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The Question
Coding

Trapping Rain Water

Given an array of 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: Input: height = [0,1,0,2,1,0,1,3,2,1,2,1] Output: 6 Constraints: - n == height.length - 1 <= n <= 2 * 10^4 - 0 <= height[i] <= 10^5
Java
Two Pointers
Questions & Insights

Clarifying Questions

What are the constraints on the input array size $N$ and the values of the heights? (Assumption: N can be up to 10^5, and heights are non-negative integers up to 10^5).
How should we handle empty arrays or arrays with fewer than 3 elements? (Assumption: At least 3 elements are needed to trap any water; return 0 for smaller inputs).
Is the input array mutable, or should we treat it as read-only? (Assumption: Read-only, though our optimal solution won't require modification anyway).
What are the space complexity requirements? (Assumption: We aim for the most optimal O(1) auxiliary space solution).

Thinking Process

The amount of water trapped at any index is determined by the "limiting factor" of its boundaries: min(max_height_to_left, max_height_to_right) - height[i].
A naive approach would pre-calculate prefix and suffix maximums in O(N) time and O(N) space, but we can optimize this using two pointers.
By maintaining leftMax and rightMax while moving pointers from both ends of the array, we can always determine the water at the pointer pointing to the smaller "max" because that smaller value is guaranteed to be the global bottleneck for that specific position.
We iterate until the pointers meet, accumulating the trapped water volume at each step where the current height is less than its respective side's maximum.
Implementation Breakdown

Problem Set

Functional Requirements:
Input: An array of non-negative integers.
Output: Total units of trapped rain water.
Constraints:
Time Complexity: O(N)
Space Complexity: O(1)
Input size up to 10^5.

Approach

Algorithm: Two Pointers
Data Structure: Array
Complexity:
Time: O(n) where n is the length of the height array.
Space: O(1) as we only store a few primitive variables.

Implementation

Wrap Up

Advanced Topics

Readability vs. Performance: While the two-pointer approach is O(1) space, the Dynamic Programming approach (using two arrays for leftMax and rightMax) is often considered more readable and easier to debug during a live interview.
Monotonic Stack: One could also solve this using a monotonic decreasing stack. This approach calculates water "horizontally" (layer by layer) rather than "vertically" (column by column). This is useful if the problem asks for the specific coordinates of the trapped water pools.
Parallelization: This problem is not easily parallelizable in its two-pointer form because the state depends on previous maximums. However, the DP approach can be parallelized by splitting the array into chunks, calculating local maxes, and then merging results.