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

Here is my solution, it passes this level and pretty fast, easy to understand The idea is very simple: first, you figure out the maximum of the heights (it could be multiple maximum), then you chop the landscape into 3 parts, from the beginning to the left most maximum heights, between the left most max to the right most max, and from the right most max to the end.

In the middle part, it's easy to collect the rains, one for loop does that. Then for the first part, you keep on updating the current max height that is less than the max height of the landscape. one loop does that. Then for the third part, you reverse what you have done to the first part

def answer(heights):
    sumL = 0
    sumM = 0
    sumR = 0
    L = len(heights)
    MV = max(heights)
    FI = heights.index(MV)
    LI = L - heights[::-1].index(MV) - 1
    if LI-FI>1:
        for i in range(FI+1,LI):
            sumM = sumM + MV-heights[i]

    if FI>0:
        TM = heights[0]
        for i in range(1,FI):
            if heights[i]<= TM:
                sumL = sumL + TM-heights[i]
            else:
                TM = heights[i]
    if LI<(L-1):
        TM = heights[-1]
        for i in range(L-1,LI,-1):
            if heights[i]<= TM:
               sumL = sumL + TM-heights[i]
            else:
               TM = heights[i]
    return(sumL+sumM+sumR)