parsing nested parentheses in python, grab content by level

Below is my Python solution with a time complexity of O(N)

str1 = "(a(b(c)d)(e(f)g)hi)"

def content_by_level(str1, l):
    level_dict = {}
    level = 0
    level_char = ''
    for s in str1:
        if s == '(':
            if level not in level_dict:
                level_dict[level] = [level_char]
            elif level_char != '':
                level_dict[level].append(level_char)
            level_char = ''
            level += 1
        elif s == ')':
            if level not in level_dict:
                level_dict[level] = [level_char]
            elif level_char != '':
                level_dict[level].append(level_char)
            level_char = ''
            level -= 1
        else:
            level_char += s
    
    print(level_dict) # {0: [''], 1: ['a', 'hi'], 2: ['b', 'd', 'e', 'g'], 3: ['c', 'f']}
    return level_dict[l]

print(content_by_level(str1,0)) # ['']
print(content_by_level(str1,1)) # ['a', 'hi']
print(content_by_level(str1,2)) # ['b', 'd', 'e', 'g']
print(content_by_level(str1,3)) # ['c', 'f']

Parentheses matching requires a parser with a push-down automaton. Some libraries exist, but the rules are simple enough that we can write it from scratch:

def push(obj, l, depth):
    while depth:
        l = l[-1]
        depth -= 1

    l.append(obj)

def parse_parentheses(s):
    groups = []
    depth = 0

    try:
        for char in s:
            if char == '(':
                push([], groups, depth)
                depth += 1
            elif char == ')':
                depth -= 1
            else:
                push(char, groups, depth)
    except IndexError:
        raise ValueError('Parentheses mismatch')

    if depth > 0:
        raise ValueError('Parentheses mismatch')
    else:
        return groups

print(parse_parentheses('a(b(cd)f)')) # ['a', ['b', ['c', 'd'], 'f']]

You don't make it clear exactly what the specification of your function is, but this behaviour seems wrong to me:

>>> ParseNestedParen('(a)(b)(c)', 0)
['a)(b)(c']
>>> nested_paren.ParseNestedParen('(a)(b)(c)', 1)
['b']
>>> nested_paren.ParseNestedParen('(a)(b)(c)', 2)
['']

Other comments on your code:

• Docstring says "generate", but function returns a list, not a generator.
• Since only one string is ever returned, why return it in a list?
• Under what circumstances can the function return the string fail?
• Repeatedly calling re.findall and then throwing away the result is wasteful.
• You attempt to rebalance the parentheses in the string, but you do so only one parenthesis at a time:

>>> ParseNestedParen(')' * 1000, 1)
RuntimeError: maximum recursion depth exceeded while calling a Python object

As Thomi said in the question you linked to, "regular expressions really are the wrong tool for the job!"

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The usual way to parse nested expressions is to use a stack, along these lines:

def parenthetic_contents(string):
    """Generate parenthesized contents in string as pairs (level, contents)."""
    stack = []
    for i, c in enumerate(string):
        if c == '(':
            stack.append(i)
        elif c == ')' and stack:
            start = stack.pop()
            yield (len(stack), string[start + 1: i])

>>> list(parenthetic_contents('(a(b(c)(d)e)(f)g)'))
[(2, 'c'), (2, 'd'), (1, 'b(c)(d)e'), (1, 'f'), (0, 'a(b(c)(d)e)(f)g')]