However, if the dataset is split recursively into two equal halves each time, only powers of 2 allow perfect halving to 1. Since 64000 is not a power of 2, the process never ends at 1. But the problem implies it stops.

Sun, 03 May 2026 11:00:22 +0000

Understanding Recursive Splitting of Datasets: Why Powers of 2 Are Key (and Why 64000 Poses a Challenge) When working with data, recursive splitting is a common technique used in algorithms, machine learning, and efficient data processing. One frequently discussed approach splits a dataset into two equal halves repeatedly until a desired condition is met—such as reaching a single data point. But what happens when the dataset size isn’t a power of 2, like 64,000? Why does this case cause issues, and why do perfect halving only work with powers of 2? ### Recursive Splitting and the Power of 2 Splitting recursively into two equal halves works smoothly when your dataset size is a power of 2 (e.g., 2, 4, 8, 16, 32, 64, 128...). This is because 2ⁿ divisions preserve divisibility by 2 all the way to 1. For example: