NQueens Project

NQueens Project
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项目平台	BOINC
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项目类别
优化程序	无
计算特点	CPU密集： 支持0分享率： 支持GPU计算：
官方网址	NQueens Project
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NQueens Projecte试图解决象棋中的N皇后问题。你可以在你的计算机上通过下载并且运行免费的程序来参加本项目。

如何加入项目

该项目基于 BOINC 平台，简要的加入步骤如下（已完成的步骤可直接跳过）：

1. 下载并安装 BOINC 的客户端软件（官方下载页面或程序下载）
2. 点击客户端简易视图下的“Add Project”按钮，或高级视图下菜单中的“工具->加入项目”，将显示向导对话框
3. 点击下一步后在项目列表中找到并单击选中 NQueens Project 项目（如未显示该项目，则在编辑框中输入项目网址：http://nqueens.ing.udec.cl/ ），然后点击下一步
4. 输入您可用的电子邮件地址，并设置您在该项目的登录密码（并非您的电子邮件密码）
5. 再次点击下一步，如项目服务器工作正常（并且有适合自身操作系统的计算程序），即已成功加入项目

更详细的加入方法说明，请访问 BOINC 新手指南 或 BOINC 使用教程。

本站推荐您加入 Team China 团队，请访问项目官方网站的 团队检索页面，搜索（Search）并进入 Team China 的团队页面，点击页面中的 Join 并输入用户登录信息即可加入！

BACKGROUND 项目背景

The original eight queens problem:

最初的八皇后问题：

The original eight queens problem consisted of trying to find a way to place eight queens on a chessboard so that no queen would attack any other queen. An alternate way of expressing the problem is to place eight anythings on an eight by eight grid such that none of them share a common row, column, or diagonal.

最初的八皇后问题就是：尝试找出在8×8格的国际象棋棋盘上放置八个皇后，使得各个皇后不会互相攻击（即不在同一行、同一列或同一斜线上）的摆放方法。

It has long been known that there are 92 solutions to the problem. Of these 92, there are 12 distinct patterns. All of the 92 solutions can be transformed into one of these 12 unique patterns using rotations and reflections.

很久以前人们就发现八皇后问题有92种解决方法。在这些办法中，有12种典型。所有92种解都能通过旋转和倒映转换为12种典型之一。

Expanding the problem to N Queens on an NxN chessboard:

将问题拓展到N个皇后在一个NxN棋盘上的情况

If we increase the size of the chessboard beyond 8 rows/columns, we might want to find how many solutions exist for any arbitrary board size N. For example, if N = 10, then there are 724 solutions. Of these, 92 are distinct.

如果将8横8纵的棋盘延伸出去，我们就想去探究当N为某正整数值时，N皇后问题有多少种解法。比如当N = 10时，该问题就有724种解法，其中有92种典型。

Current Knowledge:

目前所知

To date, it's known that for N = 25 there are 2,207,893,435,808,352 solutions. This result were obtained by two diferent sources:

• from Objectweb ProActive INRIA Team (proactive(AT)objectweb.org), Jun 11 2005 [Communicated by Alexandre Di Costanzo (Alexandre.Di_Costanzo(AT)sophia.inria.fr)]. This calculation took about 53 years of CPU time.
• been confirmed by the NTU 25Queen Project at National Taiwan University and Ming Chuan University, led by Yuh-Pyng (Arping) Shieh, Jul 26 2005. This computation took 26613 days CPU time.

I don't know any project trying to solve the N=26 problem.

迄今为止，人们已算出当N = 25时，该问题共有2,207,893,435,808,352种解法。这一结果曾被两次计算出：
1. 2005年6月11日，由Objectweb ProActive INRIA Team算得（代表为Alexandre Di Costanzo）。这次计算花费了相当于大约53年的计算时间。
2. 2005年7月26日，NTU 25Queen小组进行验算，该小组由国立台湾大学和铭传大学建立，由谢育平（Arping Shieh）教授领导。花费约26613天计算时间（73年）。
原作者目前尚未获知有任何项目尝试计算N = 26的情况。

Board	Solutions	Time	Board	Solutions	Time (h:m:s)
1	1		14	365 596	00:00:01
2	0	< 0 s	15	2 279 184	00:00:04
3	0	< 0 s	16	14 772 512	00:00:23
4	2	< 0 s	17	95 815 104	00:02:38
5	10	< 0 s	18	666 090 624	00:19:26
6	4	< 0 s	19	4 968 057 848	02:31:24
7	40	< 0 s	20	39 029 188 884	20:35:06
8	92	< 0 s	21	314 666 222 712	174:53:45
9	352	< 0 s	22	2 691 008 701 644	?
10	724	< 0 s	23	24 233 937 684 440	?
11	2 680	< 0 s	24	227 514 171 973 736	?
12	14 200	< 0 s	25	2 207 893 435 808 352	?
13	73 712	< 0 s	26	?	?

THE PROJECT

What's About?

This project it's an attempt to find the results of the NQueen problem using a BOINC framework for board sizes starting from N=19.

How?

In the N Queen problem the number of solutions and the time taken to solve the whole problem increases in order of n!. So doing it on a sigle ordinary PC it's a marathonic problem after N=19.

But, due the nature of the problem, it's a perfect candidate for paralelization. That's done by placing Queens in all different positions of the first Col/Row of the board, and then solve the results problems. The solution of the original problem it's the sum of all solutions of the subproblems.

For example in the 8 Queens problem we have:

That way, you can solve a N sized board as N N-1 boards (N boards with a queen already placed in the first row/col). And keep on doing that until the problem it's small enough to be computed in a PC in a reasonable time.

Crunching

For each board, the project send jobs for the first n/2 positions of the first Queen, then the number of solutions must be doubled to get the real solution of the problem. In odd n boards the proccess it's similar, compute (n-1)/2 and for the (n+1)/2 position, the second queen it's placed only in the fisrt half of the board.

Currently, the code runing in the project it's based on the Jeff Somers Code[2], modified to work with subboards, checkpoint, and the BOINC framework.