he-006

# HumanEval/6

Implement a file **`solution.py`** that completes the function below. Keep the given name and signature; your file must define it at module level.

```python
from typing import List


def parse_nested_parens(paren_string: str) -> List[int]:
    """ Input to this function is a string represented multiple groups for nested parentheses separated by spaces.
    For each of the group, output the deepest level of nesting of parentheses.
    E.g. (()()) has maximum two levels of nesting while ((())) has three.

    >>> parse_nested_parens('(()()) ((())) () ((())()())')
    [2, 3, 1, 3]
    """
```

<!-- imported from OpenAI HumanEval (HumanEval/6) -->

# Auto-generated from OpenAI HumanEval HumanEval/6. Do not edit by hand.
from solution import *  # noqa: F401,F403 (prompt helpers may be referenced by tests)
from solution import parse_nested_parens as candidate

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}


def check(candidate):
    assert candidate('(()()) ((())) () ((())()())') == [2, 3, 1, 3]
    assert candidate('() (()) ((())) (((())))') == [1, 2, 3, 4]
    assert candidate('(()(())((())))') == [4]


def test_he_006():
    check(candidate)

You are an expert programmer. Solve the task exactly as specified. Output your solution as fenced code blocks using the required file name(s) and the exact function/type signatures requested. Prefer correctness; do not include prose outside code unless asked.

```python
from typing import List

def parse_nested_parens(paren_string: str) -> List[int]:
    result = []
    for group in paren_string.split():
        current_depth = 0
        max_depth = 0
        for char in group:
            if char == '(':
                current_depth += 1
                if current_depth > max_depth:
                    max_depth = current_depth
            elif char == ')':
                current_depth -= 1
        result.append(max_depth)
    return result
```

The user wants me to implement a function `parse_nested_parens` that takes a string containing multiple groups of nested parentheses separated by spaces, and returns a list of integers representing the maximum nesting depth for each group.

Let's break down the problem:
1. The input string contains multiple groups of parentheses separated by spaces.
2. For each group, I need to calculate the maximum nesting depth.
3. Return a list of these maximum depths.

Example: `'(()()) ((())) () ((())()())'`
Groups: `'(()())'`, `'((()))'`, `'()'`, `'((())()())'`
Depths:
- `'(()())'`: max depth is 2
- `'((()))'`: max depth is 3
- `'()'`: max depth is 1
- `'((())()())'`: max depth is 3
Output: `[2, 3, 1, 3]`

Algorithm:
1. Split the input string by spaces to get individual groups.
2. For each group, iterate through the characters.
3. Keep track of the current nesting depth and the maximum depth encountered.
4. When encountering '(', increment current depth. Update max depth if current depth exceeds it.
5. When encountering ')', decrement current depth.
6. Store the max depth for each group.
7. Return the list of max depths.

Edge cases:
- Empty string? The problem says "multiple groups", but we should handle empty input gracefully. If `paren_string` is empty or just spaces, splitting might give empty strings or we should filter them out. Actually, `paren_string.split()` handles multiple spaces and empty strings well.
- What if a group is empty? The problem implies valid parentheses groups. We can assume valid input as per typical HumanEval problems.

Let's write the code:

```python
from typing import List

def parse_nested_parens(paren_string: str) -> List[int]:
    groups = paren_string.split()
    result = []
    for group in groups:
        current_depth = 0
        max_depth = 0
        for char in group:
            if char == '(':
                current_depth += 1
                if current_depth > max_depth:
                    max_depth = current_depth
            elif char == ')':
                current_depth -= 1
        result.append(max_depth)
    return result
```

Wait, should I handle cases where `paren_string` might be empty? `paren_string.split()` on an empty string returns `[]`, so the loop won't run, and it returns `[]`, which is correct.

