java - n组所有可能的组合

Question

我有 n 个集合。每个 Set 都有不同数量的元素。我想编写一个算法，为我提供集合中所有可能的组合。例如，假设我们有:

S1={1,2}, S2={A,B,C}, S3={$,%,£,!}

组合应该是这样的

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

……等等。可能的组合数将为 2*3*4 = 24

请帮我用Java写这个算法。

Answer 1

递归是你的 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 + ",");
    }
  }
}

在回答 OP 关于将其泛化为对象集的问题时:

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);
    }
  }
}

最后是迭代变体。它基于增加一个计数器数组，当计数器达到集合的大小时，计数器会进行包装和进位:

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) + "}";
  }
}