% This program solves the dominant queens 
% problem for the 4x4 board using brute force method.
% It starts by placing one queen (on all places) and checking the 
% number of attacked positions. Then it places two queens
% (tries all possibilities) and checks the attacked positions,
% and so on until the solution is found.
% The solution is found when all positions on the board
% are attacked.

clear
clc

N = 5;
A = zeros(N);

% attackedPositions = zeros(N);
positions = 1 : N^2;
solutions = [];
no_solutions = [];
for numQueens = 1 : N   % i represents the number of queens on the board in the current step

    Q = nchoosek(positions, numQueens);    
    possibilities = numel(Q) / numQueens;
    for i = 1 : possibilities
       temp = Q(i, :);
       A(temp) = 1;
       B = attackedPositions(A, N);
        if sum(sum(B)) == N^2
            solutions(:, :, end+1) = A;
        else
            no_solutions(:, :, end+1) = A;
        end
        A = zeros(N);
    end    
end
solutions(:,:,1) = [];
no_solutions(:, :, 1) = [];