Can Nested Brackets Be Matched Without Recursion or Balancing Groups?

Matching Nested Brackets Without Recursion or Balancing Groups

Matching nested brackets using regular expressions can prove challenging, especially in languages like Java, where recursion and balancing groups are not supported. Fortunately, it's indeed possible to overcome this limitation using forward references.

Matching Outer Groups

The following regex [1] matches outer groups of brackets without imposing limits on depth:

(?=\()(?:(?=.*?\((?!.*?)(.*\)(?!.*).*))(?=.*?\)(?!.*?)(.*)).)+?.*?(?=)[^(]*(?=$)

Here, the expression looks ahead for opening parentheses, excluding unmatched opening parentheses, and captures the corresponding closing parentheses. The captured substrings, though useless, serve as placeholders to complete the match.

Matching Inner Groups

To include inner groups, we can capture the following expression [2]:

(?=\()(?=((?:(?=.*?\((?!.*?)(.*\)(?!.*).*))(?=.*?\)(?!.*?)(.*)).)+?.*?(?=)[^(]*(?=$))) 

By adding a capturing group and adjusting the backreference indices, this expression captures the inner groups as well.

How It Works

The method iterates through the string, matching the next opening and closing parentheses while capturing the remaining string in each case. The lookaheads ensure that the parentheses match in a balanced manner.

The expression is constructed as follows:

Component	Description
(?=()	Asserts that '(' precedes complex parsing
(?:	Start of non-capturing group for repeated string processing
(?=	Assert that the next '(' follows
.?((?!.?1)	Match until the next '(' not followed by group 1
(.)(?!.2).*	Fill group 1 with the string, ensuring another ')' exists
)	Assert that the matching ')' is valid
.?)(?!.?2)	Assert that the next ')' not followed by group 2 exists
(.*)	Fill group 2 with the remaining string
)	Assert that the matching ')' is valid
	Consume a single character to continue matching within the group
) ?	Repeat the group (in the inner loop)
.*?(?=1)	Match up to and including the last '(' found
1*(?=2$)	Match up to the last ')' (but within the valid group)

This method allows for efficient matching of nested brackets without the need for recursion or balancing groups.

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