Graph traversal is a process designed to ensure each node in a graph is visited. There are a variety of algorithms that can be applied to engage this process, but most can be classified broadly into two categories by the order in which the nodes are visited. Depth$-$first search $($DFS$)$ algorithms start with the root node, then visit all nodes of one branch $($children$)$ as deep as possible before backtracking to begin again down the next branch. BFS algorithms also start from the root node but visit all nodes of current depth $($neighbors$)$ before moving to the next depth in the tree. Within each category is a variety of approaches to developing the algorithms. Part A$-$Identify a DFS algorithm of your choice. Part B$-$Then, compare the advantages and disadvantages of the search algorithm you chose $($with respect to time and space complexity$)$ with the BFS algorithm. Part C$-$Finally, provide an instance for which your chosen algorithm provides an advantage over the BFS algorithm. Be specific.