生成字符组合的所有排列时，每个数组的数组和长度＃不明 [英] Generating All Permutations of Character Combinations when # of arrays and length of each array are unknown

问题描述

我不知道怎么问我的问题在简洁的方式，所以我会用实例开始，并从那里展开。我与VBA的工作，但我觉得这个问题是不特定语言，并会只需要一个聪慧的头脑，可以提供一个伪code框架。在此先感谢您的帮助！

I'm not sure how to ask my question in a succinct way, so I'll start with examples and expand from there. I am working with VBA, but I think this problem is non language specific and would only require a bright mind that can provide a pseudo code framework. Thanks in advance for the help!

例如：
我有3个字符数组，像这样：

Example: I have 3 Character Arrays Like So:

Arr_1 = [X,Y,Z] 
Arr_2 = [A,B]
Arr_3 = [1,2,3,4]

我想生成字符数组的所有可能的排列，像这样：

I would like to generate ALL possible permutations of the character arrays like so:

XA1
XA2
XA3
XA4
XB1
XB2
XB3
XB4
YA1
YA2
.
.
.
ZB3
ZB4

这可以用3迎刃而解while循环或循环。我的问题是我该如何解决这个，如果阵列的＃是未知的，每个数组的长度未知？

This can be easily solved using 3 while loops or for loops. My question is how do I solve for this if the # of arrays is unknown and the length of each array is unknown?

，以便与4字符数组的例子：

So as an example with 4 character arrays:

Arr_1 = [X,Y,Z]
Arr_2 = [A,B]
Arr_3 = [1,2,3,4]
Arr_4 = [a,b]

我需要生成：

XA1a
XA1b
XA2a
XA2b
XA3a
XA3b
XA4a
XA4b
.
.
.
ZB4a
ZB4b  

因此​​，广义的例子是：

So the Generalized Example would be:

Arr_1 = [...]
Arr_2 = [...]
Arr_3 = [...]
.
.
.
Arr_x = [...]

有没有办法来组织，这将产生一个未知号码循环和循环通过每个数组的长度，生成排列的函数？或者，也许有思考问题的更好的办法？

Is there a way to structure a function that will generate an unknown number of loops and loop through the length of each array to generate the permutations? Or maybe there's a better way to think about the problem?

谢谢大家！

推荐答案

这实际上是最简单，最简单的解决方案。以下是在Java中，但它应该是有启发性：

Recursive solution

This is actually the easiest, most straightforward solution. The following is in Java, but it should be instructive:

public class Main {
    public static void main(String[] args) {
        Object[][] arrs = {
            { "X", "Y", "Z" },
            { "A", "B" },
            { "1", "2" },
        };
        recurse("", arrs, 0);
    }
    static void recurse (String s, Object[][] arrs, int k) {
        if (k == arrs.length) {
            System.out.println(s);
        } else {
            for (Object o : arrs[k]) {
                recurse(s + o, arrs, k + 1);
            }
        }
    }
}

（查看完整的输出）

注：Java数组是基础，所以 K 从云 0..arrs.length-1 递归，直到在 K == arrs.length 时，它的递归的终点。

Note: Java arrays are 0-based, so k goes from 0..arrs.length-1 during the recursion, until k == arrs.length when it's the end of recursion.

它也可以写一个非递归的解决方案，但坦率地说，这是不太直观。这实际上是非常相似的基转换，例如从十进制为十六进制;这是一个广义的形式，其中每个位置有自己的一套价值观。

It's also possible to write a non-recursive solution, but frankly this is less intuitive. This is actually very similar to base conversion, e.g. from decimal to hexadecimal; it's a generalized form where each position have their own set of values.

public class Main {
    public static void main(String[] args) {
        Object[][] arrs = {
            { "X", "Y", "Z" },
            { "A", "B" },
            { "1", "2" },
        };
        int N = 1;
        for (Object[] arr : arrs) {
            N = N * arr.length;
        }
        for (int v = 0; v < N; v++) {
            System.out.println(decode(arrs, v));
        }
    }
    static String decode(Object[][] arrs, int v) {
        String s = "";
        for (Object[] arr : arrs) {
            int M = arr.length;
            s = s + arr[v % M];
            v = v / M;
        }
        return s;
    }
}

（查看完整的输出）

这会产生不同的顺序的tuplets。如果你想生成他们在相同的顺序递归的解决方案，那么你通过 ARRS 落后在德code 如下：

This produces the tuplets in a different order. If you want to generate them in the same order as the recursive solution, then you iterate through arrs "backward" during decode as follows:

static String decode(Object[][] arrs, int v) {
    String s = "";
    for (int i = arrs.length - 1; i >= 0; i--) {
        int Ni = arrs[i].length;
        s = arrs[i][v % Ni] + s;
        v = v / Ni;
    }
    return s;
}

（查看完整的输出）

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