鉴于什么是 k 排列(http://en.wikibooks.org/wiki/Probability/Combinatorics),您正在寻找 k 从 1 到 D 变化的 k 排列,其中 D 是数据集合的大小。
这意味着要计算 - 我的第一篇文章我无法发布图片,所以请查看位于的等式:
为了做到这一点,您可以使 k 变化,并且对于每个 k 可能 n 变化(即仅处理子数组或数据以枚举 k 排列)。这些 k 排列可以通过使用递归将数组向右和向左移动来找到。
这是一个快速引导程序,可以证明需要枚举什么:
public class EnumUrl {
private Set<String> enumeration = null;
private List<String> data = null;
private final String baseUrl = "http://localhost:8080/service/USERID=101556000/";
public EnumUrl(List<String> d) {
data = d;
enumeration = new HashSet<String>(); // choose HashSet : handle duplicates in the enumeration process
}
public Set<String> getEnumeration() {
return enumeration;
}
public static void main(String[] args) {
List<String> data = new ArrayList<String>();
data.add("A");
data.add("B");
data.add("C");
EnumUrl enumerator = new EnumUrl(data);
for (int k = 0; k < data.size(); k++) {
// start from any letter in the set
for (int i = 0; i < data.size(); i++) {
// enumerate possible url combining what's on the right of indice i
enumerator.enumeratePossibleUrlsToRight(data.get(i), i);
// enumerate possible url combining what's on the left of indice i
enumerator.enumeratePossibleUrlsToLeft(data.get(i), i);
}
// make a circular permutation of -1 before the new iteration over the newly combined data
enumerator.circularPermutationOfData();
}
// display to syso
displayUrlEnumeration(enumerator);
}
private void circularPermutationOfData() {
String datum = data.get(0);
for (int i = 1; i < data.size(); i++) {
data.set(i - 1, data.get(i));
}
data.set(data.size() - 1, datum);
}
private static void displayUrlEnumeration(EnumUrl enumerator) {
for (String url : enumerator.getEnumeration()) {
System.out.println(url);
}
}
private void enumeratePossibleUrlsToRight(String prefix, int startAt) {
enumeration.add(baseUrl + prefix);
if (startAt < data.size() - 1) {
startAt++;
for (int i = startAt; i < data.size(); i++) {
int x = i;
enumeratePossibleUrlsToRight(prefix + "," + data.get(x), x);
}
}
}
private void enumeratePossibleUrlsToLeft(String prefix, int startAt) {
enumeration.add(baseUrl + prefix);
if (startAt > 0) {
startAt--;
for (int i = startAt; i >= 0; i--) {
int x = i;
enumeratePossibleUrlsToLeft(prefix + "," + data.get(x), x);
}
}
}
}
{A,B,C} 的程序输出:
http://localhost:8080/service/USERID=101556000/B,C
http://localhost:8080/service/USERID=101556000/B,A,C
http://localhost:8080/service/USERID=101556000/B,C,A
http://localhost:8080/service/USERID=101556000/B,A
http://localhost:8080/service/USERID=101556000/C
http://localhost:8080/service/USERID=101556000/B
http://localhost:8080/service/USERID=101556000/C,B,A
http://localhost:8080/service/USERID=101556000/A,C,B
http://localhost:8080/service/USERID=101556000/A,C
http://localhost:8080/service/USERID=101556000/A,B
http://localhost:8080/service/USERID=101556000/A,B,C
http://localhost:8080/service/USERID=101556000/A
http://localhost:8080/service/USERID=101556000/C,B
http://localhost:8080/service/USERID=101556000/C,A
http://localhost:8080/service/USERID=101556000/C,A,B
对于 {A,B,C,D} :
