Problem $1$: Traverse the graph below in Breadth$-$First order, starting from vertex $2.$ Whenever you examine neighbors of a vertex, process them in increasing order of vertex number. Problem $2$: Read section $15\mathrm{.}1($An activity$-$selection problem$)$ from the book You are given a set of activities to schedule among a large number of lecture halls, where any activity can take place in any lecture hall. You wish to schedule all the activities using as few lecture halls as possible. Give an efficient greedy algorithm to determine which activity should use which lecture hall. Determine the two elements of the greedy strategy.