function [dims, isndarray, maxlevel, count] = nestbracket2dim(str, brackets, testndarray)
%
% [dims, isndarray, maxlevel, count] = nestbracket2dim(str,brackets)
%
% Extracting the dimension vector of a JSON string formatted array
% by analyzing the pairs of opening/closing bracket tokenss; this function
% only returns valid dimension information when the array is an N-D array
%
% authors:Qianqian Fang (q.fang <at> neu.edu)
%
% input:
%      str: a string-formatted JSON array using square-brackets for enclosing
%           elements and comma as separators between elements
%      brackets: (optional), a string of length 2, with the first character
%               being the opening token and the 2nd being the closing token.
%               if not given, brackets is set to '[]' to find matching square-brackets;
%               for example, '{}' looks for a matching closing curly-bracket in
%               the string key(pos(startpos,:end))
%      testndarray: (optional), 1 to test if the input string contains an
%               ND array, i.e. with uniform element lengths (recursively)
%
% output:
%      dims: the speculated dimension vector with the length matching the maximum
%            depth of the embedded bracket pairs. When the input string encodes an
%            N-D array, the dims vector contains all integers; however, returning
%            an all-integer dims vector does not mean the array is
%            rectangular. if testndarray is set to 1, dims returns isndarray
%      isndarray: 1 to indicate the input string contains an ND array,
%            otherwise, 0
%      maxlevel: return the depth of the enclosed brackets in the string, i.e. the
%            length of the dims vector.
%      count: the relative depth from the level 0 - scanning from the left
%            to right of the string, an opening token increases the level by 1
%            and a closing token decreases the level by 1; a zero indicates
%            the positions of a matching bracket of the same level.
%
% example:
%      str='[[ [1,2,3], [4,2,1]], [ [10,1,0], [2,5,10]] ]'; % an N-D array
%      [dim,dep]=nestbracket2dim(str)
%      str='[[ [1,2,3], [4,2,1]], [ [10,1,0], [2,5]] ]'; % an invalid N-D array
%      [dim,dep]=nestbracket2dim(str)
%
% license:
%     BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
%
% -- this function is part of JSONLab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
%

if (nargin < 2)
    brackets = '[]';
end
str = str(str == brackets(1) | str == brackets(2) | str == ',');
count = cumsum(str == brackets(1)) - cumsum(str == brackets(2));
isndarray = testuniform(count, max(count));
if (nargin > 2 && testndarray)
    dims = isndarray;
    return
end
maxlevel = max(count);
dims = histc(count, 1:maxlevel);
dims(1:end - 1) = dims(1:end - 1) * 0.5;
dims(2:end) = dims(2:end) ./ dims(1:end - 1);
dims = fliplr(dims);

function isndarray = testuniform(count, maxval)
isndarray = false;
if (length(count) > 2)
    idx = find(count(2:end) == count(1), 1);
    if (idx == length(count) - 2 && count(1) < maxval)
        isndarray = testuniform(count(2:end - 1), maxval);
        return
    end
    if (~isempty(idx) && mod(length(count) - 1, idx + 1) == 0)
        count2d = reshape(count(1:end - 1), idx + 1, []);
        if (all(diff(count2d') == 0))
            isndarray = true;
        end
    end
end