Extract balanced parantheses from String

Question

Hi community,
I am getting back to work on LabVIEW after long.
Currently implementing an algorithm and I need to work with tree like structures presented in the form of strings with parantheses.
So, for example, a string such as A(B(c,d),P(q,r),U(V(w),X(y,z,o))) has a tree with root node A, and there are three children of A, namely B, P, U, and all of them also represent a tree (sub-tree of the original tree A). So that, B is the root of the sub-tree where c and d are the two nodes. U also has two children that represent individual sub-trees, namely V (with one child) and X (with three children).
Although, there is one detail, which may actually help the process a bit. The trees are simplified, so that all the nodes that represent some tree (or sub-tree) are just called S.
To extract all these trees, I am going to check one element at a time and then build the sub-trees one by one.
Just thought to ask here if someone has a better idea (or if some function from OpenG may help here if someone has done something similar). Always ready to learn!
Thanks ahead!
Vaibhav

Answer 1

Ok, I just finished the function to validate the input string, extract all the valid sub-trees and list them.
The VI and the required Sub-VI are in the attachment.
This is just to show what output do I need. Any suggestions to improvements are most welcome.
And if someone finds this solution as useful, I would appreciate acknowledgement of that too (Kudos ).
But my main objective is to know how this could be done in a smarter way.
Try to play with the function with different valid and invalid tree automata strings. Be careful with the root symbol.
In the above post I used "S" as the root symbol, and in the VI, I am using "X" by default. So just change either of them.
Try for example,
X(a,b)     - valid  - 1 tree
X(X(a,b))     - valid - 2 sub-trees
X((a,b))     - invalid
X(a,b))     - invalid
X(X(a,b)     - invalid
X(X(a),  X(X(b)),X(c,X(d )) )     - valid (it will remove the unnecessary spaces that the user might add mistakenly) - 6 sub-trees.
Could I get these results through regular expressions?
Remark: I didn't put small checks like if the user gives a multi-char string as the Root symbol or things like that, just to implement quickly. I assume the user will not make deliberate mistakes like this.
In the front panel of the main VI (Validate and Extract Sub-trees.VI), you may ignore the array A2, as it was mainly for my debugging purposes. The array A2 is filled while the program runs, and you may see my logic in those cells. But ignore otherwise.
Cheers!
[Edited 03/24/2014: Attachment with private information removed at poster's request]
Vaibhav