0042-trapping-rain-water

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Description

Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it can trap after raining.

 

Example 1:

Input: height = [0,1,0,2,1,0,1,3,2,1,2,1]
Output: 6
Explanation: The above elevation map (black section) is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped.

Example 2:

Input: height = [4,2,0,3,2,5]
Output: 9

 

Constraints:

• n == height.length
• 1 <= n <= 2 * 104
• 0 <= height[i] <= 105

Solution(Python)

class Solution:
    def trap(self, height: List[int]) -> int:
        #
        #  At position i
        #     left_max = tallest bar to the left of i
        #      right_max = tallest bar to right of i
        #    water levle at i = min(left_max, right_max)
        #   net water trapped = water level - height[i]
        # 4,2,0,3,2,5]
        #  trapped = 0
        #  
        trapped = 0
        n = len(height)
        left = 0
        right = n - 1
        left_max = height[left]
        right_max =  height[right]

        while left <= right: 
            if left_max < right_max:
                left_max = max(left_max, height[left])
                trapped += left_max - height[left]
                left += 1
            else:
                right_max = max(right_max, height[right])
                trapped += right_max - height[right]
                right -= 1
        return trapped