Problem $4.(14$ points$)$ Perform a depth first search on the graph in Figure $1.$ Your answer should show both the discovery time and finish time for each node. When moving to new nodes in the DFS$,$ follow alphabetical order. Write down the forest you get from this DFS that is obtained by including all edges that define a parent$-$child relationship.

${?}^1$ Note that this question can be answered by adding a few extra lines of code in the correct place, without deleting any existing lines. It is okay if your answer does delete or change some lines, but you should attempt to accomplish this task using only a small number of edits.

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