I couldn't understand the sentence in Editorial.

Let's choose arbitrary permutation p and add orientation for all edges of G with respect of p i.e. if (x,y) belongs to E and p^-1(x) < p^-1(y) then edge is directed like x -> y.

If I could find an arbitrary permutation that fits in a ucg like the problem statement, wouldn't this permutation be the longest path?

What does it mean by p^-1(x) < p^-1(y) ?

Here is problem solution in Python Java c++ and c programming - https://programs.programmingoneonone.com/2021/07/hackerrank-walking-the-approximate-longest-path-problem-solution.html

sttill now i dont solve it 100%. so if one complete it so let me inform me . and please explain the map are given in the question.

How is this an NP Complete question? Can it be solved in polynomial time complexity? Can it be reduced to any other NP Hard problem?

i am unabling to understand the question properly.. please eleborate this