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

You can do this by scanning the array twice.

The first time you scan from top to bottom and store the value of the tallest tower you have yet to encounter when reaching each row.

You then repeat the process, but in reverse. You start from the bottom and work towards the top of the array. You keep track of the tallest tower you have seen so far and compare the height of it to the value for that tower in the other result set.

Take the difference between the lesser of these two values (the shortest of the tallest two towers surrounding the current tower, subtract the height of the tower and add that amount to the total amount of water.

int maxValue = 0;
int total = 0;
int[n] lookAhead

for(i=0;i maxValue) maxValue = input[i];
    lookahead[i] = maxValue;
}

maxValue = 0;
for(i=n-1;i>=0;i--)
{
    // If the input is greater than or equal to the max, all water escapes.
    if(input[i] >= maxValue)
    { 
        maxValue = input[i];
    }
    else
    {
        if(maxValue > lookAhead[i])
        {
            // Make sure we don't run off the other side.
            if(lookAhead[i] > input[i])
            {
                total += lookAhead[i] - input[i];
            }
        }
        else
        {
            total += maxValue - input[i];
        }
    } 
}