3. (20 points) We call a connected graph a unicycle if it has the same number of edges as vertices G.e. it is a tree plus one edge). (a) (10 points) Give an algorithm with running time O(n) that takes a unicycle as input, and outputs a minimum spanning tree. Hint: Use the cycle property discussed in class. (b) (10 points) Call a connected graph a near-tree if it has at most 10 more edges than vertices. Give an algorithm with running time O(n) that takes a near-tree as input, and outputs a minimum spanning tree. Hint: Extend your idea from part (a), and modify the Reverse-Delete algorithm