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You are given multiple integer sets and you need to find duplicates in them, ie. you need to find the intersection of all the sets.


Suppose we have 3 arrays of integer sets and we need to merge them. The fastest solution would be possible in time of O(n1 + n2 + n3) where n1, n2, n3 are the lengths of the three sets respectively. The solution lies in using two bit-vectors (also called as bit-set or a bit-array) to represent intersection between any two sets and then using the resultant to intersect with the next one, and so on.

  • Construct a running bit-set and populate it with the first array
  • Using a second bit-set intersect the first bit-set with second array
  • Now change-over the second to the first bit-set
  • And repeat the process above with the third array, fourth array and so on
public void findDuplicates(int[] array1, int[] array2, int[] array3) {
  BitSet first = new BitSet();
  BitSet result = new BitSet();

  // populate the initial one
  for(int num : array1) {
    first.setBit(num, true);

  // intersect with second
  for(int num : array2) {
    if(first.isBitSet(num)) {

  // change-over
  first = result;
  result = new BitSet();

  // intersect with third
  for(int num : array3) {
    if(first.isBitSet(num)) {

  // output
  int index = -1;
  do {
    index = result.getNextSetBit(index);
    if(index < 0) {

  } while(true);

The solution above can be extended to as many arrays as are provided in the problem definition. The time to sort will still remain O(N) where N is the sum of total number of elements across all provided arrays.

Optimizations available

  • One can make use of sparsed-bit-arrays to reduce memory consumption. Refer to brettwooldridge/SparseBitSet for one such implementation.

  • If the arrays are really, really huge - an implementation that uses file-based persistence of a bit-array can be used. Refer to one such implementation available in the jerry-core project.