Data Structures and AlgorithmsObjectives                In this session, you will learn to:                    Apply trees...
Data Structures and AlgorithmsIndexing               The on disk is an usually of an index.               Datafollowingfil...
Data Structures and AlgorithmsIndexing (Contd.)                     To access the record with key field 59, search the ind...
Data Structures and AlgorithmsImplementing a Threaded Binary Trees                One of the common operations on a binary...
Data Structures and AlgorithmsDefining Threaded Binary Trees                In such a case, it would be good if you have s...
Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.)                Consider theitfollowing binary search...
Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.)                Such a type of binary tree is node as...
Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.)                Node 30 does not have an inorder pred...
Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.)                Therefore, you of theaheader node alw...
Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.)                The threaded binary tree is represent...
Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.)                The left thread of node 30 and the ri...
Data Structures and AlgorithmsJust a minute                In a threaded binary tree, the right thread of a node points to...
Data Structures and AlgorithmsRepresenting a Threaded Binary Tree                The left and right threadin a threaded bi...
Data Structures and AlgorithmsRepresenting a Threaded Binary Tree (Contd.)                Various operations in a threaded...
Data Structures and AlgorithmsJust a minute                How do you identify a root node in a threaded binary tree?     ...
Data Structures and AlgorithmsJust a minute                How is the structure of a node of a threaded binary tree       ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree                To traverse a threaded binary tree in inord...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)  Inorder successor                               ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                Write an algorithm to traverse a t...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.)                                                  ...
Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree                Insert an algorithm to locate the p...
Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree (Contd.)                                          ...
Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree (Contd.)                                          ...
Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree (Contd.)                                          ...
Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree (Contd.)                                          ...
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
10 ds and algorithm session_14
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  • Faculty should tell the students that maintaining a header node in a threaded binary tree is optional. However, in the absence of a header node, the algorithm to implement various operations in a threaded binary tree becomes complicated. This is because in that case, you are required to keep track of certain extra conditions. There is always a trade off between space and efficiency. The decision to use a header node depends upon the problem in hand. If the tree is huge that stores million of records, then the use of an extra header node is justifiable. However, if the tree stores less amount of data, then maintaining a header node can be an additional overhead.
  • Faculty should tell the students that maintaining a header node in a threaded binary tree is optional. However, in the absence of a header node, the algorithm to implement various operations in a threaded binary tree becomes complicated. This is because in that case, you are required to keep track of certain extra conditions. There is always a trade off between space and efficiency. The decision to use a header node depends upon the problem in hand. If the tree is huge that stores million of records, then the use of an extra header node is justifiable. However, if the tree stores less amount of data, then maintaining a header node can be an additional overhead.
  • In this slide you need to show the calculation to determine the sum of an arithmetic progression for bubble sort algorithm. Refer to student guide.
  • In this slide you need to show the calculation to determine the sum of an arithmetic progression for bubble sort algorithm. Refer to student guide.
  • In this slide you need to show the calculation to determine the sum of an arithmetic progression for bubble sort algorithm. Refer to student guide.
  • Before explaining the traversal of a threaded binary tree, faculty should discuss the disadvantage of traversing the binary search tree through recursion. Tell the students that a stack is implemented internally to traverse the tree recursively.
  • Before explaining the traversal of a threaded binary tree, faculty should discuss the disadvantage of traversing the binary search tree through recursion. Tell the students that a stack is implemented internally to traverse the tree recursively.
  • 10 ds and algorithm session_14

    1. 1. Data Structures and AlgorithmsObjectives In this session, you will learn to: Apply trees to solve programming problems Implement a threaded binary tree Ver. 1.0 Session 14
    2. 2. Data Structures and AlgorithmsIndexing The on disk is an usually of an index. Datafollowingfiles isexampleorganized as records containing several fields, one of which is often used as a key field. The key field is used to uniquely identify each record in a Key field Offset file. 36 0 52 200 Indexing is one of the data access methods for accessing 24 400 records from the disk files. 44 600 Indexing is implemented through a table called index. 40 800 Index consists of two entries: 1000 68 59 1200 Key fields of all the records 55 1400 Offset position of each record 72 1600 35 1800 43 2000 Ver. 1.0 Session 14
    3. 3. Data Structures and AlgorithmsIndexing (Contd.) To access the record with key field 59, search the index for You can implement a binary search tree to store these this key value to retrieve its corresponding offset value, index values. which is 1200. enables faster search for a key value. This approach Read the record from the file starting from this offset Key field Offset 52 36 position. 0 52 200 36 68 24 400 44 600 40 800 24 44 59 72 68 1000 59 1200 40 55 55 1400 72 1600 35 43 35 1800 43 2000 Index Key Fields Stored in a Binary Search Tree Ver. 1.0 Session 14
