JAVA PROGRAM:

In section 11.5, 1. implment the insertion operation of (2,4) tree, reappear the example of Figure 11.25. 2. implment the deletion ooperation of (2,4) tree, reappear the example of Figure 11.27 and 11.28. Your program should print out all the trees in Figure 11.25, 11.27 and 11.28.

Figure 11.24: A node split: (a) overflow at a 5-node w; (b) the third key of w inserted into the parent u of w;(c) node w replaced with a 3-node w and a 2-node w. Figure 11.25: An insertion in a (2,4) tree that causes a cascading split: (a) before the insertion; (b) insertion of 17, causing an overflow; (c) a split; (d) after the split a new overflow occurs; (e) another split, creating a new root node; (f) final tree. Chapter 11. Search Trees (1) Figure 11.27: A sequence of removals from a (2,4) tree: (a) removal of 4 , causing an underflow; (b) a transfer operation; (c) after the transfer operation; (d) removal of 12 , causing an underflow; (e) a fusion operation; (f) after the fusion operation; (g) removal of 13 ; ( h ) after removing 13