The solution requires the knowledge of basic geometry. The question is asking for the Euclidean distance between two points in ~N~-dimensional space.

First of all, it should be known that the formula for calculating Euclidean distance in ~2~-dimensional space is:

$$\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

For the first subtask, the ~2~-dimensional distance formula can be expanded to ~3~ dimensions.

$$\displaystyle \begin{align*} d &= \sqrt{\left(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\right)^2 + (z_2 - z_1)^2} \\ &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \end{align*}$$

For the second and last subtasks, the ~2~-dimensional distance formula can be expanded to ~N~-dimensions. The formula for calculating Euclidean distance in ~N~-dimensional space is

$$\displaystyle d = \sqrt{\sum_{i=1}^N (b_i - a_i)^2}$$

The proof is left as an exercise for the reader.

The second subtask was specifically dedicated to those who used 32-bit floating-point variables instead of 64-bit floating-point variables in their calculations.

Time Complexity: ~\mathcal O(N)~