Efficient subset generation

Question

Trying to find an efficient method of taking a list of values e.g. [1,2,3,4,5] and generating a list of all possible subsets. Anyone got any ideas on approaches, I have seen a couple of things that use Gray codes to help efficiency but not really sure what these are tbh!
Cheers

Answer 1

Thanks for your help dwq. Your quite right about
that. It was fun listening to the computer trying to
cope though! I was wondering if there are any
techniques to solve this problem more efficiently
than our current approaches?Hi Alex,
Here's a different approach to solve the problem more efficiently.
This doesnt use any in-memory Lists.
I tried it on sets > 10 and it gives the results fast enough.
For sets = 24, it is fast if the System.out.println to print the output on
console is commented out.
Let me know what you think.
Interesting problem :-)
Ajay
import java.util.*;
public class Subsets {
  public static void main(String [] args) {
    int [] set = new int[16];
    for (int i=0; i<set.length; i++) {
      set[i] = i;
    for (int i=1; i <= set.length; i++) {
      System.out.println("Subsets of size " + i);
      SubsetIterator iterator = new SubsetIterator(set, i);
      int[] subset = iterator.nextSubset();
      while (subset != null) {
        for (int j=0; j<subset.length; j++) {
          System.out.print(subset[j] + " ");
     System.out.println("");
        subset = iterator.nextSubset();
      System.out.println();
  static class SubsetIterator {
    private int [] set;
    private int setSize;
    private int subsetSize;
    private int[] subsetIndices;
    private boolean firstTime = true;
    public SubsetIterator(int [] set, int subsetSize) {
      this.set = set;
      this.setSize = set.length;
      this.subsetSize = subsetSize;
      subsetIndices = new int[subsetSize];
      for (int i=0; i<subsetSize; i++) {
          subsetIndices[i] = i;
     * Returns the next subset (or null if there are no more subsets)
    public int [] nextSubset() {
      if (!firstTime) incrementSubsetIndices();
      firstTime = false;
      int[] subset = new int[subsetSize];
      for (int i=0; i<subsetSize; i++) {
        if (subsetIndices[i] >= setSize) return null;
     subset[i] = set[subsetIndices];
return subset;
private void incrementSubsetIndices() {
for (int i=subsetSize-1; i>=0; i--) {
subsetIndices[i]++;
int upperBound = setSize + i - subsetSize;
if (subsetIndices[i] > upperBound) continue;
for(int j=i+1; j<subsetSize; j++) {
subsetIndices[j] = subsetIndices[j-1] + 1;
break;
/** @TODO
public boolean hasNextSubset() {