The N-Queens problem (originally the 8-Queens problem) has been studied for more than a century [3, 10, 11, 13]. The problem attracted the attention of several famous mathematicians, including Gauss [10, 13] and P61ya [14]. During the last three decades, the problem has been discussed in the context of computer science and used as an example of backtracking algorithms, permutation generation, the divide and conquer paradigm, program development methodology, constraint satisfaction problems, integer programming, and specification [7]. Some practical applications, such as parallel memory storage schemes, VLSI testing, traffic control, and deadlock prevention are also mentioned in the literature [7, 81. The N-Queens problem is to place N mutually nonattacking queens on an N x N chessboard. In other words, the objective is to place N queens on an N X N chessboard in such a way that no two are on the same row, column or diagonal. Example board configurations for 2-, 3-, and 4-Queens problems are given in FIGURE 1. As can be observed, there is no solution for the 2-Queens and the 3-Queens problem. However, there is a solution for the 4-Queens problem. In this configuration, none of the queens are on the same row, column, or diagonal.
[1]
Bernd-Jürgen Falkowski,et al.
A Note on the Queens' Problem
,
1986,
Inf. Process. Lett..
[2]
Matthias Reichling,et al.
A Simplified Solution of the n Queens Problem
,
1987,
Information Processing Letters.
[3]
Paul J. Campbell,et al.
Gauss and the eight queens problem: A study in miniature of the propagation of historical error
,
1977
.
[4]
W. Ahrens,et al.
Mathematische Unterhaltungen und Spiele
,
2009
.
[5]
Murat M. Tanik,et al.
Different perspectives of the N-Queens problem
,
1992,
CSC '92.
[6]
Suku Nair,et al.
A circulant matrix based approach to storage schemes for parallel memory systems
,
1993,
Proceedings of 1993 5th IEEE Symposium on Parallel and Distributed Processing.
[7]
Zekeriya Aliyazicioglu,et al.
Linear Congruence Equations for the Solutions of the N-Queens Problem
,
1992,
Inf. Process. Lett..
[8]
E. J. Hoffman,et al.
Constructions for the Solution of the m Queens Problem
,
1969
.
[9]
Dean S. Clark.
A Combinatorial Theorem on Circulant Matrices
,
1985
.