This problem is to find an arrangement of N queens on a chess board, such that no queen can attack any other queens on the board.
The chess queens can attack in any direction as horizontal, vertical, horizontal and diagonal way.
A binary matrix is used to display the positions of N Queens, where no queens can attack other queens.
1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0
Hill Climbing with random restart: This is a local search algorithm. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by incrementally changing a single element of the solution. If the change produces a better solution, an incremental change is made to the new solution, repeating until no further improvements can be found.
The hill-climbing algorithms often fail to find a goal when one exists because they can get stuck on local maxima. Random-restart can be used to solve the problem of local maxima, as it conducts a series of hill-climbing searches from randomly generated initial states, until a goal is found.