Guide for Collecting Rainwater - Visuals Included for Ease of Understanding
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The Trapping Rainwater Problem is a classic algorithmic challenge that aims to calculate the amount of water that can be trapped in an elevation array after rainfall. Here, we explore several efficient methods that improve upon the brute force approach, offering linear time complexity and minimal extra space.
Brute Force Approach
The brute force approach has a time complexity of O(n^2) and a space complexity of O(1), but it is not efficient due to its repeated calculations of max heights.
Two-Pointer Approach (Optimal solution)
The two-pointer approach is the fastest and most memory-efficient solution, processing the array in one pass with constant extra space (O(1)). It uses two pointers starting at both ends of the height array, maintaining the maximum heights seen so far from the left and right. At each step, water trapped is determined by the smaller max boundary.
Prefix and Suffix Arrays
Another efficient method involves precomputing two arrays: one with the tallest bar to the left (prefix max) of each index and another with the tallest bar to the right (suffix max). For each index, trapped water is the minimum of prefix and suffix max minus the current height. This method runs in linear time (O(n)) but requires O(n) extra space.
Stack-Based Approach
The stack-based approach uses a stack to track bars and water trapped when finding a bounding right wall higher than the current top of the stack. It runs in linear time (O(n)) but uses O(n) space, making it an alternate linear time approach.
Summary Table
| Algorithm | Time Complexity | Space Complexity | Notes | |-----------------------|-----------------|------------------|--------------------------------| | Brute Force | O(n^2) | O(1) | Not efficient - recalculates max height repeatedly | | Prefix & Suffix Max | O(n) | O(n) | Easy to understand and implement | | Two Pointers (Optimal)| O(n) | O(1) | Fastest, most memory-efficient, single pass | | Stack | O(n) | O(n) | Alternative linear time approach |
These algorithms calculate trapped water at each position based on the shortest boundary on its left and right, summing across positions to find the total water trapped. The insight that water depth depends on the minimum of the tallest bars to the left and right underpins all efficient methods.
For detailed code and explanation, see GeeksforGeeks, 2025-08-12 or CodeandDebug.in, 2025-08-11.
- The two-pointer approach, an optimal solution, processes an elevation array in a single pass with constant extra space (O(1)), using two pointers starting at both ends of the height array.
- Prefix and suffix arrays, another efficient method, precomputes two arrays: one with the tallest bar to the left (prefix max) of each index and another with the tallest bar to the right (suffix max).
- The stack-based approach uses a stack to track bars, and calculates water trapped when finding a bounding right wall higher than the current top of the stack, running in linear time (O(n)) but using O(n) space.
- Math and data structures such as arrays, trie, and algorithms like suffix array play essential roles in solving the Trapping Rainwater Problem, offering efficient solutions that improve upon the brute force approach.
