Figure 12.1 A binary search tree of a) maximum height; b) minimum height

Figure 12.1 A binary search tree of a) maximum height; b) minimum height

Figure 12.2 A 2-3 tree of height 3

Figure 12.3 Nodes in a 2-3 tree a) a 2-node; b) a 3-node

Figure 12.4 A 2-3 tree

Figure 12.5 a) A balanced binary search tree; b) a 2-3 tree with the same elements

Figure 12.6 a) The binary search tree of Figure 12.5a after a sequence of insertions; b) the 2-3 tree of Figure 12.5b after the same insertions

Figure 12.7 After inserting 39

Figure 12.8 a), b) The steps for inserting 38; c) the resulting tree

Figure 12.9 After inserting 37

Figure 12.10 a), b), c) The steps for inserting 36; d) the resulting tree

Figure 12.11 The tree after the insertion of 35, 34, and 33

Figure 12.12 Splitting a leaf in a 2-3 tree

Figure 12.13 Splitting an internal node in a 2-3 tree

Figure 12.14 Splitting the root of a 2-3 tree

Figure 12.15a a), b), c), d) The steps for deleting 70

Figure 12.15b-d a), b), c), d) The steps for deleting 70

Figure 12.15e e) the resulting tree

Figure 12.16 a), b), c) The steps for deleting 100; d) the resulting tree

Figure 12.17a The steps for deleting 80

Figure 12.17b and 12.17c The steps for deleting 80

Figure 12.17d and 12.17e The steps for deleting 80

Figure 12.18 Results of deleting 70, 100, and 80 from a) the binary search tree of Figure 12.5a and b) the 2-3 tree of Figure 12.5b

Figure 12.19a and 12.19b a) Redistributing values; b) merging a leaf

Figure 12.19c and 12.19d c) redistributing values and children; d) merging internal nodes

Figure 12.19e e) deleting the root

Figure 12.1 A binary search tree of a) maximum height; b) minimum height