Tree traversals January 30, 2019 Cinda Heeren / Will Evans / - PowerPoint PPT Presentation

Tree traversals January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 1

Announcements • Attention: – If you borrowed a Macbook charger in Monday lab section 14:00- 16:00, please return it! See Piazza for details • Section 201 (that's us!) Midterm 1: – Monday, Feb.04, 19:00 – 21:00, WESB 100 January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 2

Complete binary trees It's not quite perfect, but almost • A binary tree is complete if – The leaves are on at most two A different levels, – The second to bottom level is B C completely filled in and – The leaves on the bottom level are as far to the left as possible D E F January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 3

Binary tree traversal It's recursive! • A traversal algorithm for a binary tree visits each node in the tree – Typically, it will do something while visiting each node! • Traversal algorithms are naturally recursive • There are three traversal methods – inOrder – preOrder – postOrder January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 4

inOrder traversal algorithm void inOrder(Node* nd) { if (nd != nullptr) { inOrder(nd->leftchild); visit(nd); inOrder(nd->rightchild); } } The visit function would do whatever the purpose of the traversal is (e.g. print the data value of the node). January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 5

preOrder traversal visit(nd); preOrder(nd->leftchild); 1 preOrder(nd->rightchild); 17 2 6 visit visit 13 27 preOrder(left) preOrder(left) preOrder(right) preOrder(right) 8 5 7 3 visit visit visit 16 20 39 9 preOrder(left) preOrder(left) preOrder(left) preOrder(right) preOrder(right) preOrder(right) visit preOrder(left) 4 preOrder(right) 11 visit preOrder(left) preOrder(right) January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 6

postOrder traversal postOrder(nd->leftchild); postOrder(nd->rightchild); 8 visit(nd); 17 4 7 postOrder(left) postOrder(left) postOrder(right) 13 27 postOrder(right) visit visit 6 3 5 2 postOrder(left) postOrder(left) postOrder(left) 16 20 postOrder(right) 39 postOrder(right) 9 postOrder(right) visit visit visit postOrder(left) postOrder(right) 1 visit postOrder(left) 11 postOrder(right) visit January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 7

Exercise • What will be printed by an in-order traversal of the tree? – preOrder? postOrder? inOrder(nd->leftchild); 17 visit(nd); inOrder(nd->rightchild); 9 27 6 16 20 31 12 39 Note to Geoff: show the trick with the dots! January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 8

Not quite recursive Another type of tree traversal • We have seen pre-order, in-order, post-order traversals • What about a traversal that visits every node in a level before working on the next level? – level-order traversal 41 33 87 21 74 36 45 78 25 Use some ADT to support this? January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 9

What is "visiting"? • Some operation to be done at the current node – counting, or arithmetic – creating a node (e.g. for a copy constructor) – deleting a node (e.g. for a destructor) What is the height of • e.g. height this tree? What is the height of What is the this tree? height of this tree? int Height(Node* nd) { if (nd == nullptr) // empty tree return _____; else return _______________________; } Which type of traversal is this? Running time? January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 10

Readings for this lesson • Carrano & Henry: – Chapter 15.1 – 15.2 (Trees, tree traversals) • Next class: – Carrano & Henry: Chapter 15.2, 16.1 – 16.2 (Tree traversals, implementations) January 30, 2019 Cinda Heeren / Will Evans / Geoffrey Tien 11