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Binary tree and operations
- 2. OBJECTIVES
- 3. root node is desigated wich has no parent if the imediate predecessor of the node is parent of the node then all imediate sucessor of a node are known as child child which is on left side is called left child and hat on right side is called right child Basic terminolgies
- 5. BINARY TREES WITH EXAMPLES
- 6. PROPERTIES OF BINARY TREE
- 7. the maximum no of nodes possible in a binary tree of height h is 2power of h-1 The minimum no of nodes possible in a binary tree Height h is h a binary tree has the minimum no of nodes one every parent has one child such kind of trees are called skew binary trees
- 9. • The root N of T is stored in TREE [1]. If a node occupies TREE [k] then its is stored in TREE and its is stored into TREE
- 10. Advantage of sequential rpresentation any node can acessed from any other node by calculating the index value data are stored without any pointers to their which are mentioned implicity programing lanuage where dynamic memmory allocation is not possible such as(BASIC ,FORTRAIN)ARRAY REPREPRESENTAION IS nly means to store a tree
- 11. Disadvantage of sequential reprentation other then the full of binary trees the majority of the array entries may be empty it allows only static representation it is in no way possible to enhance the tree structure if the array size will be limited insering new node to the tree or deleting a node in a tree data moved up and moved down in an array excessive amount of processing time
- 12. linked list representation of a binary tree they are two field s to stor the address of left child and right child of the node data is the current information of the node if one knows the address of the root node then form it other node can be acessed
- 13. physical implementation of a binary tree in memmory Algorithm build a tree input:ITEM is the data contet of the node i output: a binary tree with two sub-trees of the node i data structure: array representation of a binary tree
- 14. operations of binary trees insertion: TO include a node into an existing binary tree deletion: TO delete a node from a non-empty binary tree Traversal: TO visit all the nodes in abinary tree in traversal they are three orders inorder -> LEFT->ROOT->RIGHT preorder -> ROOT->LEFT->RIGHT postorder-> LEFT->RIGHT->ROOT merge:TO merge two binary trees into a large one
- 15. in this operation to insert a new node at any position in a binary tree we have a simple insertion for ex to insert a “g “ a new node two stops search the existence node second establish the link
- 17. insert a binary tree using linked list • insert:KEY is the data content of the key node after new node is to be inserted an ITEM is the data content of the new node can be inserted • output: A node with data component ITEM inserted as an extrernal node after the node having data KEY if such a node does not exist with empty (s), that is, eiter child or both children IS/ARE ABSENT. • DATA STRUCTURE: linked structure of a binary tree. ROOT is the pointer to the root node.
- 19. algorithm • PRINT “ insertion is not possible as left child” • EXIT • EDIF • ELSE • IF(pf->RC =NULL) • new=GETNODE • new->DATA=ITEM • new->LC=new->RC=NULL • ptr->RC=new • else • print”insertion is not possibble as right child” • exit • end if • else • print”the key node is already has a child” • stop
- 20. deletion • in deletion operation can be carried out of two kinds of storage representation of binary trees • in ordernto delete a node in a binary tree it is required to reach at the parent node to be deleted • the link of the parent nodes whih stores the location of the node to be deleted is then set buy a NULL entry • input:given ITEM as data of the node with which the node can be identified for deletion • output:a binary tree without a node having a data ITEM • data stucture: array a storing binary trees SIZE denotes the size of a
- 22. WHAT IS A TRAVERSAL? THE traversal operation is frequently used operation of a binary this operation to visit each node in the tree exactly once a full traversal of a binary tree gives a linear ordering of the data in the tree if a binary tree contains an arithmetic expression then it traverse infix notations,posfix notations,prefix notations
- 27. input:two pointers ROOT1 and ROOT2 OF THE TWO BINARY TREES t1,t2 output:a binary treee containing all the node t1,t2 ptr to the root as ROOT data structure:linked the data strucure steps: if(ROOT1=NULL)THEN ROOT=ROOT2 EXIT