我想写一个组合数学算法来获得 k的所有可能的组合出 N 无重复。

I'm trying to write a combinatorics algorithm to get all the possible combinations of k out of n without repetitions.

其计算公式为：

n!/(k!(n-k)!)); 

结果最终在数组中。我实际上已经写的是这样的：

The results end up in an array. What I've actually written is this:

function Factorial($x)
{
    if ($x < 1)
    {
        echo "Factorial() Error: Number too small!";
    )

    $ans = 1;
    for ($xx = 2; $xx >= $x; $xx++)
    {
        $ans = $ans * $xx;
    }

    return($ans);
}

function Combination($selectcount,$availablecount)
{
    $ans = Factorial($availablecount) / (
        Factorial($availablecount - $selectcount) * Factorial($selectcount)
    );

    return ($ans);
}

这是实现此目的的最快方法是什么？有没有一种方法，以加快这？也许递归写呢？

Is this the fastest way to accomplish this? Is there a way to speed this up? Maybe to write it recursively?

推荐答案

这是我曾经得到了一个因子循环速度最快的：

This is the fastest I've ever managed to get a factorial loop:

function Factorial($factVal) {
    if ($factVal < 0) {
        die("Factorial() Error: Number too small!");
    }

    $factorial = 1;
    while ($factVal > 1) {
        $factorial *= $factVal--;
    }
    return $factorial ;
}