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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

TreesTrees

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

Figure 10.1Figure 10.1A general tree


Figure 10.2Figure 10.2A subtree of the tree in Figure 10.1


Figure 10.3Figure 10.3a) An organization chart; b) a family tree


Figure 10.4Figure 10.4Binary trees that represent algebraic expressions


Figure 10.5Figure 10.5A binary search tree of names


Figure 10.6Figure 10.6Binary trees with the same nodes but different heights


Figure 10.7Figure 10.7A full binary tree of height 3


Figure 10.8Figure 10.8A complete binary tree


Figure 10.9Figure 10.9Traversals of a binary tree: a) preorder; b) inorder; c) postorder


Figure 10.10aFigure 10.10aa) A binary tree of names


Figure 10.10bFigure 10.10bb) its array-basedimplementations


Figure 10.11Figure 10.11Level-by-level numbering of a complete binary tree


Figure 10.12Figure 10.12An array-based implementation of the complete binary tree in Figure 10-11


Figure 10.13Figure 10.13A reference-based implementation of a binary tree


Figure 10.14Figure 10.14Contents of the implicit stack as treeNode progresses through a given treeduring a recursive inorder traversal


Figure 10.15Figure 10.15Traversing a) the left and b) the right subtrees of 20


Figure 10.16Figure 10.16Avoiding returns to nodes B and C


Figure 10.17Figure 10.17A binary search tree


Figure 10.18aFigure 10.18aBinary search trees with the same data as in Figure 10-17


Figure 10.18bFigure 10.18bBinary search trees with the same data as in Figure 10-17


Figure 10.18cFigure 10.18cBinary search trees with the same data as in Figure 10-17


Figure 10.19Figure 10.19An array of names in sorted order


Figure 10.20Figure 10.20Empty subtree where search terminates


Figure 10.21a and 10.21bFigure 10.21a and 10.21ba) Insertion into an empty tree; b) search terminates at a leaf


Figure 10.21cFigure 10.21cc) insertion at a leaf


Figure 10.22Figure 10.22a) N with only a left child—N can be either the left or right child of P; b) afterdeleting node N


Figure 10.23Figure 10.23N with two children


Figure 10.24Figure 10.24Not any node will do


Figure 10.25Figure 10.25Search key x can be replaced by y


Figure 10.26Figure 10.26Copying the item whose search key is the inorder successor of N ’s search key


Figure 10.27Figure 10.27Recursive deletion of node N


Figure 10.28Figure 10.28A maximum-height binary tree with seven nodes


Figure 10.29Figure 10.29Binary trees of height 3


Figure 10.30Figure 10.30Counting the nodes in a full binary tree of height h


Figure 10.31Figure 10.31Filling in the last level of a tree


Figure 10.32Figure 10.32The order of the retrieval, insertion, deletion, and traversal operations for thereference-based implementation of the ADT binary search tree


Figure 10.33Figure 10.33a) A binary search tree bst; b) the sequence of insertions that result in this tree


Figure 10.34Figure 10.34A full tree saved in a file by using inorder traversal


Figure 10.35Figure 10.35A tree of minimum height that is not complete


Figure 10.36Figure 10.36A general tree


Figure 10.37Figure 10.37A reference-based implementation of the general tree in Figure 10.36


Figure 10.38Figure 10.38The binary tree that Figure 10-37 represents


Figure 10.39Figure 10.39An implementation of the n-ary tree in Figure 10.36


Figure 10.40Figure 10.40A tree for Self-Test Exercises 1, 3, 7, and 11 and for Exercises 6 and 11


Figure 10.41Figure 10.41An array for Self-Test Exercise 9


Figure 10.42Figure 10.42A tree for Self-Test Exercise 10 and for Exercise 2a


Figure 10.43Figure 10.43A binary search tree for Exercise 3


Figure 10.44Figure 10.44A minimax tree for Exercise 17

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