Welcome to this exciting analysis lesson! In this unit, we're going to take a practical approach and utilize several intriguing techniques such as Skipping Redundant Cases, Optimization Using Precalculation, and Picking the Best Variable to Iterate Over. Our platform for this unit is an array-based problem, where we'll apply these techniques to formulate an efficient and optimized solution. Ready for the challenge? Then, let's get started!

Our task here involves an array composed of at most 1,000 elements and potentially millions of queries. Each query is a pair of integers denoted as l and r, which correspond to some indices in the array. Your goal is to write a Java method that, for each query, returns the minimum value in the array between indices l and r (inclusive).

The catch is this: rather than directly finding the minimum value for each query one by one, we're required to optimize the process. The idea here is to precalculate the minimum value for each possible l and r, store these values, and then proceed with the queries. This way, we can simplify the problem and enhance the speed of our solution by eliminating redundant computations.

The method will accept three parameters: arr, Ls, and Rs. The primary array is , while and are s that hold the and values respectively for each query. For instance, let's say you have an array like and the following queries: and . The aim of our method would be to return as the minimum values within the ranges of the three queries.