Question

Given a set {1,2,3,4,5...n} of n elements, we need to find all subsets of length k .

For example, if n = 4 and k = 2, the output would be {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}.

I am not even able to figure out how to start. We don’t have to use the inbuilt library functions like next_permutation etc.

Need the algorithm and implementation in either C/C++ or Java.

Answer 1

Recursion is your friend for this task.

For each element – “guess” if it is in the current subset, and recursively invoke with the guess and a smaller superset you can select from. Doing so for both the “yes” and “no” guesses – will result in all possible subsets.

Restraining yourself to a certain length can be easily done in a stop clause.

Java code:

private static void getSubsets(List<Integer> superSet, int k, int idx, Set<Integer> current,List<Set<Integer>> solution) {
    //successful stop clause
    if (current.size() == k) {
        solution.add(new HashSet<>(current));
        return;
    }
    //unseccessful stop clause
    if (idx == superSet.size()) return;
    Integer x = superSet.get(idx);
    current.add(x);
    //"guess" x is in the subset
    getSubsets(superSet, k, idx+1, current, solution);
    current.remove(x);
    //"guess" x is not in the subset
    getSubsets(superSet, k, idx+1, current, solution);
}

public static List<Set<Integer>> getSubsets(List<Integer> superSet, int k) {
    List<Set<Integer>> res = new ArrayList<>();
    getSubsets(superSet, k, 0, new HashSet<Integer>(), res);
    return res;
}

Invoking with:

List<Integer> superSet = new ArrayList<>();
superSet.add(1);
superSet.add(2);
superSet.add(3);
superSet.add(4);
System.out.println(getSubsets(superSet,2));

Will yield:

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