All possible combination of n sets

Question

I have n Sets. Each Set has different number of elements. I would like to write an algorithm which give me all possible combinations from the sets. For example, let's say we have:

S1={1,2}, S2={A,B,C}, S3={$,%,£,!}

a combination should look like

C1={1,A,$}
C2={1,A,%}
...

...and so on. The number of possible combination will be 2*3*4 = 24

Please Help me to write this algorithm in Java.

Answer 1

The map and reduce approach

You can create a generic method to get the Cartesian product of different types and numbers of collections and their elements.

Try it online!

public static void main(String[] args) {
  Set<Integer> a = Set.of(1, 2);
  List<String> b = List.of("A", "B", "C");
  Set<Character> c = Set.of('$', '%', '£', '!');

  Set<Set<Object>> cpSet = cartesianProduct(HashSet::new, a, b, c);
  List<List<Object>> cpList = cartesianProduct(ArrayList::new, a, b, c);

  // output, order may vary
  System.out.println(cpSet);
  System.out.println(cpList);
}

/**
 * @param nCol the supplier of the output collection
 * @param cols the input array of collections
 * @param <R>  the type of the return collection
 * @return the cartesian product of the multiple collections
 */
@SuppressWarnings("unchecked")
public static <R extends Collection<?>> R cartesianProduct(
      Supplier nCol, Collection<?>... cols) {
  // check if supplier is not null
  if (nCol == null) return null;
  return (R) Arrays.stream(cols)
      // non-null and non-empty collections
      .filter(col -> col != null && col.size() > 0)
      // represent each element of a collection as a singleton collection
      .map(col -> (Collection<Collection<?>>) col.stream()
          .map(e -> Stream.of(e).collect(Collectors.toCollection(nCol)))
          .collect(Collectors.toCollection(nCol)))
      // summation of pairs of inner collections
      .reduce((col1, col2) -> (Collection<Collection<?>>) col1.stream()
          // combinations of inner collections
          .flatMap(inner1 -> col2.stream()
              // concatenate into a single collection
              .map(inner2 -> Stream.of(inner1, inner2)
                  .flatMap(Collection::stream)
                  .collect(Collectors.toCollection(nCol))))
          // collection of combinations
          .collect(Collectors.toCollection(nCol)))
      // otherwise an empty collection
      .orElse((Collection<Collection<?>>) nCol.get());
}

Output (cropped, order may vary):

[[1, A, !], [1, !, B], [A, !, 2], [1, A, £], [1, !, C]...
[[1, A, $], [1, A, %], [1, A, £], [1, A, !], [1, B, $]...

---

^{See also: Finding cartesian product in Java}

Answer 2

Great solution by krilid, I modified it a bit to return a list of all combinations.

@Test
public void testMap() throws Exception {
    char[] one = new char[]{'a', 'b', 'c'};
    char[] two = new char[]{'d', 'e', 'f'};
    char[] three = new char[]{'g', 'h', 'i', 'j'};
    char[][] sets = new char[][]{one, two, three};
    List<List<Character>> collector = new ArrayList<>();
    ArrayList<Character> combo = new ArrayList<>();
    combinations(collector, sets, 0, combo);
    System.out.println(collector);
}

private void combinations(List<List<Character>> collector,
                          char[][] sets, int n,
                          ArrayList<Character> combo) {
    if (n == sets.length) {
        collector.add(new ArrayList<>(combo));
        return;
    }
    for (char c : sets[n]) {
        combo.add(c);
        combinations(collector, sets, n + 1, combo);
        combo.remove(combo.size() - 1);
    }
}

Answer 3

In the case someone wants the matrix instead of printing, I slightly modified the code:

public class TestSetCombinations2 {
  public static void main(String[] args) {
    Double[] set1 = {2.0, 3.0};
    Double[] set2 = {4.0, 2.0, 1.0};
    Double[] set3 = {3.0, 2.0, 1.0, 5.0};
    Double[] set4 = {1.0, 1.0};
    Object[][] sets = {set1, set2, set3, set4};

