he-009

# HumanEval/9

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, Tuple


def rolling_max(numbers: List[int]) -> List[int]:
    """ From a given list of integers, generate a list of rolling maximum element found until given moment
    in the sequence.
    >>> rolling_max([1, 2, 3, 2, 3, 4, 2])
    [1, 2, 3, 3, 3, 4, 4]
    """
```

<!-- imported from OpenAI HumanEval (HumanEval/9) -->

# Auto-generated from OpenAI HumanEval HumanEval/9. Do not edit by hand.
from solution import *  # noqa: F401,F403 (prompt helpers may be referenced by tests)
from solution import rolling_max as candidate

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


def check(candidate):
    assert candidate([]) == []
    assert candidate([1, 2, 3, 4]) == [1, 2, 3, 4]
    assert candidate([4, 3, 2, 1]) == [4, 4, 4, 4]
    assert candidate([3, 2, 3, 100, 3]) == [3, 3, 3, 100, 100]


def test_he_009():
    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 generate a list of rolling maximum elements from a given list of integers. The rolling maximum at each position is the highest value encountered up to that point in the sequence.

### Approach
1. **Check for Empty List**: If the input list is empty, return an empty list immediately.
2. **Initialize Variables**: Start by initializing the result list with the first element of the input list. This is because the rolling maximum at the first position is the element itself.
3. **Track Current Maximum**: Use a variable to keep track of the current maximum value encountered so far.
4. **Iterate Through List**: Loop through each element starting from the second element. For each element, compare it with the current maximum. If it is larger, update the current maximum.
5. **Build Result List**: Append the current maximum to the result list after each iteration.

This approach ensures that we efficiently compute the rolling maximum in a single pass through the list, resulting in a time complexity of O(n), where n is the length of the input list.

### Solution Code
```python
from typing import List

def rolling_max(numbers: List[int]) -> List[int]:
    if not numbers:
        return []
    result = [numbers[0]]
    current_max = numbers[0]
    for num in numbers[1:]:
        if num > current_max:
            current_max = num
        result.append(current_max)
    return result
```

### Explanation
- **Initialization**: The result list starts with the first element of the input list, and the current maximum is initialized to this value.
- **Iteration**: For each subsequent element, we check if it is greater than the current maximum. If it is, we update the current maximum. Regardless of whether we update the maximum, we append the current maximum to the result list.
- **Efficiency**: This method processes each element exactly once, making it efficient with a linear time complexity.

This solution effectively handles all edge cases, including empty lists and lists with negative numbers, ensuring correct results for any valid input.

Okay, I need to solve this problem where I have to implement a function called rolling_max that takes a list of integers and returns another list of integers. The returned list should contain the rolling maximum elements up to each point in the sequence. 

Let me think about what rolling maximum means. So, for each element in the input list, the corresponding element in the output list is the maximum value encountered so far, including the current element. For example, in the sample given, [1,2,3,2,3,4,2], the output is [1,2,3,3,3,4,4]. 

So, the first element is just 1 because it's the first. The second is 2, which is higher than 1. The third is 3, higher than 2. Then the fourth element is 2, but the maximum so far is still 3, so it's 3. The fifth is 3, same as before. The sixth is 4, which is higher, so it becomes 4. The last element is 2, but the maximum remains 4.

So the approach is to iterate through each number in the input list, keep track of the current maximum, and for each step, add the current maximum to the result list.

How do I implement this? Well, I can initialize a variable, say current_max, to the first element. Then, for each number in the list starting from the second, I compare it with current_max. If it's larger, I update current_max. Then, I append current_max to the result list.

Wait, but what if the input list is empty? Oh, the problem says it's a list of integers, but I should handle the case where the list is empty. But looking at the sample, the function is called with a non-empty list, but perhaps in the code, I should handle empty lists by returning an empty list.

So, the steps are:

1. Check if the input list is empty. If yes, return an empty list.
2. Initialize the result list with the first element of the input list.
3. Set current_max to the first element.
4. Iterate over the input list starting from the second element.
5. For each element, compare it with current_max. If it's larger, update current_max.
6. Append current_max to the result list.
7. After processing all elements, return the result list.

Let me test this logic with the sample input.

Sample input: [1,2,3,2,3,4,2]
- result starts as [1]
- current_max is 1
- next element is 2: 2>1 → current_max=2 → result becomes [1,2]
- next is 3>2 → current_max=3 → result [1,2,3]
- next is 2: not >3 → current_max remains 3 → result appends 3 → [1,2,3,3]
- next is 3: not >3 → append 3 → [1,2,3,3,3]
- next is 4>3 → current_max=4 → append 4 → [1,2,3,3,3,4]
- next is 2: not >4 → append 4 → [1,2,3,3,3,4,4]
Which matches the sample output.

Another test case: what if the list is [5,4,3,2,1]?
The output should be [5,5,5,5,5].

What about a single element list? Like [10], output is [10].

What about an empty list? The function should return an empty list.

So, in code:

def rolling_max(numbers: List[int]) -> List[int]:
    if not numbers:
        return []
    result = [numbers[0]]
    current_max = numbers[0]
    for num in numbers[1:]:
        if num > current_max:
            current_max = num
        result.append(current_max)
    return result

Wait, but what if the list has negative numbers? Let's see. For example, [-1, -2, -3]. The output should be [-1, -1, -1]. Because each step, the current_max is the highest so far.

Yes, the code handles that correctly.

So, I think this should work. Now, I'll write the code as per the function signature given.