Given a string, str, rearrange it so that any two adjacent characters are not the same. If such a reorganization of the characters is possible, output any possible valid arrangement. Otherwise, return an empty string.

Constraints:

• $1\leq$ str.length $\leq500$
• Input string consists of lowercase English letters.

So far, you’ve probably brainstormed some approaches and have an idea of how to solve this problem. Let’s explore some of these approaches and figure out which one to follow based on considerations such as time complexity and any implementation constraints.

The naive approach is to generate all possible permutations of the given string and check if the generated string is a valid arrangement or not. If any permutation satisfies the condition of a valid reorganization of the string, return that permutation of the input string. If no permutation is a valid reorganization of the string, return an empty string.

The number of possible permutations for a string of length $n$ is $n!$, and it might require iterating through the $n$ characters to construct each permutation. Therefore, it will take $O(n! \times n)$ time to generate all these permutations. Then, for each permutation, we need to check whether it satisfies the condition of having no adjacent characters that are the same. Checking this condition requires iterating through the permutation once, which takes $O(n)$ ...