ch12 carrano java - com sci · pdf filea 2-3-4 tree with the same items as the 2-3 tree in...

Data Abstraction and Problem Solving with JAVA Walls and MirrorsFrank M. Carrano and Janet J. Prichard © 2001 Addison Wesley

Data Abstraction and Problem Solving with JAVA:Data Abstraction and Problem Solving with JAVA:Walls and MirrorsWalls and Mirrors

CarranoCarrano / / PrichardPrichard

Advanced ImplementationsAdvanced Implementationsof Tablesof Tables

Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley

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


Figure 12.2Figure 12.2A 2-3 tree of height 3


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


Figure 12.4Figure 12.4A 2-3 tree


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


Figure 12.6Figure 12.6a) The binary search tree of Figure 12.5a after a sequence of insertions; b) the2-3 tree of Figure 12.5b after the same insertions


Figure 12.7Figure 12.7After inserting 39


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


Figure 12.9Figure 12.9After inserting 37


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


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


Figure 12.12Figure 12.12Splitting a leaf in a 2-3 tree


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


Figure 12.14Figure 12.14Splitting the root of a 2-3 tree


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


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


Figure 12.15eFigure 12.15ee) the resulting tree


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


Figure 12.17aFigure 12.17aThe steps for deleting 80


Figure 12.17b and 12.17cFigure 12.17b and 12.17cThe steps for deleting 80


Figure 12.17d and 12.17eFigure 12.17d and 12.17eThe steps for deleting 80


Figure 12.18Figure 12.18Results of deleting 70, 100, and 80 from a) the binary search tree of Figure12.5a and b) the 2-3 tree of Figure 12.5b


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


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


Figure 12.19eFigure 12.19ee) deleting the root


Figure 12.20Figure 12.20A 2-3-4 tree with the same items as the 2-3 tree in Figure 12-6b


Figure 12.21Figure 12.21A 4-node in a 2-3-4 tree


Figure 12.22Figure 12.22Inserting 20 into a one-node 2-3-4 tree


Figure 12.23Figure 12.23After inserting 50 and 40


Figure 12.24Figure 12.24The steps for inserting 70


Figure 12.25Figure 12.25After inserting 80 and 15


Figure 12.28Figure 12.28Splitting a 4-node root during insertion


Figure 12.29Figure 12.29Splitting a 4-node whose parent is a 2-node during insertion


Figure 12.30Figure 12.30Splitting a 4-node whose parent is a 3-node during insertion


Figure 12.31Figure 12.31Red-black representation of a 4-node


Figure 12.32Figure 12.32Red-black representation of a 3-node


Figure 12.33Figure 12.33A red-black tree that represents the 2-3-4 tree in Figure 12.20


Figure 12.34Figure 12.34Splitting a red-black representation of a 4-node that is the root


Figure 12.35Figure 12.35Splitting a red-black representation of a 4-node whose parent is a 2-node


Figure 12.36aFigure 12.36aSplitting a red-black representation of a 4-node whose parent is a 3-node


Figure 12.36bFigure 12.36bSplitting a red-black representation of a 4-node whose parent is a 3-node


Figure 12.36cFigure 12.36cSplitting a red-black representation of a 4-node whose parent is a 3-node


Figure 12.37Figure 12.37a) An unbalanced binary search tree; b) balanced tree after rotation;c) a balanced tree after insertion


Figure 12.38Figure 12.38a) An unbalanced binary search tree; b) a balanced tree after a single leftrotation


Figure 12.39Figure 12.39Before and after a single left rotation that decreases the tree’s height


Figure 12.40Figure 12.40a) An unbalanced binary search tree; b) a balanced tree after a single leftrotation


Figure 12.41Figure 12.41Before and after a single left rotation that does not affect the tree’s height


Figure 12.42Figure 12.42a) Before; b) during; and c) after a double rotation


Figure 12.43Figure 12.43Before and after a double rotation that decreases the tree’s height


Figure 12.44Figure 12.44Address calculator


Figure 12.45Figure 12.45A collision


Figure 12.46Figure 12.46Linear probing with

h(x) = x mod 101


Figure 12.47Figure 12.47Quadratic probing with

h(x) = x mod 101


Figure 12.48Figure 12.48Double hashing during the

insertion of 58, 14, and 91


Figure 12.49Figure 12.49Separate chaining


Figure 12.50Figure 12.50The relative efficiency of four collision-resolution methods


Figure 12.51Figure 12.51Two data structures that share the same data: a) a sorted linked list; b) areference-based queue


Figure 12.52Figure 12.52A queue referencing a sorted linked list


Figure 12.53Figure 12.53A queue referencing into a doubly linked list


Figure 12.54Figure 12.54A queue referencing a double linked binary search tree


Figure 12.55Figure 12.55A red-black tree for Exercise 7

ch12 carrano java - com sci · pdf filea 2-3-4 tree with the same items as the 2-3 tree in...

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