Here is a detailed Markdown blog post for the problem "Array Transformation with Repeated Steps and Modulo Operation":

Array Transformation with Repeated Steps and Modulo Operation

Summary

Given an array, we need to transform it by repeating certain steps until no more changes can be made. Each step involves applying a modulo operation on all elements of the array. The goal is to find the final transformed array.

Detailed Explanation

To solve this problem, we'll start with an understanding of the given constraints and requirements. We are provided with an integer array arr and an integer k. Our task is to repeatedly apply a transformation step until no further changes can be made.

The transformation step involves taking each element in the array, adding k, and then taking the remainder when divided by n, where n is the length of the array. We'll repeat this process until the array remains unchanged after one iteration.

Here's a step-by-step breakdown of the solution:

1. Initialize an empty array result.
2. Repeat the following steps until no further changes can be made:
   • For each element x in the array, add k and take the remainder when divided by n. This gives us the new value for x.
   • Update the original array with the new values.
3. Return the final transformed array.

Let's analyze the time complexity of this solution:

• We're performing a constant-time operation (adding k and taking the remainder) for each element in the array, which takes O(n) time.
• Since we're doing this repeatedly until no further changes can be made, the total time complexity is O(n * k).
• The space complexity is O(n), as we need to store the original array and the transformed array.

Optimized Solutions

Java