In problem description, "Then, for each 1≦i≦N, he will paint one of the following four regions:", paint to what? black or white or other color? It should be clearly mentioned in problem description.

Snuke always use black for painting. Thanks for pointing it out, we will update the statement.

In the constraints of E, 1 <= V_j <= K should be 1 <= V_j <= N.
Eの制約において、1 <= V_j <= Kは1 <= V_j <= Nであるべきです。

はい。(※現在の問題文は修正されています)

>  Similarly to the original game of Reversi, when a white stone is placed, all black stones between the new white stone and another white stone, turn into white stones, and vice versa.

What does the word 'another' mean ? Does it mean 'next'?

Yes, it means 'next' (closest to the new one).