Return a Largest Pairwise-Divisible Subset

# Return a Largest Pairwise-Divisible Subset Given a list `nums` of distinct positive integers, return a subset with the greatest possible number of elements such that every pair of its elements divides in at least one direction. For any two selected values `a` and `b`, either `a % b == 0` or `b % a == 0` must hold. If several maximum-size subsets exist, return any one of them. ### Function `vector<int> largestDivisibleSubset(vector<int>& nums)` ### Example 1 ```text Input: nums = [2,3,6] One valid output: [2,6] ``` `[3,6]` is also valid and has the same maximum size. The subset `[2,3,6]` is invalid because neither `2` nor `3` divides the other. ### Example 2 ```text Input: nums = [4,8,16] Output: [4,8,16] ``` ### Constraints - `1 <= nums.length <= 1000`. - `1 <= nums[i] <= 2000000000`. - All values are distinct. ### Clarifications Return selected values, not their count or indices. Reusing a value is not allowed. A subset has no required display order. Different optimal subsets may have different members; there is no required tie-breaking rule. ### What a Strong Answer Covers - The condition on every selected pair. - Why the returned subset has maximum size. - Single-element inputs and multiple equally good outputs. - A correctness argument and resource bounds at the stated limits. ### Follow-up Questions - If two implementations return different subsets for the same input, what would you check to decide whether both are correct without requiring their chosen members or display order to match?