👉 The presented math involves analyzing the growth and efficiency of a specific algorithm, likely related to data compression or encoding techniques. The core idea is to compare the time complexity and space complexity of two different algorithms, one being a naive approach and the other an optimized method. The naive algorithm processes data sequentially, which results in a time complexity of O(n^2) due to nested loops iterating over the data. In contrast, the optimized algorithm employs a more sophisticated method, such as using a hash table or a dictionary to map values to indices, reducing the time complexity to O(n). This optimization not only speeds up the process but also significantly reduces memory usage, making it more efficient for large datasets. The analysis highlights the trade-offs between simplicity and performance in algorithm design, showcasing how strategic choices can lead to substantial improvements in computational efficiency.
