% 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 = 4;
A = zeros(N);

% attackedPositions = zeros(N);
positions = 1 : N^2;
solutions = [];
no_solutions = [];
solutionsNoAttack = [];
%for numQueens = 1 : N   % i represents the number of queens on the board in the current step
% uncomment the previous line and comment out the next line and the program
% will find the solutions for all number of queens.
    numQueens = 3;
    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;
            numAttacks = find_attacks_gen(A);
            if numAttacks == 0
                solutionsNoAttack(:, :, end+1) = A;
            end
        else
            no_solutions(:, :, end+1) = A;
        end
        A = zeros(N);
%         if (numel(solutionsNoAttack)>0)     % to find all solutions
%             break;                          % comment out these
%         end                                 % three lines.

    end    
%end
solutions(:,:,1) = [];
no_solutions(:, :, 1) = [];
solutionsNoAttack(:, :, 1) = [];