让我试着用Kotlin来解决这个问题:

fun <T> List<T>.permutations(): List<List<T>> {
    //escape case
    if (this.isEmpty()) return emptyList()

    if (this.size == 1) return listOf(this)

    if (this.size == 2) return listOf(listOf(this.first(), this.last()), listOf(this.last(), this.first()))

    //recursive case
    return this.flatMap { lastItem ->
        this.minus(lastItem).permutations().map { it.plus(lastItem) }
    }
}

核心概念:将长链表分解成小链表+递归

长答案与示例列表[1,2,3,4]:

即使是一个4种组合的列表，在脑海中列出所有可能的排列已经有点令人困惑了，我们需要做的就是避免这种情况。我们很容易理解如何对大小为0、1和2的列表进行排列，因此我们所需要做的就是将它们分解为这些大小中的任何一个，并将它们正确地组合起来。想象一台头奖机器:这个算法将从右向左旋转，然后写下

当列表大小为0或1时，返回空/列表为1 当列表大小为2时处理(例如[3,4])，并生成2个排列([3,4]& [4,3]) 对于每一项，将其标记为最后一项中的最后一项，并找到列表中其余项目的所有排列。(例如，把[4]放在桌子上，把[1,2,3]重新排列) 现在对它的子元素进行所有的排列，把它自己放回列表的末尾(例如:[1,2,3][，4]，[1,3,2][，4]，[2,3,1][，4]，…)

其中一个简单的解决方案是使用两个指针继续递归地交换字符。

public static void main(String[] args)
{
    String str="abcdefgh";
    perm(str);
}
public static void perm(String str)
{  char[] char_arr=str.toCharArray();
    helper(char_arr,0);
}
public static void helper(char[] char_arr, int i)
{
    if(i==char_arr.length-1)
    {
        // print the shuffled string 
            String str="";
            for(int j=0; j<char_arr.length; j++)
            {
                str=str+char_arr[j];
            }
            System.out.println(str);
    }
    else
    {
    for(int j=i; j<char_arr.length; j++)
    {
        char tmp = char_arr[i];
        char_arr[i] = char_arr[j];
        char_arr[j] = tmp;
        helper(char_arr,i+1);
        char tmp1 = char_arr[i];
        char_arr[i] = char_arr[j];
        char_arr[j] = tmp1;
    }
}
}

这对我很有效。

import java.util.Arrays;

public class StringPermutations{
    public static void main(String args[]) {
        String inputString = "ABC";
        permute(inputString.toCharArray(), 0, inputString.length()-1);
    }

    public static void permute(char[] ary, int startIndex, int endIndex) {
        if(startIndex == endIndex){
            System.out.println(String.valueOf(ary));
        }else{
            for(int i=startIndex;i<=endIndex;i++) {
                 swap(ary, startIndex, i );
                 permute(ary, startIndex+1, endIndex);
                 swap(ary, startIndex, i );
            }
        }
    }

    public static void swap(char[] ary, int x, int y) {
        char temp = ary[x];
        ary[x] = ary[y];
        ary[y] = temp;
    }
}

让我们以输入abc为例。

从集合(["c"])中的最后一个元素(c)开始，然后将最后第二个元素(b)添加到它的前面，末尾和中间的每个可能位置，使其["bc"， "cb"]，然后以同样的方式将后面的下一个元素(a)添加到集合中的每个字符串中，使其:

"a" + "bc" = ["abc", "bac", "bca"]  and  "a" + "cb" = ["acb" ,"cab", "cba"] 

因此整个排列:

["abc", "bac", "bca","acb" ,"cab", "cba"]

代码:

public class Test 
{
    static Set<String> permutations;
    static Set<String> result = new HashSet<String>();

    public static Set<String> permutation(String string) {
        permutations = new HashSet<String>();

        int n = string.length();
        for (int i = n - 1; i >= 0; i--) 
        {
            shuffle(string.charAt(i));
        }
        return permutations;
    }

    private static void shuffle(char c) {
        if (permutations.size() == 0) {
            permutations.add(String.valueOf(c));
        } else {
            Iterator<String> it = permutations.iterator();
            for (int i = 0; i < permutations.size(); i++) {

                String temp1;
                for (; it.hasNext();) {
                    temp1 = it.next();
                    for (int k = 0; k < temp1.length() + 1; k += 1) {
                        StringBuilder sb = new StringBuilder(temp1);

                        sb.insert(k, c);

                        result.add(sb.toString());
                    }
                }
            }
            permutations = result;
            //'result' has to be refreshed so that in next run it doesn't contain stale values.
            result = new HashSet<String>();
        }
    }

    public static void main(String[] args) {
        Set<String> result = permutation("abc");

        System.out.println("\nThere are total of " + result.size() + " permutations:");
        Iterator<String> it = result.iterator();
        while (it.hasNext()) {
            System.out.println(it.next());
        }
    }
}

倒计时Quickperm算法的通用实现，表示#1(可伸缩，非递归)。

/**
 * Generate permutations based on the
 * Countdown <a href="http://quickperm.org/">Quickperm algorithm</>.
 */
public static <T> List<List<T>> generatePermutations(List<T> list) {
    List<T> in = new ArrayList<>(list);
    List<List<T>> out = new ArrayList<>(factorial(list.size()));

    int n = list.size();
    int[] p = new int[n +1];
    for (int i = 0; i < p.length; i ++) {
        p[i] = i;
    }
    int i = 0;
    while (i < n) {
        p[i]--;
        int j = 0;
        if (i % 2 != 0) { // odd?
            j = p[i];
        }
        // swap
        T iTmp = in.get(i);
        in.set(i, in.get(j));
        in.set(j, iTmp);

        i = 1;
        while (p[i] == 0){
            p[i] = i;
            i++;
        }
        out.add(new ArrayList<>(in));
    }
    return out;
}

private static int factorial(int num) {
    int count = num;
    while (num != 1) {
        count *= --num;
    }
    return count;
}

它需要list，因为泛型不能很好地使用数组。

这是一个更快的解决方案，因为它不受字符串连接计算复杂度O(n^2)的影响。另一方面它是无循环的，完全递归的

public static void main(String[] args) {
    permutation("ABCDEFGHIJKLMNOPQRSTUVWXYZ");
}

private static void permutation(String str) {
    char[] stringArray = str.toCharArray();
    printPermutation(stringArray, 0, stringArray.length, 0, 1);
}

private static void printPermutation(char[] string, int loopCounter, int length, int indexFrom, int indexTo) {
    // Stop condition
    if (loopCounter == length)
        return;

    /* 
     When reaching the end of the array:
     1- Reset loop indices.
     2- Increase length counter. 
    */ 
    if (indexTo == length) {
        indexFrom = 0;
        indexTo = 1;
        ++loopCounter;
    }

    // Print.
    System.out.println(string);

    // Swap from / to indices.
    char temp = string[indexFrom];
    string[indexFrom] = string[indexTo];
    string[indexTo] = temp;

    // Go for next iteration.
    printPermutation(string, loopCounter, length, ++indexFrom, ++indexTo);
}