Trapping Rain Water in Ruby: Mastering Algorithms
The Trapping Rain Water problem is a prominent challenge in the realm of algorithms and has been a staple in many coding interviews. It presents a scenario where given an array of integers representing elevations, the task is to determine how much rainwater can be trapped between the elevations after a downpour. In this article, we’ll delve into the problem and discuss a comprehensive approach to solving it using Ruby.
Imagine you have an elevation map where the width of each bar is 1 unit. The height of each bar represents the elevation at that point. Now, after a heavy rain, water would accumulate between these bars. The question is — how much water can be trapped?
Consider the elevation map represented by the following array:
[0,1,0,2,1,0,1,3,2,1,2,1]. If you plot this on a graph, it will form a series of peaks and valleys. Water will accumulate in the valleys between the peaks. In this example, the total trapped rainwater is 6 units.
Visualizing the Problem
visualizing the Trapping Rain Water problem in plaintext is an excellent way to understand it. Let’s take the example array:
Height: 0 1 0 2 1 0 1 3 2 1 2 1
Elevation: . | . | | . | | | | | |
. | . | | . | | | | | |
. . . | | . | | | | | |
. . . | . . | | | | | |
. . . . . . . | | | | .
Water: . . . W W W W . W W W .
In the visualization above:
.represents empty space.
|represents an elevation block.
Wrepresents trapped water.
The trapped water can be seen in the spaces between the elevation blocks. In this example, the total trapped rainwater is represented by 6
W characters, which means 6 units of trapped water.