77. Combinations

Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.

Example:

Input: n = 4, k = 2
Output:
[
  [2,4],
  [3,4],
  [2,3],
  [1,2],
  [1,3],
  [1,4],
]

vector<vector<int>> combine(int n, int k) { // time: O(C(n, k)); space: O(C(n, k))
    vector<vector<int> > res;
    vector<int> cur;
    helper(res, cur, n, k, 1);
    return res;
}
void helper(vector<vector<int> >& res, vector<int>& cur, int n, int k, int start) {
    if (cur.size() >= k) {
        res.push_back(cur);
    } else {
        for (int i = start; i <= n; ++i) {
            cur.push_back(i);
            helper(res, cur, n, k, i + 1);
            cur.pop_back();
        }
    }
}

vector<vector<int>> combine(int n, int k) { // time: O(C(n, k)); space: O(C(n, k))
    vector<vector<int> > res;
    vector<int> cur(k, 0);
    int i = 0;
    while (i >= 0) {
        ++cur[i];
        if (cur[i] > n) {
            --i;
        } else if (i == k - 1) {
            res.push_back(cur);
        } else {
            ++i;
            cur[i] = cur[i - 1];
        }
    }
    return res;
}