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原来是威佐夫的变形啊，谢谢大牛的表了！！

Posted by lijunle at 2010-09-15 16:31:36 on Problem 2348
In Reply To:发现这题和 1067 一样，也是黄金比例系数。 Posted by:ImLazy at 2008-07-17 16:35:28

> 我算了一下前 30 × 30 的 Sprague-Grundy 函数表，如下：
> 
>       0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 
>    -----------------------------------------------------------------------------------------------
>  0 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 
>  1 |  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 
>  2 |  0  2  1  0  2  1  3  3  4  4  5  5  6  6  7  7  8  8  9  9 10 10 11 11 12 12 13 13 14 14 15 
>  3 |  0  3  0  1  0  1  2  1  2  3  2  3  4  4  4  5  5  5  6  6  6  7  7  7  8  8  8  9  9  9 10 
>  4 |  0  4  2  0  1  0  0  1  2  1  1  2  3  2  3  3  4  3  4  4  5  5  5  5  6  6  6  6  7  7  7 
>  5 |  0  5  1  1  0  1  0  0  0  1  2  1  2  2  2  3  2  3  3  3  4  3  4  4  4  5  4  5  5  5  6 
>  6 |  0  6  3  2  0  0  1  0  0  0  1  1  2  1  1  1  2  2  3  2  2  3  3  3  4  3  4  4  4  4  5 
>  7 |  0  7  3  1  1  0  0  1  0  0  0  0  1  1  2  1  1  2  2  2  2  3  2  2  3  3  3  3  4  3  4 
>  8 |  0  8  4  2  2  0  0  0  1  0  0  0  0  1  1  1  2  1  1  1  1  2  2  2  3  2  2  3  3  3  3 
>  9 |  0  9  4  3  1  1  0  0  0  1  0  0  0  0  0  1  1  1  2  1  1  1  2  2  2  2  2  3  2  2  2 
> 10 |  0 10  5  2  1  2  1  0  0  0  1  0  0  0  0  0  0  1  1  1  2  1  1  1  2  1  2  2  2  2  3 
> 11 |  0 11  5  3  2  1  1  0  0  0  0  1  0  0  0  0  0  0  1  1  1  1  2  1  1  1  1  2  2  2  2 
> 12 |  0 12  6  4  3  2  2  1  0  0  0  0  1  0  0  0  0  0  0  0  1  1  1  1  2  1  1  1  1  1  1 
> 13 |  0 13  6  4  2  2  1  1  1  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1  1  1  2  1  1  1  1 
> 14 |  0 14  7  4  3  2  1  2  1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1  1  1  1  2  1  1 
> 15 |  0 15  7  5  3  3  1  1  1  1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  1  1  1  1  1  2 
> 16 |  0 16  8  5  4  2  2  1  2  1  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  1  1  1  1  1 
> 17 |  0 17  8  5  3  3  2  2  1  1  1  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  1  1  1 
> 18 |  0 18  9  6  4  3  3  2  1  2  1  1  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  1 
> 19 |  0 19  9  6  4  3  2  2  1  1  1  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0 
> 20 |  0 20 10  6  5  4  2  2  1  1  2  1  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0 
> 21 |  0 21 10  7  5  3  3  3  2  1  1  1  1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0 
> 22 |  0 22 11  7  5  4  3  2  2  2  1  2  1  1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0 
> 23 |  0 23 11  7  5  4  3  2  2  2  1  1  1  1  1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0 
> 24 |  0 24 12  8  6  4  4  3  3  2  2  1  2  1  1  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 
> 25 |  0 25 12  8  6  5  3  3  2  2  1  1  1  1  1  1  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0 
> 26 |  0 26 13  8  6  4  4  3  2  2  2  1  1  2  1  1  1  0  0  0  0  0  0  0  0  0  1  0  0  0  0 
> 27 |  0 27 13  9  6  5  4  3  3  3  2  2  1  1  1  1  1  0  0  0  0  0  0  0  0  0  0  1  0  0  0 
> 28 |  0 28 14  9  7  5  4  4  3  2  2  2  1  1  2  1  1  1  0  0  0  0  0  0  0  0  0  0  1  0  0 
> 29 |  0 29 14  9  7  5  4  3  3  2  2  2  1  1  1  1  1  1  0  0  0  0  0  0  0  0  0  0  0  1  0 
> 30 |  0 30 15 10  7  6  5  4  3  2  3  2  1  1  1  2  1  1  1  0  0  0  0  0  0  0  0  0  0  0  1 
> 
> 发现 “0” 的边缘处的斜率很接近 1.618，于是试着提交了一下，果然 AC 了！
> 为什么会出现黄金比例系数呢，世界真奇妙。

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