Bracket matcher in Python
Doesn't look like you've done this:


  Explain the correctness of your code, and analyze its time and space complexities.




This is an anti-pattern:

    length = len(text)

    for i in range(length):
        # code using only `text[i]`, but never using `i`


You are computing the length of text, then using a for loop of over the range(length), assigning the index to i, but then never using i for anything other than fetching the character text[i].

Far, far better is looping over the letters of text:

    for ch in text:
        # use `ch` here.




Efficiency:

        if text[i] == '(':
           # ...
        elif text[i] == ')':
           diffCounter -= 1
        if diffCounter &lt; 0:
           diffCounter += 1
           # ...


Will diffCounter ever be negative, without first subtracting 1 from it?  No?  Perhaps the next test belongs in the elif clause:

        if text[i] == '(':
           # ...
        elif text[i] == ')':
           diffCounter -= 1
           if diffCounter &lt; 0:
              diffCounter += 1
              # ...


But that is still subtracting 1 and then (possibly) immediately adding 1 again.  Better: check for the underflow condition first.

        if text[i] == '(':
           # ...
        elif text[i] == ')':
           if diffCounter &gt; 0:
              diffCounter -= 1
           else:
              # ...




While the diffCounter is an understandable variable name (barely), the variable named answer is completely mysterious.  Answer to what?  Why is it incremented when there is an underflow?  Why is it added to diffCounter at the end.  Not a comment in sight, and the code is anything but self documenting.



Follow PEP-8 coding standards, and use pylint or other style checker.  For instance, variables should not be camelCase, and answer +=1 needs an extra space.