Showing problems belong to $\backslash (\backslash$mathbf$\{$P$\}\backslash )$

Problem $1.$ Consider the Shortest Path problem that takes as input a graph $\backslash ($ G$=($V$,$ E$)\backslash )$ and two vertices $\backslash ($ v$,$ t $\backslash$in V $\backslash )$ and returns the shortest path from $\backslash ($ v $\backslash )$ to $\backslash ($ t $\backslash ).$ The shortest path decision problem takes as input a graph $\backslash ($ G$=($V$,$ E$)\backslash ),$ two a vertices $\backslash ($ v$,$ t $\backslash$in V $\backslash ),$ and a value $\backslash ($ k $\backslash ),$ and returns True if there is a path from $\backslash ($ v $\backslash )$ to $\backslash ($ t $\backslash )$ that is at most $\backslash ($ k $\backslash )$ edges and False otherwise. Show that the shortest path decision problem is in P$.$ You are welcome and encouraged to cite algorithms we have previously covered in class, including known facts about their runtime. $[$Note: To gauge the level of detail, we expect your solutions to this problem will be $\backslash (2-4\backslash )$ sentences. We are not asking you to analyze an algorithm in great detail.$][20$ pts$]$

Answer.