Water collected between towers

Question

I recently came across an interview question asked by Amazon and I am not able to find an optimized algorithm to solve this question:

You are given an input array wh

Answer 1

I have a solution that only requires a single traversal from left to right.

def standing_water(heights):

    if len(heights) < 3:
        return 0

    i = 0   # index used to iterate from left to right
    w = 0   # accumulator for the total amount of water

    while i < len(heights) - 1:

        target = i + 1
        for j in range(i + 1, len(heights)):

            if heights[j] >= heights[i]:
                target = j
                break

            if heights[j] > heights[target]:
                target = j

        if target == i:
            return w

        surface = min(heights[i], heights[target])

        i += 1

        while i < target:
            w += surface - heights[i]
            i += 1

    return w