The answer
Yes, drastically faster. As data scales into the millions, an O(N) algorithm takes millions of steps, while an O(log N) algorithm takes around 20 steps.
O(log N) Logarithmic Time: How Halving Speeds Up Code
Is O(log N) faster than O(N)?
More FAQs in O(log N) Logarithmic Time: How Halving Speeds Up Code
It means the algorithm's execution time grows very slowly because it eliminates half of the remaining data on every single step of the process.
Because computers operate in binary (base 2), and most logarithmic algorithms (like Binary Search or Tree traversal) divide the data exactly in half.
Binary Search. By repeatedly checking the middle of a sorted array and discarding half, it finds elements with incredible efficiency.
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