he-003

# HumanEval/3

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 below_zero(operations: List[int]) -> bool:
    """ You're given a list of deposit and withdrawal operations on a bank account that starts with
    zero balance. Your task is to detect if at any point the balance of account fallls below zero, and
    at that point function should return True. Otherwise it should return False.
    >>> below_zero([1, 2, 3])
    False
    >>> below_zero([1, 2, -4, 5])
    True
    """
```

<!-- imported from OpenAI HumanEval (HumanEval/3) -->

# Auto-generated from OpenAI HumanEval HumanEval/3. Do not edit by hand.
from solution import *  # noqa: F401,F403 (prompt helpers may be referenced by tests)
from solution import below_zero as candidate

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


def check(candidate):
    assert candidate([]) == False
    assert candidate([1, 2, -3, 1, 2, -3]) == False
    assert candidate([1, 2, -4, 5, 6]) == True
    assert candidate([1, -1, 2, -2, 5, -5, 4, -4]) == False
    assert candidate([1, -1, 2, -2, 5, -5, 4, -5]) == True
    assert candidate([1, -2, 2, -2, 5, -5, 4, -4]) == True


def test_he_003():
    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.

To solve this problem, we need to determine if the balance of a bank account ever falls below zero after a series of deposit and withdrawal operations. The account starts with a balance of zero, and each operation can either add to or subtract from this balance. Our task is to check if at any point the balance becomes negative.

### Approach
1. **Initialize Balance**: Start with a balance of zero.
2. **Iterate Through Operations**: Process each operation in the given list sequentially.
3. **Update Balance**: For each operation, update the balance by adding the operation value.
4. **Check for Negative Balance**: After each update, check if the balance is negative. If it is, return `True` immediately.
5. **Return Result**: If all operations are processed without the balance going negative, return `False`.

This approach ensures that we efficiently check each operation in sequence and immediately return if a negative balance is detected, minimizing unnecessary computations.

### Solution Code

```python
from typing import List

def below_zero(operations: List[int]) -> bool:
    balance = 0
    for op in operations:
        balance += op
        if balance < 0:
            return True
    return False
```

### Explanation
- **Initialization**: The balance is initialized to zero.
- **Processing Each Operation**: Each operation is processed in the order they appear in the list. The balance is updated by adding the operation value.
- **Immediate Check**: After each update, we check if the balance is negative. If it is, we immediately return `True`, indicating that the balance fell below zero.
- **Final Check**: If all operations are processed without the balance going negative, we return `False`.

This solution efficiently handles the problem by processing each operation exactly once, ensuring an optimal time complexity of O(n), where n is the number of operations.

Okay, I need to solve this problem where I have to determine if the bank account balance ever goes below zero after a series of operations. Let's think about how to approach this.

So, the function is called below_zero and it takes a list of integers called operations. The account starts at zero, and each operation is either a deposit (positive) or a withdrawal (negative). I need to check after each operation if the balance drops below zero. If it does at any point, return True; otherwise, return False.

Hmm, how do I model the balance? I'll probably need to keep a running total. Start with zero, then add each operation in sequence, checking after each step if the balance is negative.

Wait, but what about the order of operations? Oh right, the operations are applied in the order they appear in the list. So I have to process them sequentially.

Let me outline the steps:

1. Initialize the balance to 0.
2. Iterate over each operation in the list.
3. For each operation, add it to the balance.
4. After each addition, check if the balance is less than zero.
5. If at any point it is, return True immediately.
6. If all operations are processed and balance never goes below zero, return False.

That makes sense. So for example, in the first sample input [1,2,3], the balance goes 1, 3, 6—never negative, so return False.

In the second sample [1,2,-4,5], the balance after each step is 1, 3, -1 (which is below zero), so return True.

What about edge cases? Like if the first operation is negative. For example, operations = [-5], then balance is -5, which is below zero, so return True.

Another case: operations = [5, -5], balance goes to 0, which is not below zero, so return False.

Wait, the problem says "falls below zero"—so zero is not considered below zero. So only when balance is negative.

So, the algorithm is clear. Now, how to implement this in Python.

I'll write a function that initializes balance as 0. Then loop through each op in operations, adding to balance. After each addition, check if balance < 0. If yes, return True. If loop finishes without that happening, return False.

Let me think about the code structure.

Function definition is given. So inside the function:

balance = 0
for op in operations:
    balance += op
    if balance < 0:
        return True
return False

Yes, that should work.

Testing the sample inputs:

Sample 1: [1,2,3]
balance steps: 1, 3, 6. No negatives. Return False.

Sample 2: [1,2,-4,5]
After 1: 1 → no. After 2: 3 → no. After -4: -1 → yes. Return True.

Another test case: operations = [-3]. Balance is -3 → return True.

Another test: operations = [3, -3]. Balance after first op is 3, then 0. So no negatives. Return False.

What about an empty list? According to the problem statement, probably the list is non-empty, but the function should handle it. If operations is empty, the balance is 0, so return False.

So the code should handle all these cases.

I think that's the correct approach. Now, I'll write the code accordingly.