Henry V: A linear time algorithm for solving the N-Queens Problem using only 5 patterns

It has been known that the time complexity of solving the N-Queens problem, a classic problem with many applications in computer science is Nondeterministic Polynomial (NP). Many different approaches have been proposed for solving the problem since its first presentation in 1848 including genetic algorithms, brute force search and propositional logic statements. In this paper, a novel idea called Layouts have been proposed to solve this problem in θ(n) time complexity. Layouts are patterns for placing queens on the chessboard. Correctness of the proposed approach has been proven for all natural numbers using proof by contradiction and exhaustion. It is shown that by using only 5 layouts, N-Queens with any size can be solved in linear time. The proposed approach has been verified by being applied to 60 different sizes of the N-Queens problem where the size has been chosen by randomly selecting a number between 1000 and 10000.