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Problem 816

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Shortest distance among points

We create an array of points $P_n$ in a two dimensional plane using the following random number generator:

$s_0=290797$

$s_{n+1}=s_n^2 \bmod 50515093$

$P_n=(s_{2n},s_{2n+1})$

Let $d(k)$ be the shortest distance of any two (distinct) points among $P_0, \cdots, P_{k - 1}$.

E.g. $d(14)=546446.466846479$

Find $d(2000000)$. Give your answer rounded to $9$ places after the decimal point.

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随机点集最短距离

使用下列随机数生成器生成二维随机点列$P_n$：

$s_0=290797$

$s_{n+1}=s_n^2 \bmod 50515093$

$P_n=(s_{2n},s_{2n+1})$

记$d(k)$为$P_0, \cdots, P_{k - 1}$中任意（不同的）两点间最短距离。

已知$d(14)=546446.466846479$。

求$d(2000000)$，并将你的答案四舍五入至小数点后$9$位。

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