he-001

# HumanEval/1

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 separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """
```

<!-- imported from OpenAI HumanEval (HumanEval/1) -->

# Auto-generated from OpenAI HumanEval HumanEval/1. Do not edit by hand.
from solution import *  # noqa: F401,F403 (prompt helpers may be referenced by tests)
from solution import separate_paren_groups as candidate

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


def check(candidate):
    assert candidate('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert candidate('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert candidate('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert candidate('( ) (( )) (( )( ))') == ['()', '(())', '(()())']


def test_he_001():
    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 separate_paren_groups(paren_string: str) -> List[str]:
    result = []
    current_group = []
    depth = 0
    
    for char in paren_string:
        if char == ' ':
            continue
        if char == '(':
            depth += 1
            current_group.append(char)
        elif char == ')':
            depth -= 1
            current_group.append(char)
            if depth == 0:
                result.append(''.join(current_group))
                current_group = []
                
    return result
```

The user wants me to implement a function `separate_paren_groups` that takes a string containing multiple groups of nested parentheses and separates them into a list of strings.

Key requirements:
1. Input is a string with multiple groups of nested parentheses
2. Separate groups are balanced and not nested within each other
3. Ignore spaces in the input string
4. Return a list of strings, each representing a separate group

Example:
Input: `'( ) (( )) (( )( ))'`
Output: `['()', '(())', '(()())']`

Let's think about the algorithm:
1. Remove spaces from the input string
2. Iterate through the string, keeping track of the current group
3. Use a counter to track nesting depth
4. When depth goes from 0 to 1, start a new group
5. When depth goes back to 0, end the current group and add it to the result list

Let's trace through the example:
Input after removing spaces: `'()(( ))(( )( ))'` -> `'()(())(()())'`

Wait, let's trace carefully:
`'()(( ))(( )( ))'` -> remove spaces -> `'()(())(()())'`

Characters:
`(` -> depth = 1, start group
`)` -> depth = 0, end group -> `'()'`
`(` -> depth = 1, start group
`(` -> depth = 2
`)` -> depth = 1
`)` -> depth = 0, end group -> `'(())'`
`(` -> depth = 1, start group
`(` -> depth = 2
`)` -> depth = 1
`(` -> depth = 2
`)` -> depth = 1
`)` -> depth = 0, end group -> `'(()())'`

Result: `['()', '(())', '(()())']` - matches!

Algorithm:
```python
def separate_paren_groups(paren_string: str) -> List[str]:
    result = []
    current_group = []
    depth = 0
    
    for char in paren_string:
        if char == ' ':
            continue
        if char == '(':
            depth += 1
            current_group.append(char)
        elif char == ')':
            depth -= 1
            current_group.append(char)
            if depth == 0:
                result.append(''.join(current_group))
                current_group = []
                
    return result
```

Wait, what if the input has no parentheses? The problem says "multiple groups of nested parentheses", so we can assume valid input. But let's handle edge cases gracefully.

Let's test with the example:
`'( ) (( )) (( )( ))'`
- `(`: depth=1, current=['(']
- ` `: skip
- `)`: depth=0, current=['(', ')'], depth==0 -> result=['()'], current=[]
- ` `: skip
- `(`: depth=1, current=['(']
- `(`: depth=2, current=['(', '(']
- ` `: skip
- `)`: depth=1, current=['(', '(', ')']
- `)`: depth=0, current=['(', '(', ')', ')'], depth==0 -> result=['()', '(())'], current=[]
- ` `: skip
- `(`: depth=1, current=['(']
- `(`: depth=2, current=['(', '(']
- ` `: skip
- `)`: depth=1, current=['(', '(', ')']
- `(`: depth=2, current=['(', '(', ')', '(']
- `)`: depth=1, current=['(', '(', ')', '(', ')']
- `)`: depth=0, current=['(', '(', ')', '(', ')', ')'], depth==0 -> result=['()', '(())', '(()())'], current=[]

Returns `['()', '(())', '(()())']`. Correct!

The solution looks solid. Let's write it out.

One minor thing: should I handle cases where there might be trailing/leading spaces or empty groups? The problem statement says "Ignore any spaces in the input string" and "Separate groups are balanced". So the algorithm should work fine.

Let's double check the function signature:
```python
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
```

The implementation matches.

I'll write the complete solution.
No extra fluff.
Code:
```python
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    result = []
    current_group = []
    depth = 0
    
    for char in paren_string:
        if char == ' ':
            continue
        if char == '(':
            depth += 1
            current_group.append(char)
        elif char == ')':
            depth -= 1
            current_group.append(char)
            if depth == 0:
                result.append(''.join(current_group))
                current_group = []
                
    return result
```

Wait, should I consider that `current_group` could be empty if there are consecutive spaces? The `if depth == 0` check only triggers after a `)`, so `current_group` will have at least `()` when appended. That's fine.

What about input like `'()'`? Works.
What about input like `'() ()'`? Works.
What about input with only spaces? Returns `[]`. That's acceptable.

The solution is correct and efficient. O(n) time complexity.

I will output the solution as requested.
One thing: the prompt says "Keep the given name and signature; your file must define it at module level."
I'll include the import as well.

Final check of the code:
```python
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    result = []
    current_group = []
    depth = 0
    
    for char in paren_string:
        if char == ' ':
            continue
        if char == '(':
            depth += 1
            current_group.append(char)
        elif char == ')':
            depth -= 1
            current_group.append(char)
            if depth == 0:
                result.append(''.join(current_group))
                current_group = []
                
    return result
```

Looks good. I'll produce this.
No additional text.
Done. 
Let's verify one more time with the exact example from the docstring:
`separate_paren_groups('( ) (( )) (( )( ))')`
Output: `['()', '(())', '(()())']`
Matches exactly.
Ready. 
Output matches requirements.
Proceeds. 
Self-Correction/Refinement during thought: 
Could there be a case where `paren_string` contains characters other than `(`, `)`, and spaces? The problem says "string containing multiple groups of nested parentheses", so we can assume only parentheses and spaces. Even if there are other characters, the problem says "Ignore any spaces", implying other characters aren't expected or should be treated as part of the group. But typically in these problems, it's just parentheses and spaces. The current implementation handles it correctly.

One minor point: `current_group` is a list of characters, joined at the end. This is efficient.
All good.
Output matches.✅
Proceeds. 
Generating response. 
```python
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    result = []
    current_group = []
    depth = 0
    
    for char in paren_string:
        if char == ' ':
            continue
        if char == '(':
            depth += 1
            current_group.append(char)
        elif char == ')':
            depth -= 1
            current_group.append(char)
            if depth == 0:
                result.append(''.join(current_group))
                current_group = []
                
    return result
```
This is correct. I will wrap it in the required format.
Done. 
Output matches request.
Proceeds. 
[Final Check]
The prompt asks for a file `solution.py`. I will provide the code block with the exact function.
All good. 
Output generation. 
(Self-Correction/Note during generation prep)
I should make sure the indentation and formatting are correct.
The code is straightforward.
I'll output it now. 
✅