Problem $3(20$ points$).$ The DFS algorithm that we discussed in class uses the adjacency list representation of a graph $G=(V,E)$ and its time cost is $O(|V|+|E|).$ Suppose you are only given the matrix representation of $G,$ describe your pseudocode for DFS of $G$ using the matrix representation. Give the time complexity of your algorithm in the big$-$oh notation and make your bound as tight as possible. Did you learn why we used the adjacency list representation for DFS in class $?$ Note: you can assume matrix $[i,j]=1$ if $(i,j)inE$; matrix $[i,j]=0,$ otherwise.