$4.$ For the following graph, apply Bellman$-$Ford algorithm to fnd the shortest path distance from vertex A to all other vertices. You need to show the recurrence formula $($which is in the textbook$),$ and show the update of the table distk$[$u$]$ for all the k and u $($similar to Figure $5\mathrm{.}10,$ in the textbook, p$.291).$ You don't have to show the shortest path as a sequence of vertices.

$5.$ Given a sequence $\backslash ($ X $\backslash )$ of symbols, a subsequence of $\backslash ($ X $\backslash )$ is defined to be any contiguous portion of $\backslash ($ X $\backslash ).$ For example, if $\backslash ($ X$=$a$,$ b$,$ c$,$ d$,$ e$,$ b$,$ c $\backslash ),$ then $\backslash ($ c$,$ d$,$ e$,$ b $\backslash )$ is a subsequence of $\backslash ($ X $\backslash ).$

Given two sequences $\backslash ($ X $\backslash )$ and $\backslash ($ Y $\backslash ),$ you are asked to present an algorithm that will find the longest subsequence that is common to both $\backslash ($ X $\backslash )$ and $\backslash ($ Y $\backslash ).$ This problem is known as the longest common subsequence problem. You will not get credit if you just give an inefficient brute$-$force search algorithm.

What is the time complexity of your algorithm?