COMP 103 RECAP/TODAY. Recap: General Tree Examples. Recap: Planning. General Trees. Taxonomies e.g. game genres. Tic Tac Toe search tree for moves

Transcription

1 P ecture 21 eneral rees arcus rean, indsay roves, Peter ndreae, and homas uehne, VUW indsay roves Sool of ngineering and omputer Science, Victoria University of Wellington 2 PRVIUSY RP/Y inary trees, binary tree traversals, binary sear trees, recursion eneral trees - Nodes can have any number of ildren (ecture 13) Used to represent hierarical relationships, su as inheritance structure for Java programs, nesting of statements, organisational structures, Y Representing eneral rees in Java Some basic operations on trees: printll, countnodes, raversing trees 3 Recap: eneral ree xamples axonomies e.g. game genres rganisational harts, managers, employees, slaves, iling systems e.g., the folder structure of your hard drive omputer raphics models ctrees, for partitioning 3 space ecision processes 4 Recap: Planning ic ac oe sear tree for moves X X X X X X X X X X often not represented explicitly; only implicitly created by recursion X X 1

2 5 Recap: ree erminology tree is a collection of s in a strict hierarical structure. a is in a node of the tree. he root is at the top. he leaves are at the bottom. a node may have ild nodes except a leaf, whi has none. a node has one - except the root, whi has none. n edge joins a node to its may be labelled. subtree is a node plus all its descendents. he depth of a node is its distance from the root. hildren may be ordered/unordered he height or depth of a tree is the depth of the lowest leaf. evel = set/list of nodes at the same depth. ran = sequence of nodes on a path from root to a leaf. ree may or may not store explicit references 6 Recap: Representing trees in Java eneralised inkednode eneral ree Nodes some collection type (ordered or unordered) 7 Representing eneral rees Need to represent ea node, and information stored there Use an object for ea node Need to connect s and ildren Usually store links from to ildren Sometimes store link from ild to hildren may be ordered (list) or unordered (set) Sometimes associate information with edges x: how would you do that? 8 Representing eneral rees myree Set of Nodes to reference ildren data public class enreenode<> { private ; private Set<enreeNode<>> ildren; private enreenode<> ; not always needed 2

3 9 lass enreenode public class enreenode<> { public enreenode( it) { = it; public enreenode( it, enreenode<> p, Set<enreeNode<>> c ) { = it; = p; ildren = c; public void setparent(enreenode<> p) { = p; public enreenode<> getparent() { return ; public void sethildren( Set<enreeNode<>> c) { ildren = c; public Set<enreeNode<>> gethildren() { return ildren; public void addhild( enreenode<> c) { ildren.add(c); We can use the usual set/list operations on ildren anything missing? 10 dding a hild public class enreenode<> { public void addhild(enreenode<> newhild) { // add ild to set of ildren ildren.add(newhild); // connect ild to newhild.setparent(this); example of a useful setter method 11 Useful Setters 12 raversing a eneral ree WIHU USU Setter k.setparent(g); g.addhild(k); m.setparent(g); g.addhild(m); t.setparent(k); k.addhild(t); z.setparent(k); k.addhild(z); a.setparent(m); m.addhild(a); any operations on general trees involve visiting every node in the tree..g.: Print all values what order? WIH USU Setter g.addhild(k); g.addhild(m); k.addhild(t); k.addhild(z); m.addhild(a); ount the nodes Sum the node values 3

4 13 raversing a eneral ree 14 Printing values in a tree Recursion is the most natural and easiest approa Iterate through the ildren at ea node printll() Recursion is the most natural and easiest approa Iterate through the ildren at ea node printll() public void printll() { System.out.println(); public void printll() { System.out.println(); printll() printll() printll() printll() printll() for (enreenode<> ild : ildren) ild.printll(); for (enreenode<> ild : ildren) ild.printll(); Hint: inding is like Printing with an early exit potential 15 ounting nodes Identical traversal but this time we are returning a value public int count() { // counting the node itself int nodeount = 1; // sum over ildren for (reenode ild : ildren) nodeount += ild.count(); return nodeount; ounting Nodes 16 public int count() { // counting the node itself int nodeount = 1; // sum over ildren for (reenode ild : ildren) nodeount += ild.count(); return nodeount; count() 12 count() 4

5 17 ounting Nodes 6 count() 3 count() 2 count() 18 ore operations on trees ind the height of a tree Sum the values at nodes ind a node containing a given value ind the greatest number of ildren for any node ind the number of nodes containing a given value, or with values satisfying some property What others can you think of? ll involve (potentially) visiting every node in the tree 19 rees and Recursion Why do trees go together with recursion like Peace and ove? trees are recursive structures ea tree node is the root of a subtree global results are formed from local (sub-) results 20 Recap: epth-first traversals Variations: 1. pre-order: node, then ildren 2. in-order: left ild, node, right ild 3. post-order: ildren, then node It is possible to traverse a tree iteratively but you ll have to do your own bookkeeping we ll get to that later 5

6 21 rithmetic expression trees + x / Prefix Notation (Polish notation) + x 5 2 / plus( times(5, 2), divide( minus(7, 3), 9 ) ) Infix Notation (5 x 2 ) + ( ( 7 3) / 9) 22 epth-irst raversal in eneral rees Visit the subtree under ea ild before going to the next ild Pre-order: process the node, then process the subtrees Post-order: process the subtrees, then process the node No Parentheses Postfix Notation (Reverse Polish) 5 2 x / + I J H 23 epth-first raversal, recursively e.g., list all employee names Use recursion (and iteration to step through the ildren) 24 anaging epth-irst raversal Need to remember what nodes are still being worked on, and whi of their ildren have been processed already In a recursive depth-first traversal (eg. "istll"), activation stack and loop control take care of the bookkeeping! public void listll() { System.out.println(this.name); for (rgreenode ild : this.ildren) ild.listll(); Whi traversal order does this implement? I J H 1. print own name 2. process 1. print ildren... own name 3. return 2. process 1. print ildren... own name 3. return 2. process ildren return 6

7 25 readth-first raversal What about printing the nodes by level? root first then second level, then third level,. H I J 7