如何获得具有不同数量元素的n个数组的所有可能组合？ [英] How to get all possible combinations for n arrays with different number of elements?

问题描述

我有一些在编程时未知的数组，也许是3或4或7 ...每个数组都有一些元素，即

I have some number of arrays which is unknown at programming time, maybe it is 3 or 4 or 7 ... each array has some elements, i.e,

a={1 2 3 4}
b={6 7 5 2 1}
c={22 4 6 8 4 8 5 4}
d={....}
e, f, g, ...

我想得到通过从每个数组中采样一个数字来获得所有可能的组合，例如，一种情况是我从a拾取 1，从b拾取 7，从c拾取第一个 8，d [3]，e [5]。 ..制成 1,7,8，d [3]，e [5]，...。无法使用嵌套的for循环，因为我不知道编译时的数组数量。如果已知例如4个数组（a，b，c，d），我可以使用4个循环：

I want to get get all possible combinations by sampling one number from each array for example one case is that I pick up "1" from a, "7" from b, first "8" from c, d[3], e[5],... to make "1,7,8,d[3],e[5],...". It's not possible to use nested for loops because I don't know the number of arrays at compile time. If it was known for example 4 arrays (a,b,c,d) I could use 4 loops:

for (int i = 0; i <= a.Length-1; i++)
{
   for (int j = 0; i <= b.Length-1; j++)
   {
      for (int k = 0; i <= c.Length-1; k++)
      {
         for (int m = 0; i <= d.Length-1; m++)
         {
            Response[f++] = a[i].toString()+","+b[j].toString()+","+c[k].toString()+","+d[m].toString();
         }
      }
   }
}

但对于不同数量的数组，我不知道。

but for different number of arrays, I don't have any idea.

推荐答案

这可行：

Func<
    IEnumerable<IEnumerable<int>>,
    IEnumerable<IEnumerable<int>>> f0 = null;
f0 = xss =>
{
    if (!xss.Any())
    {
        return new [] { Enumerable.Empty<int>() };
    }
    else
    {
        var query =
            from x in xss.First()
            from y in f0(xss.Skip(1))
            select new [] { x }.Concat(y);
        return query;
    }
};

Func<IEnumerable<IEnumerable<int>>, IEnumerable<string>> f =
    xss => f0(xss).Select(xs => String.Join(",", xs));

因此，如果我输入以下内容：

So if I have this input:

var input = new []
{
    new [] { 1, 2, 3, 4, },
    new [] { 6, 7, 5, 2, 1, },
    new [] { 22, 4, 6, 8, 4, 8, 5, 4, },
};

我可以这样获得结果：

var results = f(input);

以下是根据注释中的请求简单汇总结果的版本：

Here's a version which simply sums the results, as per the request in the comments:

Func<IEnumerable<IEnumerable<int>>, IEnumerable<int>> f = null;
f = xss =>
{
    if (!xss.Any())
    {
        return new [] { 0 };
    }
    else
    {
        var query =
            from x in xss.First()
            from y in f(xss.Skip(1))
            select x + y;
        return query;
    }
};

var input = new []
{
    new [] { 1, 2, 3, 4, },
    new [] { 6, 7, 5, 2, 1, },
    new [] { 22, 4, 6, 8, 4, 8, 5, 4, },
};

var results = f(input);

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