NTowersPuzzle( varargin )

function [ indices board ] = NTowersPuzzle( varargin )
% [Indices] = NTowersPuzzle( [entry]);
% [Indices Board] = NTowersPuzzle( [entry]);
% 
% Input formats:
% NTowersPuzzle( [empty] or [invalid] )       =>   default
% NTowersPuzzle( P )                     =>   startposition is (P, P)
% NTowersPuzzle( L, C)              =>   startposition is (L, C)
% NTowersPuzzle( L, C, N)      =>   startposition is (L, C) on N-by-N board
%
% This is my very limited version of the Eight Queens Puzzle (chess).
% It produces a N-number Towers on a N-by-N chess board, ence the name.
% The board is considered to be a N-by-N matrix.
% The pieces positions are signed by ONEs and the positions without pieces
% are signed by ZEROs.
% The user is allowed to decide the position of the starting piece.
% If not empty or invalid input, the default board size is 8-by-8.
% If starting piece position is invalid, it produces random position.
% The function itself may return two different arguments:
% the first is a vector with the coordinates of the pieces;
% the second is the matrix with signed position of the pieces.
% It prints the coordinates and the board.
%
% @ ACx // Janeiro 2013



[startL startC nLC] = treatEntry( varargin );
indices = zeros(1,nLC);
indices(1,startL) = startC;
valid = true;

while valid
    [indices valid] = newplacement( indices, nLC, valid );
end

board = renderboard(indices, nLC);
printpos(indices, nLC);
disp(board)

disp('Thank you for stopping by...')
end

%%

function [a b nLC] = treatEntry( varargin )

a = 0; b = 0; t = 0; cc = 0; nLC = 0;

if nargin == 1
    [~, cc] = size(varargin{1,1});
    
    if cc == 3
        nLC = varargin{1,1}{1,3}(1);
    end
end

if cc > 0
    a = varargin{1,1}{1,1}(1);
    b = a;
    if cc > 1
        b = varargin{1,1}{1,2}(1);
    end
end

if ~isnumeric(nLC) || nLC < 1 || nLC ~= round(nLC)
    if isnumeric(nLC) && nLC < 1
        nLC = abs(nLC);
    end
    if ~isnumeric(nLC) || nLC < 0 || nLC ~= round(nLC)
    nLC = 8;
    end
end
if ~isnumeric(a) || a < 1 || a > nLC || a ~= round(a)
    t = a;
    a = randi(nLC);
    if cc == 1
        b = a;
    end
end
if ~isnumeric(b) || b < 1 || b > nLC || b ~= round(b)
    if b == t
        b = a;
    else
        b = randi(nLC);
    end
end

end

%%

function [indEks valid] = newplacement( indEks, nLC, valid )

npieces = sum(indEks ~= 0);
if npieces == nLC
    valid = false;
    
else
    newindc = randi(nLC);
    while any(newindc == indEks)
        newindc = randi(nLC);
    end
    
    [~, newindl] = min(indEks);
    
    indEks(newindl) = newindc;
end

end

%%

function [board] = renderboard(indeks, nLC)
board = zeros(nLC);
for i = 1:nLC
    board(i,indeks(i)) = 1;
end
end

%%

function printpos(indEks, nLC)
for i = 1:nLC
    fprintf('          L => ( %i , %i ) <= C \n', i, indEks(1,i))
end
end