查找表中元素的每个组合(Lua/PseudoCode)

Question

我正在尝试使用表中的每个元素组合来执行函数。(在Lua中)。表和元素可以更改，但结构将保持不变。对表进行组织，使其中的1个参数成为函数的第一个参数，依此类推。

如果这是我的桌子，

Table = {
    [1] = {Player1, Player2}
    [2] = {PlayerA, PlayerB, PlayerC}
    [3] = {PlayerOne, PlayerTwo}
}

如果我手动写出来，它可能看起来像这样：(给定函数名为Exe)。

Exe(Player1, PlayerA, PlayerOne)
Exe(Player2, PlayerA, PlayerOne)
Exe(Player3, PlayerA, PlayerOne)

Exe(Player1, PlayerB, PlayerOne)
Exe(Player2, PlayerB, PlayerOne)
Exe(Player3, PlayerB, PlayerOne)

Exe(Player1, PlayerC, PlayerOne)
Exe(Player2, PlayerC, PlayerOne)
Exe(Player3, PlayerC, PlayerOne)


Exe(Player1, PlayerA, PlayerTwo)
Exe(Player2, PlayerA, PlayerTwo)
Exe(Player3, PlayerA, PlayerTwo)

Exe(Player1, PlayerB, PlayerTwo)
Exe(Player2, PlayerB, PlayerTwo)
Exe(Player3, PlayerB, PlayerTwo)

Exe(Player1, PlayerC, PlayerTwo)
Exe(Player2, PlayerC, PlayerTwo)
Exe(Player3, PlayerC, PlayerTwo)

然而，我不想写出来，它打破了我的一般经验法则，如果你在一个程序中复制和粘贴，你就做错了。

因此，我想浏览一下这个表，执行每一个可能的组合。问题在于，表中可能(潜在地)包含任意数量的表，并且表中的表可能具有无限数量的值。

例如，该表最终可能如下所示：

Table = {
    [1] = {Player1, Player2}
    [2] = {PlayerA}
    [3] = {PlayerOne}
}

在这种情况下，手动执行的结果如下所示：

Exe(Player1, PlayerA, PlayerOne)
Exe(Player2, PlayerA, PlayerOne)

此外，该表可能会以如下形式结束：

Table = {
    [1] = {Player1, Player2}
    [2] = {PlayerA}
    [3] = {PlayerOne}
    [4] = {PlayerUno, PlayerDos}
    [5] = {PlayerApple, PlayerBoy, PlayerCat, PlayerDog}
}

其中的执行结果就像..。

Exe(Player1, PlayerA, PlayerOne, PlayerUno, PlayerApple)
Exe(Player2, PlayerA, PlayerOne, PlayerUno, PlayerApple)

Exe(Player1, PlayerA, PlayerOne, PlayerDos, PlayerApple)
Exe(Player2, PlayerA, PlayerOne, PlayerDos, PlayerApple)


Exe(Player1, PlayerA, PlayerOne, PlayerUno, PlayerBoy)
Exe(Player2, PlayerA, PlayerOne, PlayerUno, PlayerBoy)

Exe(Player1, PlayerA, PlayerOne, PlayerDos, PlayerBoy)
Exe(Player2, PlayerA, PlayerOne, PlayerDos, PlayerBoy)


Exe(Player1, PlayerA, PlayerOne, PlayerUno, PlayerCat)
Exe(Player2, PlayerA, PlayerOne, PlayerUno, PlayerCat)

Exe(Player1, PlayerA, PlayerOne, PlayerDos, PlayerCat)
Exe(Player2, PlayerA, PlayerOne, PlayerDos, PlayerCat)


Exe(Player1, PlayerA, PlayerOne, PlayerUno, PlayerDog)
Exe(Player2, PlayerA, PlayerOne, PlayerUno, PlayerDog)

Exe(Player1, PlayerA, PlayerOne, PlayerDos, PlayerDog)
Exe(Player2, PlayerA, PlayerOne, PlayerDos, PlayerDog)