    Object[][] combinations = getCombinations(sets);

    for (int i = 0; i < combinations.length; i++) {
      for (int j = 0; j < combinations[0].length; j++) {
        System.out.print(combinations[i][j] + " ");
      }
      System.out.println();
    }
  }

  private static Object[][] getCombinations(Object[][] sets) {
    int[] counters = new int[sets.length];
    int count = 1;
    int count2 = 0;

    for (int i = 0; i < sets.length; i++) {
      count *= sets[i].length;
    }

    Object[][] combinations = new Object[count][sets.length];

    do {
      combinations[count2++] = getCombinationString(counters, sets);
    } while (increment(counters, sets));

    return combinations;
  }

  private static Object[] getCombinationString(int[] counters, Object[][] sets) {
    Object[] o = new Object[counters.length];
    for (int i = 0; i < counters.length; i++) {
      o[i] = sets[i][counters[i]];
    }
    return o;
  }

  private static boolean increment(int[] counters, Object[][] sets) {
    for (int i = counters.length - 1; i >= 0; i--) {
      if (counters[i] < sets[i].length - 1) {
        counters[i]++;
        return true;
      } else {
        counters[i] = 0;
      }
    }
    return false;
  }
}

Answer 4

Recursion is your friend:

public class PrintSetComb {
  public static void main(String[] args) {
    String[] set1 = {"1", "2"};
    String[] set2 = {"A", "B", "C"};
    String[] set3 = {"$", "%", "£", "!"};
    String[][] sets = {set1, set2, set3};

    printCombinations(sets, 0, "");
  }

  private static void printCombinations(String[][] sets, int n, String prefix) {
    if (n >= sets.length) {
      System.out.println("{" + prefix.substring(0, prefix.length() - 1) + "}");
      return;
    }
    for (String s : sets[n]) {
      printCombinations(sets, n + 1, prefix + s + ",");
    }
  }
}

In response to question from OP about generalizing it to sets of Objects:

public class PrintSetComb {
  public static void main(String[] args) {
    Integer[] set1 = {1, 2};
    Float[] set2 = {2.0F, 1.3F, 2.8F};
    String[] set3 = {"$", "%", "£", "!"};
    Object[][] sets = {set1, set2, set3};

    printCombinations(sets, 0, new Object[0]);
  }

  private static void printCombinations(Object[][] sets, int n, Object[] prefix) {
    if (n >= sets.length) {
      String outp = "{";
      for (Object o : prefix) {
        outp = outp + o.toString() + ",";
      }
      System.out.println(outp.substring(0, outp.length() - 1) + "}");
      return;
    }
    for (Object o : sets[n]) {
      Object[] newPrefix = Arrays.copyOfRange(prefix, 0, prefix.length + 1);
      newPrefix[newPrefix.length - 1] = o;
      printCombinations(sets, n + 1, newPrefix);
    }
  }
}

And finally an iterative variant. It is based on increasing an array of counters where the counter wraps and carries when it reaches the size of the set:

public class PrintSetCombIterative {
  public static void main(String[] args) {
    String[] set1 = {"1", "2"};
    String[] set2 = {"A", "B", "C"};
    String[] set3 = {"$", "%", "£", "!"};
    Object[][] sets = {set1, set2, set3};

    printCombinations(sets);
  }

  private static void printCombinations(Object[][] sets) {
    int[] counters = new int[sets.length];

    do {
      System.out.println(getCombinationString(counters, sets));
    } while (increment(counters, sets));
  }

  private static boolean increment(int[] counters, Object[][] sets) {
    for (int i = counters.length - 1; i >= 0; i--) {
      if (counters[i] < sets[i].length - 1) {
        counters[i]++;
        return true;
      } else {
        counters[i] = 0;
      }
    }
    return false;
  }

  private static String getCombinationString(int[] counters, Object[][] sets) {
    String combo = "{";
    for (int i = 0; i < counters.length; i++) {
      combo = combo + sets[i][counters[i]] + ",";
    }
    return combo.substring(0, combo.length() - 1) + "}";
  }
}