Trapping Rain Water

Problem 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 the 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 * 10^4
• 0 <= height[i] <= 10^5

Code Template

class Solution:
    def trap(self, height: List[int]) -> int:
        # Write your code here
        pass

Solutions

• Solution 1: This approach uses precomputed arrays to store the maximum heights to the left and right of each position. It has a time complexity of O(n) and a space complexity of O(n).
• Solution 2: This approach uses two pointers to optimize space usage. It has a time complexity of O(n) and a space complexity of O(1).

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