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Solving the Rainwater Trapping Problem with an Optimized Python Script

Solving the Rainwater Trapping Problem with an Optimized Python Script

February 06, 2025 Digital

Solving the Rainwater Trapping Problem with an Optimized Python Script

The rainwater trapping problem is a challenging yet fascinating algorithmic puzzle that has garnered interest across the programming community. This article will explore a solution to the problem, presenting an optimized Python script that not only fulfills the requirements but also performs efficiently. Let's dive into the details.

Understanding the Problem

The rainwater trapping problem involves calculating the amount of rainwater that can be trapped between a series of bars of different heights. Given a list of bar heights, the task is to determine the total amount of rainwater the bars can trap.

Existing Solutions

To solve the rainwater trapping problem, there are several existing solutions available online. These solutions range from basic to optimized, with some offering optimal time complexity. The linked page, for instance, provides six different solutions, including two that run in O(n) time with O(1) auxiliary space. However, the solution presented here aims to optimize both time and space complexity while maintaining readability.

Optimized Python Script

The Python script provided below is an optimized solution to the rainwater trapping problem. It utilizes a prefix and suffix array to precompute the maximum heights to the left and right of each bar. This approach ensures that the solution is computed in a single pass, making it both efficient and effective.

def rain_trapping(E):
    n  len(E)
    L  [0] * n  # Max height to the left of each bar
    R  [0] * n  # Max height to the right of each bar
    T  [0] * n  # Amount of water trapped at each bar
    max_l  0
    for i in range(n):
        max_l  max(max_l, E[i])
        L[i]  max_l
    max_r  0
    for i in range(n-1, -1, -1):
        max_r  max(max_r, E[i])
        R[i]  max_r
    for i in range(n):
        T[i]  min(L[i], R[i]) - E[i]
    return sum(T)

Example Usage

The script is tested with the examples provided by GeeksforGeeks:

EE  [
    [2, 0, 2],
    [3, 0, 2, 0, 4],
    [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]
]
for E in EE:
    print(f'E: {E}')
    print(f'Water Trapped: {rain_trapping(E)}')

The output for the given examples is as follows:

E: [2, 0, 2]
Water Trapped: 2 E: [3, 0, 2, 0, 4]
Water Trapped: 7 E: [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]
Water Trapped: 6

Additional Notes and Tips

While the provided script is efficient, it is always a good practice to further optimize the solution based on specific constraints. For example, if the input list is very large, consider using more advanced data structures or algorithms.

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Feel free to leave your comments or insights if you have any further questions or improvements to share!

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