Enumerate Every Fixed-Size Choice from a Range

### Problem Return all distinct combinations of `k` different integers selected from the inclusive range 1 through `n`. A combination is a choice of members, so changing their order does not create a new combination. Include every such choice exactly once; the returned combinations may be listed in any order. ```cpp vector<vector<int>> combine(int n, int k); ``` No particular ordering inside a combination is required to represent its members. Increasing order is a valid implementation choice, not an added input/output condition. ### Examples ```text Input: n = 5, k = 3 One valid output: [[1,2,3],[1,2,4],[1,2,5],[1,3,4],[1,3,5],[1,4,5],[2,3,4],[2,3,5],[2,4,5],[3,4,5]] ``` ```text Input: n = 3, k = 2 One valid output: [[3,2],[1,3],[2,1]] ``` The latter collection represents the choices `{2,3}`, `{1,3}`, and `{1,2}` once each. ### Constraints & Assumptions - `1 <= n <= 20`. - `1 <= k <= n`. - A member cannot be repeated within a combination. - Permutations of the same members are not separate combinations. ### Clarifying Questions to Ask - Is `[2,1]` a different choice from `[1,2]`? No. - Are combinations containing a repeated number allowed? No; select different numbers from the range. ```hint Distinguish a choice from a sequence The answer enumerates member sets. Reordering an already returned choice does not add a new one. ``` ### What a Strong Answer Covers - Completeness of the k-member choices and exclusion of repeats within or across choices. - A clear construction convention without turning that convention into a source requirement. - Output-sensitive cost for storing all combinations. ### Follow-up Questions - How can equivalent answers be compared without fixing either list order or each choice's presentation order? - What do the answers look like for `k=1` and `k=n`?