BinaryTree 1 October 2020 OSU CSE 1
BinaryTree • The BinaryTree component family allows you to manipulate values modeled as mathematical binary trees with any label type T (i.e., binary tree of T ) – Another generic type like Sequence and Set 1 October 2020 OSU CSE 2
Interfaces and Classes Standard Iterable extends extends BinaryTree- Kernel extends BinaryTree implements BinaryTree1 1 October 2020 OSU CSE 3
Interfaces and Classes Standard Iterable extends extends BinaryTree- Kernel BinaryTreeKernel extends has contracts for BinaryTree three methods: assemble implements disassemble size BinaryTree1 1 October 2020 OSU CSE 4
Interfaces and Classes BinaryTree has contracts for four methods (the last of Standard Iterable which we will skip): root extends extends replaceRoot BinaryTree- height Kernel inOrderAssemble extends BinaryTree implements BinaryTree1 1 October 2020 OSU CSE 5
Interfaces and Classes There is really an abstract Standard Iterable class as usual in the chain here, but it is not shown extends extends because these slides describe the client view, and a BinaryTree- client needs only interface Kernel BinaryTree and class extends BinaryTree1 . BinaryTree implements BinaryTree1 1 October 2020 OSU CSE 6
Mathematical Model type BinaryTreeKernel is modeled by binary tree of T 1 October 2020 OSU CSE 7
No-argument Constructor • Ensures: this = empty_tree 1 October 2020 OSU CSE 8
Example Code State BinaryTree<NaturalNumber> bn = new BinaryTree1<>(); 1 October 2020 OSU CSE 9
Example Code State BinaryTree<NaturalNumber> bn = new BinaryTree1<>(); bn = 1 October 2020 OSU CSE 10
assemble void assemble(T root, BinaryTree<T> left, BinaryTree<T> right) • Assembles in this a binary tree with root label root and subtrees left and right ; the declaration notwithstanding, the dynamic type of left and right must be the same as the dynamic type of this . • Aliases: reference root • Replaces: this • Clears: left , right • Ensures: this = compose (root, #left, #right) 1 October 2020 OSU CSE 11
Example Code State x = 70 bn = ? lt = rt = bn.assemble(x, lt, rt); 1 October 2020 OSU CSE 12
Example Code State x = 70 bn = ? lt = rt = bn.assemble(x, lt, rt); x = 70 bn = 70 lt = rt = 1 October 2020 OSU CSE 13
Example Code State Note the alias created x = 70 bn = ? here, which you cannot lt = see in the tracing table. rt = bn.assemble(x, lt, rt); x = 70 bn = 70 lt = rt = 1 October 2020 OSU CSE 14
disassemble T disassemble(BinaryTree<T> left, BinaryTree<T> right) • Disassembles this into its root label, which is returned as the value of the function, and subtrees left and right ; the declaration notwithstanding, the dynamic type of left and right must be the same as the dynamic type of this . • Replaces: left , right • Clears: this • Requires: this /= empty_tree • Ensures: # this = compose (disassemble, left, right) 1 October 2020 OSU CSE 15
Example Code State lt = ? bn = 13 rt = ? NaturalNumber root = bn.disassemble(lt, rt); 1 October 2020 OSU CSE 16
Example Code State lt = ? bn = 13 rt = ? NaturalNumber root = bn.disassemble(lt, rt); root = 13 bn = lt = rt = 1 October 2020 OSU CSE 17
size int size() • Reports the size of this . • Ensures: size = | this | 1 October 2020 OSU CSE 18
iterator Iterator<T> iterator() • Returns an iterator over a set of elements of type T . • Ensures: ~this.seen * ~this.unseen = IN_ORDER( this ) 1 October 2020 OSU CSE 19
Traversal Orders • There are three named traversal orders for the nodes of a binary tree, named according to when the root is “visited” relative to the (recursive) traversals of the left and right subtrees – Pre-order : root is visited before left and right – In-order : root is visited between left and right – Post-order : root is visited after left and right 1 October 2020 OSU CSE 20
Traversal Orders • There are three named traversal orders The iterator method for the nodes of a binary tree, named returns an Iterator<T> according to when the root is “visited” that visits the node labels in this order. relative to the (recursive) traversals of the left and right subtrees – Pre-order : root is visited before left and right – In-order : root is visited between left and right – Post-order : root is visited after left and right 1 October 2020 OSU CSE 21
4 2 5 1 3 • Pre-order traversal: <4, 2, 1, 3, 5> • In-order traversal: <1, 2, 3, 4, 5> • Post-order traversal: <1, 3, 2, 5, 4> 1 October 2020 OSU CSE 22
root T root() • Reports the root of this . • Aliases: reference returned by root • Requires: this /= empty_tree • Ensures: there exists lt, rt: binary tree of T ( this = compose (root, lt, rt)) 1 October 2020 OSU CSE 23
Example Code State bn = 13 NaturalNumber k = bn.root(); 1 October 2020 OSU CSE 24
Example Code State bn = 13 NaturalNumber k = bn.root(); k = 13 bn = 13 1 October 2020 OSU CSE 25
Example Code State Note the alias created bn = here, which you cannot 13 see in the tracing table. NaturalNumber k = bn.root(); k = 13 bn = 13 1 October 2020 OSU CSE 26
replaceRoot T replaceRoot(T x) • Replaces the root of this with x , and returns the old root. • Aliases: reference x • Requires: this /= empty_tree • Ensures: there exists lt, rt: binary tree of T (# this = compose (replaceRoot, lt, rt) and this = compose (x, lt, rt)) 1 October 2020 OSU CSE 27
Example Code State n = 4 bn = 13 NaturalNumber k = bn.replaceRoot(n); 1 October 2020 OSU CSE 28
Example Code State n = 4 bn = 13 NaturalNumber k = bn.replaceRoot(n); n = 4 bn = 4 k = 13 1 October 2020 OSU CSE 29
Example Code State Note the alias created n = 4 bn = here, which you cannot 13 see in the tracing table. NaturalNumber k = bn.replaceRoot(n); n = 4 bn = 4 k = 13 1 October 2020 OSU CSE 30
Another Example Code State n = 4 bn = 13 n = bn.replaceRoot(n); 1 October 2020 OSU CSE 31
Another Example Code State n = 4 bn = 13 n = bn.replaceRoot(n); n = 13 bn = 4 1 October 2020 OSU CSE 32
Another Example Code State This use of the method avoids creating an alias: it n = 4 bn = 13 swaps n with the old root. n = bn.replaceRoot(n); n = 13 bn = 4 1 October 2020 OSU CSE 33
height int height() • Reports the height of this . • Ensures: height = ht ( this ) 1 October 2020 OSU CSE 34
Resources • OSU CSE Components API: BinaryTree – http://cse.osu.edu/software/common/doc/ • Big Java (4th ed) , Sections 16.6 – https://library.ohio-state.edu/record=b8540788~S7 1 October 2020 OSU CSE 35
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