L2 · Working engineerStacks & queues~8 min · 7 tests#43

Balanced Parentheses Checker

Check whether brackets (), [] and {} are balanced and correctly nested using a stack in O(n). One of the most-asked Python interview questions.

The problem

Return True if every bracket in s — (), [], {} — is closed by the right type, in the right order. Any other character is ignored.

Examples

Example 1
Input
```
is_balanced('{[()]}')
```
Expected output
```
True
```
Example 2
Input
```
is_balanced('([)]')
```
Expected output
```
False
```
Example 3
Input
```
is_balanced('((')
```
Expected output
```
False
```

+ 4 hidden tests on Submit — closer before opener, other characters ignored.

Edge cases to ask about

Empty string
Closer first
Unclosed openers
Wrong nesting '([)]'

Hints

0/3

How an interviewer scores this

0/9

1. Understand the problemRestate it, ask about edge cases and input size.
2. Write a brute-force solutionCorrect first, clever later.
3. Get the correct outputautoAll visible examples pass.
4. Analyse time complexityautoCommit to a Big-O in the Complexity Lab.
5. Analyse space complexityautoExtra memory, not the input.
6. Identify the bottleneckautoMeasure your code — where does it bend?
7. OptimiseUsually: a set or dict instead of a scan.
8. Explain why it worksSay it out loud to Solvi.
9. Test the edge casesautoSubmit passes every hidden test.

Python 3.13 · is_balanced

def is_balanced(s):
    """True if (), [] and {} are balanced and properly nested."""
    # Write your solution here
    pass

⌘/Ctrl + Enter runs the examples

Your code runs in real CPython inside your browser — nothing is sent anywhere. The first run downloads the interpreter (about 6 MB, once). Your code is saved on this device as you type.

Complexity Lab

What does this cost as n grows?

Interviewers score the analysis as much as the code. Commit to an answer first — then check it, and measure your code against the optimal one at growing input sizes.

Time complexity of the optimal solution

Space complexity (extra memory)

Pick both to reveal the answer.

Measure it

Runs the function on inputs of size 250 up to 16,000 and records the time and peak memory. Slow solutions stop early — a short curve is itself the answer.

From brute force to optimal

The progression an interviewer wants to hear, one step at a time.

Approach	Time	Space	Idea
Repeatedly delete '()', '[]', '{}'	O(n²)	O(n)	Each replace pass is O(n), up to n/2 passes.
bestStack of open brackets	O(n)	O(n)	Push openers; every closer must match the top.

Walkthrough of the optimal approach (try it yourself first)

Push every opening bracket. On a closing bracket, the stack must be non-empty and its top must be the matching opener — otherwise return False. After the scan, leftover openers mean the string is unbalanced, so return not stack.

A dict from closer to opener keeps the matching logic to one line.

Complexity: O(n) time, O(n) space. One pass; in the worst case (all openers) the stack holds n characters.

Reveal the reference solution

def is_balanced(s):
    pairs = {")": "(", "]": "[", "}": "{"}
    stack = []
    for ch in s:
        if ch in "([{":
            stack.append(ch)
        elif ch in pairs:
            if not stack or stack.pop() != pairs[ch]:
                return False
    return not stack

Follow-ups interviewers ask

Return the index of the first error.
Minimum insertions to balance it.

Frequently asked interview questions

Core interview concepts, complexities, and follow-ups scored by hiring teams.

What is the time complexity of Balanced Parentheses Checker in Python?

The optimal solution runs in O(n) time and O(n) auxiliary space. One pass; in the worst case (all openers) the stack holds n characters.

What is the brute-force approach, and how do you optimise it?

Repeatedly delete '()', '[]', '{}': O(n²) time, O(n) space. Each replace pass is O(n), up to n/2 passes. Stack of open brackets: O(n) time, O(n) space. Push openers; every closer must match the top.

What follow-up questions do interviewers ask about Balanced Parentheses Checker?

Return the index of the first error. Minimum insertions to balance it.