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

For example,
If n = 4 and k = 2, a solution is:

[
[2,4],
[3,4],
[2,3],
[1,2],
[1,3],
[1,4],
]

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public class Solution {
    public List<List<Integer>> combine(int n, int k) {
        List<List<Integer>> result = new ArrayList<>();
        combination(result, new ArrayList<Integer>(), n, k, 1);
        return result;
    }
    
    public void combination(List<List<Integer>> result, ArrayList<Integer> cur, int n, int k, int start) {
        if (cur.size() == k) {
            result.add(new ArrayList<Integer>(cur));
        } else {
            for (int i = start; i <= n; i++) {
                cur.add(i);
                combination(result, cur, n, k, i + 1);
                cur.remove(cur.size() - 1);
            }
        }
    }
}

Another solution based on mathmetical properties

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public class Solution {
    public List<List<Integer>> combine(int n, int k) {
    	// base case
        if (k == n || k == 0) {
            List<Integer> row = new LinkedList<>();
            for (int i = 1; i <= k; ++i) {
                row.add(i);
            }
            return new LinkedList<>(Arrays.asList(row));
        }
        List<List<Integer>> result = this.combine(n - 1, k - 1); // n is selected
        result.forEach(e -> e.add(n));
        result.addAll(this.combine(n - 1, k)); // n is not selected
        return result;
    }
}