查看“NQueens Project”的源代码

{{Infobox Project
| name =NQueens Project
| logo =
| screenshot =无屏保图形
| caption =
| developer =
| released =
| operating system =[[Image:Windows.png]]
| platform =BOINC
| program info =
| work unit info =
| status =已关闭
| genre =
| optimization =无
| website =http://nqueens.ing.udec.cl/
}}
'''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。


{{JoinBoincProject
|Project=NQueens Project
|URL=http://nqueens.ing.udec.cl/
}}

==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。

{| class="wikitable" border="1"
|-
|  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==
 关于本项目

===What's About?===
 研究对象是什么？

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. 
 本项目是一次探究N皇后问题的尝试。使用BOINC框架。从N=19的情况开始。

===How?===
 如何研究？
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. 

 在对N皇后问题的研究过程中，解法的数量和解题所需时间以阶乘形式（n！）递增，所以在单台PC上解决N=19以后的计算将会是一场超级马拉松。
 然而，拜其特性所赐，这个问题非常适合并行计算（即在棋盘的第一纵或横上摆放皇后，然后判断随之而来的情形，每一分步中所获得的结果之和即为所求）。
 以8皇后问题为例：
 你可以将NxN棋盘视作N个（N—1）x（N—1）棋盘（这些棋盘上已经在一个角落放置了一个皇后）。不断重复该过程，直到问题适合单台PC以合理的时间完成处理。

===Crunching===
 数据处理

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. 

 就每种棋盘而言，本项目发送关于首个皇后附近前n / 2个位置的任务包，所以所得结果为真实结果的一半。对格子数为奇数的棋盘也一样，先计算首个皇后附近的(n-1)/2，然后是剩下的(n+1)/2，第二个皇后只放置在离首个皇后较近的一半位置。
 目前，本项目所用代码以Jeff Somers Code为基础，并加以修改以适应BOINC框架。


{{BOINC topics}}

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