Exercise $7\mathrm{.}14$a $($Escape Problem$)$

Question: Please the correct algorithm $($Pseudo code format$),$ run$-$time analysis, and proof of correctness. Some hints: Some are assuming that the input graph G for the Escape Problem consists only of populated nodes X and safe nodes S$.$ But in fact the nodes of G could have many other nodes in it$,$ not only the ones in X and S$.$ In other words, the union of X and S is not necessarily all of V$!$

Some also have thought that each node in X has to have a unique node in S to escape to$.$ That is not implied for part a$.$