Shortest path

1000ms

262144K

Description:

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?

Input:

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.

Output:

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 $$$10^-6$$$;

Sample Input:

Sample Output:

7.478709

Note:

The shortest path consists of these moves:

2 -> 5

5 -> 4

4 -> 1

1 -> 3

There isn't any shorter path possible.

Informação

Provedor Codeforces

Código CF1599G