Matching Nested Structures With Regular Expressions in Python

Solution 1:

Regular expressions cannot parse nested structures. Nested structures are not regular, by definition. They cannot be constructed by a regular grammar, and they cannot be parsed by a finite state automaton (a regular expression can be seen as a shorthand notation for an FSA).

Today's "regex" engines sometimes support some limited "nesting" constructs, but from a technical standpoint, they shouldn't be called "regular" anymore.

Solution 2:

You can't do this generally using Python regular expressions. (.NET regular expressions have been extended with "balancing groups" which is what allows nested matches.)

However, PyParsing is a very nice package for this type of thing:

from pyparsing import nestedExpr

data = "( (a ( ( c ) b ) ) ( d ) e )"
print nestedExpr().parseString(data).asList()

The output is:

[[['a', [['c'], 'b']], ['d'], 'e']]

More on PyParsing:

• http://pyparsing.wikispaces.com/Documentation

Solution 3:

Edit: falsetru's nested parser, which I've slightly modified to accept arbitrary regex patterns to specify delimiters and item separators, is faster and simpler than my original re.Scanner solution:

import re

def parse_nested(text, left=r'[(]', right=r'[)]', sep=r','):
    """ https://stackoverflow.com/a/17141899/190597 (falsetru) """
    pat = r'({}|{}|{})'.format(left, right, sep)
    tokens = re.split(pat, text)
    stack = [[]]
    for x in tokens:
        if not x or re.match(sep, x):
            continue
        if re.match(left, x):
            # Nest a new list inside the current list
            current = []
            stack[-1].append(current)
            stack.append(current)
        elif re.match(right, x):
            stack.pop()
            if not stack:
                raise ValueError('error: opening bracket is missing')
        else:
            stack[-1].append(x)
    if len(stack) > 1:
        print(stack)
        raise ValueError('error: closing bracket is missing')
    return stack.pop()

text = "a {{c1::group {{c2::containing::HINT}} a few}} {{c3::words}} or three"

print(parse_nested(text, r'\s*{{', r'}}\s*'))

yields

['a', ['c1::group', ['c2::containing::HINT'], 'a few'], ['c3::words'], 'or three']

Nested structures can not be matched with Python regex alone, but it is remarkably easy to build a basic parser (which can handle nested structures) using re.Scanner:

import re

class Node(list):
    def __init__(self, parent=None):
        self.parent = parent

class NestedParser(object):
    def __init__(self, left='\(', right='\)'):
        self.scanner = re.Scanner([
            (left, self.left),
            (right, self.right),
            (r"\s+", None),
            (".+?(?=(%s|%s|$))" % (right, left), self.other),
        ])
        self.result = Node()
        self.current = self.result

    def parse(self, content):
        self.scanner.scan(content)
        return self.result

    def left(self, scanner, token):
        new = Node(self.current)
        self.current.append(new)
        self.current = new

    def right(self, scanner, token):
        self.current = self.current.parent

    def other(self, scanner, token):
        self.current.append(token.strip())

It can be used like this:

p = NestedParser()
print(p.parse("((a+b)*(c-d))"))
# [[['a+b'], '*', ['c-d']]]

p = NestedParser()
print(p.parse("( (a ( ( c ) b ) ) ( d ) e )"))
# [[['a', [['c'], 'b']], ['d'], 'e']]

By default NestedParser matches nested parentheses. You can pass other regex to match other nested patterns, such as brackets, []. For example,

p = NestedParser('\[', '\]')
result = (p.parse("Lorem ipsum dolor sit amet [@a xxx yyy [@b xxx yyy [@c xxx yyy]]] lorem ipsum sit amet"))
# ['Lorem ipsum dolor sit amet', ['@a xxx yyy', ['@b xxx yyy', ['@c xxx yyy']]],
# 'lorem ipsum sit amet']

p = NestedParser('<foo>', '</foo>')
print(p.parse("<foo>BAR<foo>BAZ</foo></foo>"))
# [['BAR', ['BAZ']]]

Of course, pyparsing can do a whole lot more than the above code can. But for this single purpose, the above NestedParser is about 5x faster for small strings:

In [27]: import pyparsing as pp

In [28]: data = "( (a ( ( c ) b ) ) ( d ) e )"    

In [32]: %timeit pp.nestedExpr().parseString(data).asList()
1000 loops, best of 3: 1.09 ms per loop

In [33]: %timeit NestedParser().parse(data)
1000 loops, best of 3: 234 us per loop

and around 28x faster for larger strings:

In [44]: %timeit pp.nestedExpr().parseString('({})'.format(data*10000)).asList()
1 loops, best of 3: 8.27 s per loop

In [45]: %timeit NestedParser().parse('({})'.format(data*10000))
1 loops, best of 3: 297 ms per loop