PHP数组代challange [英] php array generation challange

问题描述

我需要随机生成由n个阵列的两维n。在本实施例中，n = 10的阵列应具有这种结构。一个例子是：

I need to randomly generate an two-dimensional n by n array. In this example, n = 10. The array should have this structure. One example:

$igra[]=array(0,1,2,3,4,5,6,7,8,9);
$igra[]=array(6,9,1,5,0,2,7,3,4,8);
$igra[]=array(2,5....................
$igra[]=array(1,7.....................
$igra[]=array(5,4...................
$igra[]=array(4,2...................
$igra[]=array(9,0.....................
$igra[]=array(8,3.....................
$igra[]=array(7,6....................
$igra[]=array(3,8....................

其中，

`$igra[x][z]!=$igra[y][z]`   (x={0,9},y={0,9});

你看它像数的它和列中的每一行的矩阵也由数字0-9组成，并且有从未一个号码在每一行或每一列中两次。
如何产生这种阵列，并随机各一次。

as you see it's like a matrix of numbers each row of it and column also consist from numbers 0-9, and there is never one number two times in each row or in each column. how to generate such an array, and each time randomly.

推荐答案

好了，这里是我的版本：

Okay, so here's my version:

$n = 10;

$v1 = range(0, $n-1);
$v2 = range(0, $n-1);
shuffle($v1);
shuffle($v2);

foreach ($v1 as $x => $value)
    foreach ($v2 as $y)
        $array[$y][$x] = $value++ % $n;

这应该是一个非常快的算法，因为它只涉及产生两个随机阵列，并且不涉及任何交换的。它应该是随机的，太多，但我不能证明这一点。 （至少我不知道如何来证明这样的事情。）

This should be a really fast algorithm, because it involves only generating two random arrays and doesn't involve any swapping at all. It should be random, too, but I cannot prove it. (At least I don't know how to prove something like this.)

这是一个很简单的算法的优化版本：

This is an optimized version of a very simple algorithm:

首先创建这样一个非随机矩阵（假设我们只想要5 * 5，而不是10 * 10）：

First a non-random matrix is created this way (imagine we want only 5*5, not 10*10):

0 1 2 3 4
1 2 3 4 0
2 3 4 0 1
3 4 0 1 2
4 0 1 2 3

在这个矩阵我们现在随机交换列。由于我们不改变列本身的规则仍然得到遵守。然后，我们随机交换行。

In this matrix we now randomly swap columns. As we don't change the columns themselves your rules still are obeyed. Then we randomly swap rows.

现在，你可以看到上面的算法不交换任何东西，它不会产生任何上述矩阵。这是因为它所产生的cols和rows预先交换（ $ V1 和 $ V2 ），然后直接写入所得数组中的正确位置。

Now, as you can see the above algorithm doesn't swap anything and it doesn't generate the above matrix either. That's because it generates the cols and rows to swap in advance ($v1 and $v2) and then directly writes to the correct position in the resulting array.

编辑：只是做了一些基准测试：对于 $ N = 500 这将在0.3秒。

Just did some benchmarking: For $n = 500 it takes 0.3 seconds.

EDIT2：更换与foreach循环回路后，只用0.2秒。

After replacing the for loops with foreach loops it only takes 0.2 seconds.

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