$3.($U&G$-$required$)[30$ points$]$

a$)[10$ points$]$ Explain how we could find that a graph has a cycle using breadth first search.

b$)[20$ points$]$ For the two graph traversal algorithms breadth first search and depth first

search, does either one always find a cycle faster than the other? If yes, indicate which one

is better and give a justification. If no$,$ give two examples in support of your answer.