http://localhost:8080/service/USERID=101556000/B,A,D,C
http://localhost:8080/service/USERID=101556000/C,D
http://localhost:8080/service/USERID=101556000/A,D,C,B
http://localhost:8080/service/USERID=101556000/A,C,D
http://localhost:8080/service/USERID=101556000/D
http://localhost:8080/service/USERID=101556000/C
http://localhost:8080/service/USERID=101556000/A,C,B
http://localhost:8080/service/USERID=101556000/B
http://localhost:8080/service/USERID=101556000/A,B,C,D
http://localhost:8080/service/USERID=101556000/A,B,C
http://localhost:8080/service/USERID=101556000/D,C,B,A
http://localhost:8080/service/USERID=101556000/C,B,A,D
http://localhost:8080/service/USERID=101556000/A,B,D
http://localhost:8080/service/USERID=101556000/D,B
http://localhost:8080/service/USERID=101556000/D,C
http://localhost:8080/service/USERID=101556000/A
http://localhost:8080/service/USERID=101556000/D,C,A
http://localhost:8080/service/USERID=101556000/D,C,B
http://localhost:8080/service/USERID=101556000/C,D,A
http://localhost:8080/service/USERID=101556000/C,D,B
http://localhost:8080/service/USERID=101556000/D,A
http://localhost:8080/service/USERID=101556000/A,D,C
http://localhost:8080/service/USERID=101556000/A,D,B
http://localhost:8080/service/USERID=101556000/C,B,D
http://localhost:8080/service/USERID=101556000/B,A,D
http://localhost:8080/service/USERID=101556000/B,C
http://localhost:8080/service/USERID=101556000/B,A,C
http://localhost:8080/service/USERID=101556000/B,C,A
http://localhost:8080/service/USERID=101556000/B,A
http://localhost:8080/service/USERID=101556000/B,C,D
http://localhost:8080/service/USERID=101556000/C,B,A
http://localhost:8080/service/USERID=101556000/A,D
http://localhost:8080/service/USERID=101556000/D,A,B
http://localhost:8080/service/USERID=101556000/A,C
http://localhost:8080/service/USERID=101556000/D,A,C
http://localhost:8080/service/USERID=101556000/B,C,D,A
http://localhost:8080/service/USERID=101556000/A,B
http://localhost:8080/service/USERID=101556000/B,D
http://localhost:8080/service/USERID=101556000/C,D,A,B
http://localhost:8080/service/USERID=101556000/D,A,B,C
http://localhost:8080/service/USERID=101556000/D,B,A
http://localhost:8080/service/USERID=101556000/D,B,C
http://localhost:8080/service/USERID=101556000/B,D,A
http://localhost:8080/service/USERID=101556000/C,B
http://localhost:8080/service/USERID=101556000/C,A,D
http://localhost:8080/service/USERID=101556000/C,A
http://localhost:8080/service/USERID=101556000/B,D,C
http://localhost:8080/service/USERID=101556000/C,A,B
这不是详尽的枚举。基本上我们应该有:
(我的第一篇文章我无法发布图片来查看我回复中的方程式,我没有发布 2 个链接的声誉……#omg)
这产生了 64 个组合,分布如下:
- 1 个元素的 4 个组合 (k=1)
- 12 个元素的 12 个组合 (k=2)
- 24 个元素的 24 个组合 (k=3)
- 24 个元素的 24 个组合 (k=4)
您可以看到我的程序对于 k=1、k=2 和 k=3 是可以的。但是对于 k=4,没有 24 个组合。为了完成该程序,您还需要迭代除循环排列之外的其他类型的数据混洗。实际上,当 k=4 时,循环置换不会生成例如 ADBC 作为输入数据(因此例如我的实现不能生成 DBCA)。在这种情况下,您将希望以所有可能的顺序枚举所有可能的包含 n 个元素的数据输入数组。这是 k 排列的一种特殊情况,其中 k=n,因此会导致找到n!
排列。n!
我们可以通过为每个可能的排列调用 EnumUrl 方法来实现这一点。
为此,您应该EnumUrl enumerator = new EnumUrl(data);
相应地更新,但我想我会让您做一些工作:-)
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