O(log n): Logarithmic Time

Logarithmic time is one of the most powerful complexity classes in computing. An O(log n) algorithm does not look at every element. Instead, it eliminates half of the remaining possibilities at each step. This halving strategy means that even enormous inputs require surprisingly few operations. Searching a sorted list of one billion elements takes at most 30 comparisons, because you only need to halve a billion 30 times to reach a single element. Why it matters: a sorted index lets the database cut the search space in half at every step. Doubling your table size adds only one extra comparison, which is why indexed queries barely slow down as data grows. The Power of Halving The logarithm answers a simple question: "How many times must I divide n by 2 to reach 1?" Start with 1,000 elements