如你所见，我发现了一种模式。我能够将上面的“执行”分成多个段/组，比如第一行和第二行有一处变化。然后，它们被复制到第4行和第5行，但下一个变量get已更改。

正如您所看到的，我在将该模式转换为代码时遇到了问题。我认为需要一些函数递归，但我不确定如何完成它或递归通过它。我在想，我将不得不使用函数...作为参数和解包函数，但我不确定这是如何工作的。

此外，之所以需要这样做，而不仅仅是手动复制和粘贴(这实际上会更容易)，是因为将生成表的内容。

你们能帮我吗？

Answer 1

使用递归。

假设有一个函数map_all (fcn, tab, idx, ...)，它将fcn映射到所有表tab[1]到tab[idx]的元素的乘积，并在前面加上...

基本情况是当idx小于1时。在这种情况下，只需应用fcn(...)

否则，对于tab[idx]中的所有<el>，返回map_all(fcn, tab, idx-1, <el>, ...)

function map_all (fcn, tab, idx, ...)
    if idx < 1 then
        fcn(...)
    else
        local t = tab[idx]
        for i = 1, #t do map_all(fcn, tab, idx-1, t[i], ...) end
    end
end

所以,

> Table = {
>>     [1] = {'Player1', 'Player2'},
>>     [2] = {'PlayerA', 'PlayerB', 'PlayerC'},
>>     [3] = {'PlayerOne', 'PlayerTwo'}
>> }
> map_all(print, Table, #Table)
Player1 PlayerA PlayerOne
Player2 PlayerA PlayerOne
Player1 PlayerB PlayerOne
Player2 PlayerB PlayerOne
Player1 PlayerC PlayerOne
Player2 PlayerC PlayerOne
Player1 PlayerA PlayerTwo
Player2 PlayerA PlayerTwo
Player1 PlayerB PlayerTwo
Player2 PlayerB PlayerTwo
Player1 PlayerC PlayerTwo
Player2 PlayerC PlayerTwo

和

> Table = {
>>     [1] = {'Player1', 'Player2'},
>>     [2] = {'PlayerA'},
>>     [3] = {'PlayerOne'}
>> }
> map_all(print, Table, #Table)
Player1 PlayerA PlayerOne
Player2 PlayerA PlayerOne

和

> Table = {
>>     [1] = {'Player1', 'Player2'},
>>     [2] = {'PlayerA'},
>>     [3] = {'PlayerOne'},
>>     [4] = {'PlayerUno', 'PlayerDos'},
>>     [5] = {'PlayerApple', 'PlayerBoy', 'PlayerCat', 'PlayerDog'},
>> }
> map_all(print, Table, #Table)
Player1 PlayerA PlayerOne   PlayerUno   PlayerApple
Player2 PlayerA PlayerOne   PlayerUno   PlayerApple
Player1 PlayerA PlayerOne   PlayerDos   PlayerApple
Player2 PlayerA PlayerOne   PlayerDos   PlayerApple
Player1 PlayerA PlayerOne   PlayerUno   PlayerBoy
Player2 PlayerA PlayerOne   PlayerUno   PlayerBoy
Player1 PlayerA PlayerOne   PlayerDos   PlayerBoy
Player2 PlayerA PlayerOne   PlayerDos   PlayerBoy
Player1 PlayerA PlayerOne   PlayerUno   PlayerCat
Player2 PlayerA PlayerOne   PlayerUno   PlayerCat
Player1 PlayerA PlayerOne   PlayerDos   PlayerCat
Player2 PlayerA PlayerOne   PlayerDos   PlayerCat
Player1 PlayerA PlayerOne   PlayerUno   PlayerDog
Player2 PlayerA PlayerOne   PlayerUno   PlayerDog
Player1 PlayerA PlayerOne   PlayerDos   PlayerDog
Player2 PlayerA PlayerOne   PlayerDos   PlayerDog
>