BINARY SEARCH TREES (CONTD) Problem Solving with Computers-II

Transcription

1 BINARY SEARCH TREES (CONTD) Problem Solving with Computers-II

2 A node in a BST class BSTNode { public: BSTNode* left; BSTNode* right; BSTNode* parent; int const data; g mroaa struct Card char suit BSTNode( const int & d ) : data(d) { left = right = parent = 0; } }; g int r'm'm value Thedata storedin any BSTnode could be ofanytype e g Card as long as theoperation's Cand are defined on that type left 6!2 parentf plowed be a class BST II in L r carob right

3 Define the BST ADT Operations Search Insert Min Max Successor Predecessor Delete Print elements in order Min 12 root kit I us e p Foundit 4 max as

4 Successor: Next largest element What is the successor of? next largest What is the successor of 50? my What is the successor of 60? key 50 f t Id int successor int Valette 90 Our algorithm will be for a private version of this function that takes a pointer to ano as input and returns a pointer to the node with the nett largest value Node B successor PrivateC Nodes n!4

5 Casek Casta nhasarightsubreet keg if n f Keys Tr child n is parent's right keylp L key n Case lb h From key Cp key Cn L keyer if if n is its parent's left child n left n parent key keyens n C keg p s They C re How does keylp compare with key CTR C Lkeycin key Cp Hey Ctr 50 keycp Can't say

6 from key Cn Keysor 5 keycp 9 case 2 n has no right theremin subtree this was left as an assignment but now that you now about the Inorder Traversal the proof might be easier to follow successor Cng its on the figure to Cesµtyy If n in the left child of parent has shown the Tk left AI of the tree would print an inordu trainset the parent's n isleft child ofparent key after painting n Therefore Caseres or P P is the successor of n Atff n is the riguchiedgetspartly then the paint's is done after n's recursive call key is punted and we proceed to the guard paid beeusive cell OR more gunally his sight child proceed all the way bypttu tree until we find a node that is the 8Pant deft child of its parent paiefuoetm.tk

7 qpane wife Predecessor: Next smallest element root What is the predecessor of? What is the predecessor of? l of I pared Sed int predessor C int value n find HC value Nodes Node return predecessor H n data predecessor H n Node!5

8 20 Delete: Case Case 1: Node is a leaf node Set parent s (left/right) child pointer to null 90 Delete the node if Inseeft II nerightis leaf node if Cn n parent left n parents left a O 60 n else n parent right 20 s leaf node delete ni!6

9 Delete: Case 2 grain 50 Case 2 Node has only one child Replace the node by its only child tee it ojf.nrnisae.tn siefiuaito7onspareu n left parent n parent if Cn n parent left n parents left n left f n parent right 8ns left!7

10 Delete: Case 3 50 n Case 3 Node has two children Swap n data withits I Can we still replace the node by one of its children? Why or Why not? P delete 60 predecessor its successor OR the predecessor 11Default Neithercases or case 2 an!8

11 In order traversal: print elements in sorted order 12 b Algorithm Inorder(tree) 1. Traverse the left subtree, i.e., call Inorder(left-subtree) 2. Visit the root. 3. Traverse the right subtree, i.e., call Inorder(right-subtree) wii what is theoutputofdoing an inorde traversal on the above tree A Tnorder r left B c'outccr data C Incorder r right the above 3 n!9

12 jayu tree outputof Tn order Traversal I i 12

13 Pre-order traversal: nice way to linearize your tree! 12 Algorithm Preorder(tree) 1. Visit the root. 2. Traverse the left subtree, i.e., call Preorder(left-subtree) 3. Traverse the right subtree, i.e., call Preorder(right-subtree) iii Oso 50!10

14 Post-order traversal: use in recursive destructors! Algorithm Postorder(tree) 1. Traverse the left subtree, i.e., call Postorder(left-subtree) 2. Traverse the right subtree, i.e., call Postorder(right-subtree) 3. Visit the root !11

15 Concept Question LinkedList::~LinkedList(){ delete head; } class Node { public: int info; Node *next; }; Which of the following objects are deleted when the destructor of Linked-list is called? (A) head tail 0 (B): only the first node (C): A and B (D): All the nodes of the linked list (E): A and D

16 Concept Question LinkedList::~LinkedList(){ delete head; } Node::~Node(){ delete next; } Which of the following objects are deleted when the destructor of Linked-list is called? (A) head tail 0 (B): All the nodes in the linked-list (C): A and B (D): Program crashes with a segmentation fault (E): None of the above

17 LinkedList::~LinkedList(){ delete head; } I head tail 11callsthefirst node's destructor Node::~Node(){ delete next; } acallsthe next node's destructor delete next deleteneat delete Og does not delete head segfeed call to destructor completes Node 3 isdelete call todestructor of 2 completes dis Node 2 is deleted Call to def destructorq node 1 completes

18 Cee Post-order traversal: use in recursive destructors! Algorithm Postorder(tree) 1. Traverse the left subtree, i.e., call Postorder(left-subtree) 2. Traverse the right subtree, i.e., call Postorder(right-subtree) 3. Visit the root U BSTNode C delete left del ele right!15