# Problem Description
This appears to be a problem about sequentially cutting a line segment and computing a special array called "h-array". The function takes two parameters:
- A length `l` representing the total length of a line segment
- A list of positions `cuts` where the line segment should be cut sequentially
The goal is to compute the h-array values after performing all cuts, where each position tracks some kind of stacking height.

# Visual Facts
1. Initial state:
   - A line segment of length 6 in both examples
   - Initial h-array is filled with 1s
   - Cut positions are marked with vertical red lines

2. Example 1 (cuts=[2,4,5]):
   - Three sequential cuts at positions 2, 4, and 5
   - After each cut, the left segments is moved and stacked on the right
   - Final h-array values change after each cut
   - Specially,
       - After cut at 2: h-array [1, 1, 1, 1, 1, 1] -> [0, 0, 2, 2, 1, 1]
       - After cut at 4: h-array [0, 0, 2, 2, 1, 1] -> [0, 0, 0, 0, 3, 3]
       - After cut at 5: h-array [0, 0, 0, 0, 3, 3] -> [0, 0, 0, 0, 0, 6]

3. Example 2 (cuts=[1,4]):
   - Two sequential cuts at positions 1 and 4
   - Similar stacking behavior
   - Specially,
       - After cut at 1: h-array [1, 1, 1, 1, 1, 1] -> [0, 2, 1, 1, 1, 1]
       - After cut at 4: h-array [0, 1, 1, 1, 1, 1] -> [0, 0, 0, 0, 3, 2]

# Visual Patterns
When you perform a cut at a new position, say `j`, relative to the previous cut at position `i`, the h-array is updated based on the following three rules:

1. **Incrementing a Segment of the h-array**:
   - **Segment to Update**: From position `j` to position `j + (j - i) - 1`. This means you're looking at a segment whose length is equal to the distance between the previous cut `i` and the current cut `j`.
   - **Operation**: For each position `k` in this segment, you add the corresponding value from the h-array segment between positions `i - 1` and `j - 1` to it.
   - **Effect**: This effectively "copies" the values from the previous segment and adds them to the new segment starting at `j`, increasing the heights based on previous cuts.

2. **Resetting the Original Segment**:
   - **Segment to Reset**: From position `i - 1` to position `j - 1`.
   - **Operation**: Set all elements in this segment of the h-array to `0`.
   - **Effect**: This clears the original segment since its values have been moved or stacked onto the new segment starting at `j`.

3. **Maintaining the Remaining h-array**:
   - **Segment to Maintain**: From position `j + (j - i)` to the end of the h-array.
   - **Operation**: Leave this part of the h-array unchanged.
   - **Effect**: Only the specified segments are modified; the rest of the h-array remains as it was before the current cut.

# Solution
from typing import List

def solution(l: int, cuts: List[int]) -> List[int]:
    """
    Performs sequential cuts on a line segment and computes the resulting h-array.

    Parameters:
        l (int): Length of the line segment
        cuts (List[int]): Ordered positions where cuts should be made

    Returns:
        List[int]: The h-array generated after making all cuts (same length as l)
    """
    h_array = [1] * l
    previous_cut = 0
    for cut in cuts:
        segment_length = cut - previous_cut
        for i in range(cut, min(l, cut + segment_length)):     
            h_array[i] += h_array[previous_cut + (i - cut)]    
        for i in range(previous_cut, cut):
            h_array[i] = 0
        previous_cut = cut
    return h_array

# Test Script
def test():
    test_cases = [
        (10, [2, 4, 6], [0, 0, 0, 0, 0, 0, 4, 4, 1, 1]),
        (6, [2, 4, 5], [0, 0, 0, 0, 0, 6]),
        (6, [1, 4], [0, 0, 0, 0, 3, 2]),
        (3, [2], [0, 0, 2]),
        (3, [1], [0, 2, 1]),
        (5, [3, 2], [0, 0, 0, 2, 2]),
        (7, [3, 3, 5], [0, 0, 0, 0, 0, 4, 3]),
        (8, [3, 4, 7], [0, 0, 0, 0, 0, 0, 0, 5]),
        (9, [1, 3, 3, 4, 5, 6], [0, 0, 0, 0, 0, 0, 7, 1, 1]),
        (6, [1, 2, 3, 4, 5], [0, 0, 0, 0, 0, 6])
    ]

    for l, cuts, expected_output in test_cases:
        try:
            output = solution(l, cuts)
        except Exception as e:
            error_message = (
                f"An exception occurred while running the test case:\n"
                f"`l`: {l}\n"
                f"`cuts`: {cuts}\n\n"
                f"Exception: '{str(e)}'"
            )
            assert False, error_message
            
        if output != expected_output:
            error_message = (
                f"The following Test Case failed:\n"
                f"`l`: {l}\n"
                f"`cuts`: {cuts}\n\n"
                f"Actual Output: {output}\n"
                f"Expected Output: {expected_output}"
            )
            assert False, error_message

test()