a) Insert into an initially empty 2-3-4 tree, in the order given, the following values: 12, 13, 17, 10, 4, 6, 9, 15, 30, 25, 20, 40. Show the intermediate trees after each insertion that causes a split.

b) Insert the values above into an initially empty red-black tree. Show the tree after each insertion that causes any color shifts or rotations.

c) From the tree derived at the end of the previous problem, delete 13 and then 12.