com"};
it.putExtra(Intent.EXTRA_EMAIL, tos);
it.putExtra(Intent.EXTRA_CC, ccs);
it.putExtra(Intent.EXTRA_TEXT, "The email body text");
it.putExtra(Intent.EXTRA_SUBJECT, "The email subject text");
it.setType("message/rfc822");
startActivity(Intent.createChooser(it, "Choose Email Client"));

//播放媒体文件
Intent it = new Intent(Intent.ACTION_VIEW);
Uri uri = Uri.parse("file:///sdcard/cwj.mp3");
it.setDataAndType(uri, "audio/mp3");
startActivity(it);

Uri uri = Uri.withAppendedPath(MediaStore.Audio.Media.INTERNAL_CONTENT_URI, "1");
Intent it = new Intent(Intent.ACTION_VIEW, uri);
startActivity(it);

//卸载APK
Uri uri = Uri.fromParts("package", strPackageName, null);
Intent it = new Intent(Intent.ACTION_DELETE, uri);
startActivity(it);

//卸载apk 2
Uri uninstallUri = Uri.fromParts("package", "xxx", null);
returnIt = new Intent(Intent.ACTION_DELETE, uninstallUri);

//安装APK
Uri installUri = Uri.fromParts("package", "xxx", null);
returnIt = new Intent(Intent.ACTION_PACKAGE_ADDED, installUri);

//播放音乐
Uri playUri = Uri.parse("file:///sdcard/download/sth.mp3");
returnIt = new Intent(Intent.ACTION_VIEW, playUri);

//发送附近
Intent it = new Intent(Intent.ACTION_SEND);
it.putExtra(Intent.EXTRA_SUBJECT, "The email subject text");
it.putExtra(Intent.EXTRA_STREAM, "file:///sdcard/cwj.mp3");
sendIntent.setType("audio/mp3");
startActivity(Intent.createChooser(it, "Choose Email Client"));

//market上某个应用信，pkg_name就是应用的packageName
Uri uri = Uri.parse("market://search?q=pname:pkg_name");
Intent it = new Intent(Intent.ACTION_VIEW, uri);
startActivity(it);

//market上某个应用信息，app_id可以通过www网站看下
Uri uri = Uri.parse("market://details?id=app_id");
Intent it = new Intent(Intent.ACTION_VIEW, uri);
startActivity(it);

//调用搜索
Intent intent = new Intent();
intent.setAction(Intent.ACTION_WEB_SEARCH);
intent.putExtra(SearchManager.QUERY,"android123")
startActivity(intent);

//调用分享菜单
Intent intent=new Intent(Intent.ACTION_SEND);   
intent.setType("text/plain");  //分享的数据类型 
intent.putExtra(Intent.EXTRA_SUBJECT, "subject");  //主题 
intent.putExtra(Intent.EXTRA_TEXT,  "content");  //内容 
startActivity(Intent.createChooser(intent, "title"));  //目标应用选择对话框的标题