$62\mathrm{.}2$ Longest Path

The challenge in this assignment is to find the longest path of increasing values in a matrix. To make the problem a little more challenging,

we are making the matrix a looped ribbon, in which on the $x-$axis, the last element is adjacent to the first.

We start by defining a path, trail, as a tuple of $(x,y)$ values, each of which is a position in matrix ribbon. In a valid path:

any $(x,y)$ value appears at most once:

if trail $[t]=(x1,y1)$ and trail $[t+1]=(x2,y2),$ then position $(x2,y2)$ must be adjacent to $(x1,y1),$ where

adjacent is defined to mean, above $($e$.$g$.x1==x2x1,y1[t]=(x1,y1)[t+1]=(x2,y2)x1,0x1,n-1x0,y1m-1,y1(x,y)m-10(x,y)((x1,y1),(x2,y2),$dots$)x,ymN=m^{***}nO(N)y1$ and $x1==x2$