What time is it? Time to build out graph search algorithms in Python!

Graph search algorithms can be tremendously helpful for path-finding between different points in a graph data structure.

First, you’ll build out a *depth-first search* algorithm using recursion that can help you determine if a path exists and, if so, provide you with the first possible path that the function finds.

Then you will build out a *breadth-first search* function that will lead you to the shortest path between two points.

Are you excited? You should be. The power of graph search compels you.

It’s possible to build graph search functions as class methods within a graph data structure implementation, but here we want to focus on the algorithms themselves. For that reason, our graphs are modeled using a Python dictionary. Within the dictionary, each key-value pair maps a vertex value to a set of that vertex’s connected vertex values:

some_vertex_value: set([connected_value_1, connected_value_2, connected_value_3])

### Instructions

**1.**

Take a look at the graphs and functions in the code editor. What do you expect the output to be when you run your code?

Run your code to see if you were right! Now run your code again. Did the DFS path change from one run to another?