What is the optimal time complexity of solving Trapping Rain Water?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Trapping Rain Water?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Trapping Rain Water?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Trapping Rain Water?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Trapping Rain Water

Learn how to solve the 'Trapping Rain Water' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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.

Write a function trap(height: List[int]) -> int.

Constraints

•n == len(height)
•1 <= n <= 2 * 10^4
•0 <= height[i] <= 10^5

Examples

Example 1

Input

height = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]

Output

Explanation

The elevation map traps 6 units of rain water. Water fills between the bars: 1 unit above index 2, 1 unit above index 4, 2 units above index 5, 1 unit above index 6, and 1 unit above index 9.

Example 2

Input

height = [4, 2, 0, 3, 2, 5]

Output

Explanation

Water trapped: 2 above index 1, 4 above index 2, 1 above index 3, 2 above index 4 = 9 total.

Need a Hint?

Use two pointer variables starting at different bounds (e.g. left = 0, right = length - 1) and shrink the search window.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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