Trapping Rain Water

1. Clarify the problem:

Before we begin, let's clarify the problem statement. The "Trapping Rain Water" problem asks us to calculate the total amount of water that can be trapped between bars given an elevation map. Each bar has a certain height, and water can only be trapped between bars.

2. Analyze the problem:

Let's analyze the problem to identify the input, output, and constraints.

Input:

• An array representing the elevation map, where each element represents the height of a bar.

Output:

• An integer representing the total amount of water that can be trapped.

Constraints:

• The input array can have up to 10^5 elements.
• The height of each bar is a non-negative integer.

3. Design an algorithm:

To solve this problem, we can use a two-pointer approach. Here's the general outline of our algorithm:

1. Initialize two pointers, left and right, at the beginning and end of the array, respectively.
2. Initialize variables left_max and right_max to keep track of the maximum bar heights encountered from the left and right, respectively.
3. Initialize a variable total_water to store the total amount of trapped water.
4. While left is less than or equal to right:
   • If height[left] is less than or equal to height[right]:
     • If height[left] is greater than left_max, update left_max to height[left].
     • Add left_max - height[left] to total_water.
     • Increment left by 1.
   • Otherwise:
     • If height[right] is greater than right_max, update right_max to height[right].
     • Add right_max - height[right] to total_water.
     • Decrement right by 1.
5. Return total_water.

4. Explain your approach:

Our approach involves using a two-pointer technique to iterate from both ends of the elevation map. We keep track of the maximum heights encountered from the left and right sides and calculate the trapped water at each position based on the minimum of the two maximum heights. By iterating through the map once, we can calculate the total trapped water efficiently.

5. Write clean and readable code:

Let's implement the algorithm in Python:

python

def trap(height):
    left = 0
    right = len(height) - 1
    left_max = right_max = total_water = 0
    
    while left <= right:
        if height[left] <= height[right]:
            if height[left] > left_max:
                left_max = height[left]
            total_water += left_max - height[left]
            left += 1
        else:
            if height[right] > right_max:
                right_max = height[right]
            total_water += right_max - height[right]
            right -= 1
    
    return total_water

6. Test your code:

Let's test our code with different test cases to ensure its correctness. We'll consider the following cases:

• Case 1:

  python

height = [0,1,0,2,1,0,1,3,2,1,2,1]
print(trap(height))

python

height = [4,2,0,3,2,5]
print(trap(height))

python

height = [0,1,2,3,4,5]
print(trap(height))

python

height = [5,4,3,2,1,0]
print(trap(height))

python