Correct the algorithm for transforming a nested dictionary into a flat one

In this exercise, you will correct and optimize an algorithm that processes a nested dictionary and transforms it into a flat (non-nested) dictionary. The goal is to ensure that all key-value pairs are correctly mapped using a key path format (e.g., parent.child.key). You will analyze the existing code, identify any logical or implementation errors, and propose an efficient solution that works correctly for various levels of nesting