(5 points) Will the operations of deleting \(i\) and then \(j\) from a binary search tree leave the same tree as deleting \(j\) and then \(i\)? Argue why it is or give a counterexample.

(5 points) Will the operations of deleting \(i\) and then \(j\) from an AVL tree leave the same tree as deleting \(j\) and then \(i\)? Argue why it is or give a counterexample.

(10 points) Consider the following graph \(G\). For now, ignore the values associated with the edges. Give the list of vertices visited in depth-first order beginning at vertex \(B\). When given a choice of which vertex to push next, push them in alphabetical order.

(10 points) Given the same graph \(G\), give the list of vertices visited in breadth-first order beginning at vertex \(B\). When given a choice of which vertex to enqueue next, enqueue them in alphabetical order.

(20 points) Given the graph \(G\), and using the edge values as weights. Trace Dijkstra’s algorithm to compute the shortest distances from vertex \(S\) to every other vertex. For every vertex draw the shortest path leading to it.