这里有一个优雅的，非递归的O(n!)解:

public static StringBuilder[] permutations(String s) {
        if (s.length() == 0)
            return null;
        int length = fact(s.length());
        StringBuilder[] sb = new StringBuilder[length];
        for (int i = 0; i < length; i++) {
            sb[i] = new StringBuilder();
        }
        for (int i = 0; i < s.length(); i++) {
            char ch = s.charAt(i);
            int times = length / (i + 1);
            for (int j = 0; j < times; j++) {
                for (int k = 0; k < length / times; k++) {
                    sb[j * length / times + k].insert(k, ch);
                }
            }
        }
        return sb;
    }

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]，…)

改进的代码相同

    static String permutationStr[];
    static int indexStr = 0;

    static int factorial (int i) {
        if (i == 1)
            return 1;
        else
            return i * factorial(i-1);
    }

    public static void permutation(String str) {
        char strArr[] = str.toLowerCase().toCharArray();
        java.util.Arrays.sort(strArr);

        int count = 1, dr = 1;
        for (int i = 0; i < strArr.length-1; i++){
            if ( strArr[i] == strArr[i+1]) {
                count++;
            } else {
                dr *= factorial(count);
                count = 1;
            }       
        }
        dr *= factorial(count);

        count = factorial(strArr.length) / dr;

        permutationStr = new String[count];

        permutation("", str);

        for (String oneStr : permutationStr){
            System.out.println(oneStr);
        }
    }

    private static void permutation(String prefix, String str) {
        int n = str.length();
        if (n == 0) {
            for (int i = 0; i < indexStr; i++){
                if(permutationStr[i].equals(prefix))
                    return;
            }        
            permutationStr[indexStr++] = prefix;
        } else {
            for (int i = 0; i < n; i++) {
                permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i + 1, n));
            }
        }
    }

下面是两个c#版本(仅供参考): 1. 打印所有排列 2. 返回所有排列

算法的基本要点是(可能下面的代码更直观-尽管如此，下面的代码是做什么的一些解释): -从当前索引到集合的其余部分，交换当前索引处的元素 -递归地获得下一个索引中剩余元素的排列 -恢复秩序，通过重新交换

注意:上述递归函数将从起始索引中调用。

private void PrintAllPermutations(int[] a, int index, ref int count)
        {
            if (index == (a.Length - 1))
            {
                count++;
                var s = string.Format("{0}: {1}", count, string.Join(",", a));
                Debug.WriteLine(s);
            }
            for (int i = index; i < a.Length; i++)
            {
                Utilities.swap(ref a[i], ref a[index]);
                this.PrintAllPermutations(a, index + 1, ref count);
                Utilities.swap(ref a[i], ref a[index]);
            }
        }
        private int PrintAllPermutations(int[] a)
        {
            a.ThrowIfNull("a");
            int count = 0;
            this.PrintAllPermutations(a, index:0, count: ref count);
            return count;
        }

版本2(与上面相同-但返回排列而不是打印)

private int[][] GetAllPermutations(int[] a, int index)
        {
            List<int[]> permutations = new List<int[]>();
            if (index == (a.Length - 1))
            {
                permutations.Add(a.ToArray());
            }

            for (int i = index; i < a.Length; i++)
            {
                Utilities.swap(ref a[i], ref a[index]);
                var r = this.GetAllPermutations(a, index + 1);
                permutations.AddRange(r);
                Utilities.swap(ref a[i], ref a[index]);
            }
            return permutations.ToArray();
        }
        private int[][] GetAllPermutations(int[] p)
        {
            p.ThrowIfNull("p");
            return this.GetAllPermutations(p, 0);
        }

单元测试

[TestMethod]
        public void PermutationsTests()
        {
            List<int> input = new List<int>();
            int[] output = { 0, 1, 2, 6, 24, 120 };
            for (int i = 0; i <= 5; i++)
            {
                if (i != 0)
                {
                    input.Add(i);
                }
                Debug.WriteLine("================PrintAllPermutations===================");
                int count = this.PrintAllPermutations(input.ToArray());
                Assert.IsTrue(count == output[i]);
                Debug.WriteLine("=====================GetAllPermutations=================");
                var r = this.GetAllPermutations(input.ToArray());
                Assert.IsTrue(count == r.Length);
                for (int j = 1; j <= r.Length;j++ )
                {
                    string s = string.Format("{0}: {1}", j,
                        string.Join(",", r[j - 1]));
                    Debug.WriteLine(s);
                }
                Debug.WriteLine("No.OfElements: {0}, TotalPerms: {1}", i, count);
            }
        }

这个没有递归

public static void permute(String s) {
    if(null==s || s.isEmpty()) {
        return;
    }

    // List containing words formed in each iteration 
    List<String> strings = new LinkedList<String>();
    strings.add(String.valueOf(s.charAt(0))); // add the first element to the list

     // Temp list that holds the set of strings for 
     //  appending the current character to all position in each word in the original list
    List<String> tempList = new LinkedList<String>(); 

    for(int i=1; i< s.length(); i++) {

        for(int j=0; j<strings.size(); j++) {
            tempList.addAll(merge(s.charAt(i), strings.get(j)));
                        }
        strings.removeAll(strings);
        strings.addAll(tempList);

        tempList.removeAll(tempList);

    }

    for(int i=0; i<strings.size(); i++) {
        System.out.println(strings.get(i));
    }
}

/**
 * helper method that appends the given character at each position in the given string 
 * and returns a set of such modified strings 
 * - set removes duplicates if any(in case a character is repeated)
 */
private static Set<String> merge(Character c,  String s) {
    if(s==null || s.isEmpty()) {
        return null;
    }

    int len = s.length();
    StringBuilder sb = new StringBuilder();
    Set<String> list = new HashSet<String>();

    for(int i=0; i<= len; i++) {
        sb = new StringBuilder();
        sb.append(s.substring(0, i) + c + s.substring(i, len));
        list.add(sb.toString());
    }

    return list;
}

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());
        }
    }
}