英语翻译The puzzle Sudoku has become the passion ofmany people t

英语翻译
The puzzle Sudoku has become the passion of
many people the world over in the past few years.The interesting fact about
Sudoku is that it is a trivial puzzle to solve.The reason it is trivial to
solve is that an algorithm exists for Sudoku solutions.
The algorithm is a tree-based search
algorithm based on backtracking in a tree until a solution is found.If all a
person needs to do is sit down at theirpersonal computer,punch in the numbers
given in the puzzle,and then watch a computer program compute the solution,we
can reasonably ask why a person would bother to struggle to solve Sudoku puzzles.
The reason is that people enjoy struggling with pencil and paper to work out
Sudoku solutions.Herzberg and Murty (2007,p.716) give two reasons for the
enjoyment of this struggle:
First,it is sufficiently difficult to posea serious mental challenge for anyone attempting to do the
puzzle.Secondly,simply by scanning rows
and columns,it is easy to enter the “missing colors”,and this gives the
solver some encouragement to persist.
This paper develops an algorithm for
solving any Sudoku puzzle by pencil and paper,especially the ones classified
as diabolical.
Definition of the Sudoku Board
Sudoku is played on a 9 × 9 board.There
are eighty-one cells on the board,which is broken down into nine 3 × 3
subboards that do not overlap.We call these subboards boxes and number them
from 1 to 9 in
typewriter order beginning in the upper left-hand corner of the board,as displayed
in Figure 1.
The notation for referring to a particular
cell on the board is to give the row number followed by the column number.For
example,the notation c (6,7)—where c denotes cell—denotes the cell at the
intersection of row 6 and column 7.The theory we develop in the next section
uses the widely known concept of matching numbers across cells.Various
authors,as suits their whim,name matching numbers differently.For example,Sheldon
(2006,p.xiv) names them partnerships,whereas Mepham (2005,p.9) names the
concept number sharing.Here,we will use the name preemptive sets,which is
more precise from a mathematical point of view.The theory developed here
applies to Sudoku boards of all sizes.

The puzzle Sudoku has become the passion of many people the world over in the past few years.The interesting fact about Sudoku is that it is a trivial puzzle to solve.The reason it is trivial to solve is that an algorithm exists for Sudoku solutions.
数独拚图游戏在过去几年已经受到世界上很多人的热爱.有趣的是,拆解数独其实是多余之举,因为已经有现成的算法可以拆解数独类拚图游戏.
The algorithm is a tree-based search algorithm based on backtracking in a tree until a solution is found.If all a person needs to do is sit down at their personal computer,punch in the numbers given in the puzzle,and then watch a computer program compute the solution,we can reasonably ask why a person would bother to struggle to solve Sudoku puzzles.The reason is that people enjoy struggling with pencil and paper to work out Sudoku solutions.Herzberg and Murty (2007,p.716) give two reasons for the enjoyment of this struggle:
该算法是一个以“树图”为基础的算法,它沿着“树图”往后搜寻,直至找到答案为止.如果我们只需要坐在个人计算机前,把拚图游戏所给定的几个数字输入去,然后便可以看着电脑程式计算出答案的话,我们便不禁要问：为甚么还有人耐烦去自己拆解数独拚图?个中原因在于：人们亲自动手拆解数独问题,会乐在其中.Herzberg 和 Murty（2007年的著作第716页）提供了两个乐在其中的原因：
First,it is sufficiently difficult to pose a serious mental challenge for anyone attempting to do the puzzle.Secondly,simply by scanning rows and columns,it is easy to enter the “missing colors”,and this gives the solver some encouragement to persist.
首先,这种游戏有足够难度可以向任何试图拆解的人提出严苛的智力挑战.第二,只需要简单地瞄一下各个横列和直行,便可以轻易地填上“缺失的颜色”；这样便足以鼓励试图拆解的人继续下去.
This paper develops an algorithm for solving any Sudoku puzzle by pencil and paper,especially the ones classified as diabolical.
本文旨在开发出一套算法,务求能够用纸和笔去拆解任何数独拚图,特别是属于 “恶魔” 类的数独拚图.
Definition of the Sudoku Board
数独图版的定义
Sudoku is played on a 9 × 9 board.There are eighty-one cells on the board,which is broken down into nine 3 × 3 subboards that do not overlap.We call these subboards boxes and number them from 1 to 9 in typewriter order beginning in the upper left-hand corner of the board,as displayed in Figure 1.The notation for referring to a particular cell on the board is to give the row number followed by the column number.For example,the notation c (6,7)—where c denotes cell—denotes the cell at the intersection of row 6 and column 7.
数独是在一块 9 格乘 9 格的图版上进行.图版上合共有八十一格,再细分成九块 3 格乘 3 格的小图版,互不重叠.我们把这些小图版称为 “框”,并从图版的左上角开始,按照打字机打字的顺序,为这些 “框” 分别编上 1 至 9 的编号,一如图 1 所示.对于图版上某个特定格子的标示和指称方法,是先说出其所在的横列数目,然后再在后面加上直行数目.例如 c(6,7) 这个标志,当中的 c 是格子的意思,而整个标志则表示位于第 6 列、第 7 行交界处的格子.
The theory we develop in the next section uses the widely known concept of matching numbers across cells.Various authors,as suits their whim,name matching numbers differently.For example,Sheldon (2006,p.xiv) names them partnerships,whereas Mepham (2005,p.9) names the concept number sharing.Here,we will use the name preemptive sets,which is more precise from a mathematical point of view.The theory developed here applies to Sudoku boards of all sizes.我们在下一章将会开发的理论,运用了已广为人知的概念,即：在多个格子中找出匹配数字.对于这个概念,每个作者都按自己的想法来为它名命.例如 Sheldon（2006 年的著作第 xiv 页）称它为 “伙伴”,而 Mepham（2005 年的著作第 9 页）把它叫作 “数字分享”.我们则会称之为 “占先数组”,因为从数学的观点,这个叫法更准确.这里所发展出的理论,适用于各种大小的数独图版.