c# - 列出字符串/整数的所有排列

Question

编程面试中的一个常见任务(虽然不是根据我的面试经验)是获取一个字符串或一个整数并列出所有可能的排列。

是否有示例说明如何完成此操作以及解决此类问题背后的逻辑？

我看过一些代码片段，但它们没有得到很好的注释/解释，因此很难理解。

Answer 1

首先:当然，它闻起来像递归!

既然你也想知道原理，那我就尽量用人话来解释了。我认为大多数时候递归非常容易。你只需要掌握两个步骤:

1. 第一步
2. 所有其他步骤(都具有相同的逻辑)

用人类语言:

In short:

1. The permutation of 1 element is one element.
   
2. The permutation of a set of elements is a list each of the elements, concatenated with every permutation of the other elements.
   

Example:

If the set just has one element -->
return it.
perm(a) -> a

If the set has two characters: foreach element in it: return theelement, with the permutation of therest of the elements added, like so:

perm(ab) ->

a + perm(b) -> ab

b + perm(a) -> ba

Further: for each character in the set: return a character, concatenated with a permutation of > the rest of the set

perm(abc) ->

a + perm(bc) --> abc, acb

b + perm(ac) --> bac, bca

c + perm(ab) --> cab, cba

perm(abc...z) -->

a + perm(...), b + perm(....)
....

我在 http://www.programmersheaven.com/mb/Algorithms/369713/369713/permutation-algorithm-help/ 上找到了伪代码 :

makePermutations(permutation) {
  if (length permutation < required length) {
    for (i = min digit to max digit) {
      if (i not in permutation) {
        makePermutations(permutation+i)
      }
    }
  }
  else {
    add permutation to list
  }
}

C#

好的，还有更详细的东西(因为它被标记为 c#)，来自 http://radio.weblogs.com/0111551/stories/2002/10/14/permutations.html :相当冗长，但我还是决定复制它，所以这篇文章不依赖于原文。

The function takes a string of characters, and writes down every possible permutation of that exact string, so for example, if "ABC" has been supplied, should spill out:

ABC、ACB、BAC、BCA、CAB、CBA。

代码:

class Program
{
    private static void Swap(ref char a, ref char b)
    {
        if (a == b) return;

        var temp = a;
        a = b;
        b = temp;
    }

    public static void GetPer(char[] list)
    {
        int x = list.Length - 1;
        GetPer(list, 0, x);
    }

    private static void GetPer(char[] list, int k, int m)
    {
        if (k == m)
        {
            Console.Write(list);
        }
        else
            for (int i = k; i <= m; i++)
            {
                   Swap(ref list[k], ref list[i]);
                   GetPer(list, k + 1, m);
                   Swap(ref list[k], ref list[i]);
            }
    }

    static void Main()
    {
        string str = "sagiv";
        char[] arr = str.ToCharArray();
        GetPer(arr);
    }
}