Exam Monday. Lecture 19: Binary Search & Splay Trees. Assignment BST

Transcription

1 Eam Monda Lecture 19: inar Search & Sla Trees S 62 Srin 2015 Kim ruce & merica hambers In class: 50 minutes Samle Eams on-line overs everthin throuh Sla trees Studin essential Do form stud rous Do roblems from samle eams Do roblems from tet ssinment ST Work first on World & Secies classes Need JUnit for both and turn in World Each creature kees a reference to its secies so it can follow the roram. Moves ho, left, riht, and infect use u turn if s and oto are free binar tree is a binar search tree iff it is emt or if the value of ever node is both reater than or equal to ever value in its left subtree and less than or equal to ever value in its riht subtree.

2 Imlementation Focus on trickiest methods: add, et, & remove rotected methods: locate, redecessor, and removeto root and value are non-null 1 - eistin tree node with the desired value, or // 2 - the node to which value should be added rotected inartree<e> locate(inartree<e> root, E value) { E rootvalue = root.value(); inartree<e> child; if (rootvalue.equals(value)) return root; // found at root // look left if less-than, riht if reater-than if (orderin.comare(rootvalue,value) < 0) { child = root.riht(); else { child = root.left(); // no child there: not in tree, return this node, // else kee searchin if (child.isemt()) { return root; else { return locate(child, value); rotected inartree<e> redecessor(inartree<e> root) { inartree<e> result = root.left(); while (!result.riht().isemt()) { result = result.riht(); return result; rotected inartree<e> successor(inartree<e> root) { inartree<e> result = root.riht(); while (!result.left().isemt()) { result = result.left(); return result; ublic void add(e value) { inartree<e> newnode = new inartree<e>(value,empty,empty); // add value to binar search tree // if there's no root, create value at root if (root.isemt()) { root = newnode; else { inartree<e> insertlocation = locate(root,value); E nodevalue = insertlocation.value(); // The location returned is the successor or redecessor // of the to-be-inserted value if (orderin.comare(nodevalue,value) < 0) { insertlocation.setriht(newnode); else { if (!insertlocation.left().isemt()) { // if value is in tree, we insert just before redecessor(insertlocation).setriht(newnode); else { insertlocation.setleft(newnode); count++;

3 Remove node General ase Remove tomost node. Left hild has a riht subtree: Eas cases: no left subtree, or no riht subtree -- eas, the are new tree left child has no riht subtree 3 redecessor( ) Remove method omleit Locate element to be deleted RemoveTo of node rooted at element Hook u resultin tree as child of elt s arent. O(h), where h is heiht of tree. O(h) to find, ould be another O(h) to find redecessor onstant to atch back toether. dd, et, contains, remove Proortional to heiht of tree an we uarantee O(lo n)? Onl if we can kee them balanced!! Secial binar search trees that sta balanced: VL trees Red-black trees We ll do sla tree, which doesn t uarantee balance but uarantees ood averae behavior easier to understand than alternatives better than others if likel to o back to recent nodes

4 Rotatin Trees Ke idea: Rotate node hiher in tree while keein it in order. Sla Trees Riht rotation Left rotation Rotatin Trees Shiftin elements toward root Rotate to root, while maintain ST structure ll nodes in subtree o u one level, all in o down one level, all in sta same. Move u two levels w/ two rotations If is left child of a left child... See code in inartree Riht rotation Left rotation

5 Shiftin elements toward root Sla Tree If is a riht child of a left child. Idea behind sla tree. Ever time find, et, add: or remove an element, move it to the root b a series of rotations. b) Other elements rotate out of wa while maintainin order. Sla means to sread outwards Smmetric if interchane left and riht