Largest Divisible Subset Coding Problem Solution

Largest Divisible Subset is a classic dynamic programming problem that shows up in coding interviews because it looks mathematical, but the real skill is building the right structure. You are given a set (or array) of distinct positive integers. You need to return the largest subset where every pair of numbers in the subset satisfies a divisibility rule. The rule is simple: for any two numbers in the subset, either one divides the other. That means if your subset contains a and b, then a % b == 0 or b % a == 0 must be true. The goal is not to find all such subsets. The goal is to find one of the maximum size. This problem becomes interesting because divisibility is not “local” in the same way sorting is. Two numbers can individually divide a third but not divide each other. So you need a strategy that ensures the entire subset stays consistent. Why a direct approach is slow A tempting approach is to try different combinations and check whether all pairs are divisible. That quickly beco