A Linear Time Pattern Based Algorithm for N-Queens Problem

Abstract

The n-queens problem is the placing of n number of queens on an nxn chessboard so that no two queens attack each other. This problem is important due to various usage fields such as VLSI testing, traffic control job scheduling, data routing, dead-lock or blockage prevention, digital image processing and parallel memory storage schemes mentioned in the literature. Besides, this problem has been used as a benchmark for developing new Artificial Intelligence search techniques. However, it is known that backtracking algorithms, one of the most frequently used algorithms to solve this problem, cannot produce all solutions in large n values due to the exponentially growing time complexity. Therefore, various methods have been proposed for producing one or more solutions, not all solutions for each n value. In this study, a pattern based approach that produces at least one unique solution for all n values (n>3) was detected. By using this pattern, a new algorithm that produces at least one unique solution for even very large n values in linear time was developed. The developed algorithm with О(n) time complexity produces quite faster solution to n-queens problem and even in some values, this algorithm produces (n-1)/2 unique solutions in linear time.