Let's test with the example:
`'(()()) ((())) () ((())()())'`
Groups: `['(()())', '((()))', '()', '((())()())']`
1. `'(()())'`: `(` -> 1, max=1; `(` -> 2, max=2; `)` -> 1; `(` -> 2; `)` -> 1; `)` -> 0. Result: 2. Correct.
2. `'((()))'`: `(` -> 1, max=1; `(` -> 2, max=2; `(` -> 3, max=3; `)` -> 2; `)` -> 1; `)` -> 0. Result: 3. Correct.
3. `'()'`: `(` -> 1, max=1; `)` -> 0. Result: 1. Correct.
4. `'((())()())'`: `(` -> 1, max=1; `(` -> 2, max=2; `(` -> 3, max=3; `)` -> 2; `)` -> 1; `(` -> 2; `)` -> 1; `(` -> 2; `)` -> 1; `)` -> 0. Result: 3. Correct.

The logic seems solid.

One minor point: `max_depth` could be updated using `max(max_depth, current_depth)` for brevity, but the `if` statement is fine.

Let's consider if there are any other characters in the string. The problem says "string represented multiple groups for nested parentheses separated by spaces." So we can assume only parentheses and spaces.

The code looks good. I will wrap it in the required format.

One thing to check: HumanEval problems sometimes have specific constraints or edge cases. But this is straightforward.

I'll produce the final solution.
No extra fluff.
Code structure:
```python
from typing import List

def parse_nested_parens(paren_string: str) -> List[int]:
    result = []
    for group in paren_string.split():
        current_depth = 0
        max_depth = 0
        for char in group:
            if char == '(':
                current_depth += 1
                if current_depth > max_depth:
                    max_depth = current_depth
            elif char == ')':
                current_depth -= 1
        result.append(max_depth)
    return result
```

Wait, should I handle the case where `paren_string` is empty or contains only spaces? `paren_string.split()` handles it correctly by returning an empty list.
What if `paren_string` has trailing/leading spaces? `split()` handles it.
All good.

I will output the solution now.
One minor improvement: using `max()` might be slightly cleaner but the `if` is fine. I'll stick with the `if` or use `max_depth = max(max_depth, current_depth)`. Both are fine.

Let's verify the function signature matches exactly:
```python
from typing import List


def parse_nested_parens(paren_string: str) -> List[int]:
```
Yes.

Final check of the prompt: "Implement a file **`solution.py`** that completes the function below. Keep the given name and signature; your file must define it at module level."

I will provide the complete code block.
All set. 
Output matches requirements.
Proceed. 
Self-Correction/Refinement during thought: 
Is there any chance `paren_string` contains empty groups due to multiple spaces? `split()` without arguments splits by any whitespace and removes empty strings, so it's safe.
What about invalid parentheses? The problem implies valid groups. We don't need to handle invalid ones.
The solution is robust enough.

I will generate the response. 
Code:
```python
from typing import List

def parse_nested_parens(paren_string: str) -> List[int]:
    result = []
    for group in paren_string.split():
        current_depth = 0
        max_depth = 0
        for char in group:
            if char == '(':
                current_depth += 1
                if current_depth > max_depth:
                    max_depth = current_depth
            elif char == ')':
                current_depth -= 1
        result.append(max_depth)
    return result
```
Looks good. Output matches.✅
Done. 
Proceeding. 
[Output Generation] -> *Self-Correction/Verification during generation prep*: 
Wait, the docstring in the prompt has `>>> parse_nested_parens('(()()) ((())) () ((())()())')` returning `[2, 3, 1, 3]`. My code produces exactly that.
The type hint `List` is imported from `typing`.
Everything is correct.
I will output the code block. 
All good. 
Output matches request.
Done. 
[Final Check of the Prompt]
"Implement a file **`solution.py`** that completes the function below."
I will provide exactly that.
No extra text.
Ready. 
```python
from typing import List

def parse_nested_parens(paren_string: str) -> List[int]:
    result = []
    for group in paren_string.split():
        current_depth = 0
        max_depth = 0
        for char in group:
            if char == '(':
                current_depth += 1
                if current_depth > max_depth:
                    max_depth = current_depth
            elif char == ')':
                current_depth -= 1
        result.append(max_depth)
    return result
```
This is correct. I'll output it. 
All steps verified. 
Proceeds. 
[Output Generation] (matches the final code block)
Done. 
(Self-Correction/Note during thought: I should make sure the indentation and formatting are perfect. The code is straightforward.)
Final Output Generation. 
✅