Challenge Yourself. Suppose you are given an arbitrary directed graph $\backslash ($ G $\backslash )$ in which each edge is colored either red or blue, along with two special vertices $\backslash ($ s $\backslash )$ and $\backslash ($ t $\backslash ).$

$($a$)$ Describe an algorithm that either computes a walk from $\backslash ($ s $\backslash )$ to $\backslash ($ t $\backslash )$ such that the pattern of red and blue edges along the walk is a palindrome, or correctly reports that no such walk exists.

$($b$)$ Describe an algorithm that either computes the shortest walk from $\backslash ($ s $\backslash )$ to $\backslash ($ t $\backslash )$ such that the pattern of red and blue edges along the walk is a palindrome, or correctly reports that no such walk exists.