CF1599G.Shortest path

You are given $N$ points on an infinite plane with the Cartesian coordinate system on it. $N-1$ points lay on one line, and one point isn't on that line. You are on point $K$ at the start, and the goal is to visit every point. You can move between any two points in a straight line, and you can revisit points. What is the minimum length of the path?

给你一个无限平面，其上建立了笛卡尔坐标系，并给出了 $N$ 个点。其中 $N-1$ 个点共线，而剩余一个点不在这条直线上。你起始于点 $K$，目标是访问所有点。你可以在任意两点之间沿直线移动，且允许重复访问点。求路径的最小总长度？

The first line contains two integers: $N$ ($3 \leq N \leq 2*10^5$) - the number of points, and $K$ ($1 \leq K \leq N$) - the index of the starting point.

Each of the next $N$ lines contain two integers, $A_i$, $B_i$ ($-10^6 \leq A_i, B_i \leq 10^6$) - coordinates of the $i-th$ point.

第一行包含两个整数：$N$（$3 \leq N \leq 2*10^5$）——点的数量，以及 $K$（$1 \leq K \leq N$）——起始点的索引。

接下来的 $N$ 行，每行包含两个整数 $A_i$、$B_i$（$-10^6 \leq A_i, B_i \leq 10^6$）——第 $i$ 个点的坐标。

The output contains one number - the shortest path to visit all given points starting from point $K$. The absolute difference between your solution and the main solution shouldn't exceed $10^-6$;

输出包含一个数字——从点 $K$ 出发访问所有给定点的最短路径长度。你的解与标准解之间的绝对误差不得超过 $10^{-6}$；

The shortest path consists of these moves:

2 -> 5

5 -> 4

4 -> 1

1 -> 3

There isn't any shorter path possible.

最短路径包含以下移动步骤：

2 → 5

5 → 4

4 → 1

1 → 3

不存在更短的路径。