G. Shortest path
brute force; geometry; math; shortest paths
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?
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.
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 \(10^-6\);
The shortest path consists of these moves: 2 -> 5 5 -> 4 4 -> 1 1 -> 3 There isn't any shorter path possible.