    4. 4. Data Structures and AlgorithmsImplementing a Threaded Binary Trees One of the common operations on a binary tree is traversal. In a linked representation of a binary tree, traversal is usually implemented through recursion. As a result, a stack is maintained in the memory. If the tree is huge, implementing recursion to traverse the tree would require a lot of memory space. In the absence of sufficient memory space, implementing recursion can lead to a memory leak. Ver. 1.0 Session 14
    5. 5. Data Structures and AlgorithmsDefining Threaded Binary Trees In such a case, it would be good if you have some mechanism by which you can traverse the tree without implementing recursion. You can solve this problem by implementing a threaded binary tree. In a binary search tree, there are many nodes that have an empty left child or empty right child or both. You can utilize these fields in such a way so that the empty left child of a node points to its inorder predecessor and empty right child of the node points to its inorder successor. Ver. 1.0 Session 14
    6. 6. Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.) Consider theitfollowing binary search tree. fields are In this case, would be good if these NULL utilized for some other useful purpose. Most of the nodes in this tree hold a NULL value in their left or right child fields. . 65 . . 40 . . 72 . 30 . 50 . 69 80 60 Ver. 1.0 Session 14
    7. 7. Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.) Such a type of binary tree is node as be used to point tree. The empty left child field of aknowncan a threaded binaryto itsfield thatpredecessor. A inorder holds the address of its inorder successor or predecessor empty right thread. Similarly, the is known as child field of a node can be used to point to its inorder successor. . 65 . . 40 . . 72 . 30 50 . 69 80 60 Ver. 1.0 Session 14
    8. 8. Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.) Node 30 does not have an inorder predecessor because it is the first node to be traversed in inorder sequence. Similarly, node 80 does not have an inorder successor. . 65 . . 40 . . 72 . 30 50 . 69 80 60 Ver. 1.0 Session 14
    9. 9. Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.) Therefore, you of theaheader node always points to itself. The right child take dummy node called the header node. Header Node . 65 . . 40 . . 72 . 30 50 . 69 80 60 Ver. 1.0 Session 14
    10. 10. Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.) The threaded binary tree is represented as the left child of the header node. Header Node . 65 . . 40 . . 72 . 30 50 . 69 80 60 Ver. 1.0 Session 14
    11. 11. Data Structures and AlgorithmsDefining Threaded Binary Trees (Contd.) The left thread of node 30 and the right thread of node 80 point to the header node. Header Node . 65 . . 40 . . 72 . . 30 50 . 69 80 . 60 Ver. 1.0 Session 14
    12. 12. Data Structures and AlgorithmsJust a minute In a threaded binary tree, the right thread of a node points to its inorder ___________, and the left thread points to its inorder ____________. Answer: successor, predecessor Ver. 1.0 Session 14
    13. 13. Data Structures and AlgorithmsRepresenting a Threaded Binary Tree The left and right threadin a threaded binary tree istwo structure of a node fields of a node can have a bit values: from that of a normal binary tree. different – 1: a normal normal link to the child node UnlikeIndicates a binary tree, each node of a threaded binary tree 0: Indicates a thread pointing of the inorder predecessor or – contains two extra pieces to information, namely left thread and successor inorder right thread. 4631 Information 2389 Left Address of Data Address of Right Thread Left Child Right Child Thread Ver. 1.0 Session 14
    14. 14. Data Structures and AlgorithmsRepresenting a Threaded Binary Tree (Contd.) Various operations in a threaded binary tree are as follows: Traversal Search Insert Delete Ver. 1.0 Session 14
    15. 15. Data Structures and AlgorithmsJust a minute How do you identify a root node in a threaded binary tree? Answer: In a threaded binary tree, the root node is identified as the left child of the header node. If the tree is empty, the left child of the header node becomes a thread pointing to itself. Ver. 1.0 Session 14
    16. 16. Data Structures and AlgorithmsJust a minute How is the structure of a node of a threaded binary tree different from that of a normal binary tree? Answer: Each node in a threaded binary tree holds two extra pieces of information known as left thread and right thread. The value of these two fields indicates whether the left/right child field of a node contains a link to a child node or a thread to its inorder predecessor/successor. Ver. 1.0 Session 14
    17. 17. Data Structures and AlgorithmsTraversing a Threaded Binary Tree To traverse a threaded binary tree in inorder sequence, you need to determine the inorder successor of a node at each step. Ver. 1.0 Session 14
    18. 18. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. Identify the node for which you want to locate the inorder successor, and Write an algorithm toinorder the inorder successor of a node Algorithm to find the locate mark it as currentNode. in a threaded a node tree. threaded 3. If the right child of currentNode is a successor of binary in a thread: binary tree. a. Mark the right child of currentNode as successor. b. Exit. 4. Make currentNode point to its right child. 6. Repeat step 5 until left child of currentNode becomes a thread. 8. Make currentNode point to its left child. 10. Mark currentNode as successor. Ver. 1.0 Session 14
    19. 19. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. Identify the node for which you want Header Node to locate the inorder successor, and mark it as currentNode. 3. If the right child of currentNode is a thread: a. Mark the right child of currentNode as successor. . 65 . b. Exit. 4. Make currentNode point to its right child. . 40 . . 72 . 6. Repeat step 5 until left child of currentNode becomes a thread. 8. Make currentNode point to its left child. 30 . 50 . 69 80 10. Mark currentNode as successor. 60 Let us find the inorder successor of node 65 Ver. 1.0 Session 14
    20. 20. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) • Identify the node for which you want Header Node to locate the inorder successor, and mark it as currentNode. • If the right child of currentNode is a thread: a. Mark the right child of currentNode as successor. currentNode . 65 . b. Exit. 4. Make currentNode point to its right child. . 40 . . 72 . 6. Repeat step 5 until left child of currentNode becomes a thread. 8. Make currentNode point to its left child. 30 . 50 . 69 80 10. Mark currentNode as successor. 60 Let us find the inorder successor of node 65. Ver. 1.0 Session 14
    21. 21. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) • Identify the node for which you want Header Node to locate the inorder successor, and mark it as currentNode. • If the right child of currentNode is a thread: a. Mark the right child of currentNode as successor. currentNode . 65 . b. Exit. 4. Make currentNode point to its right child. . 40 . . 72 . 6. Repeat step 5 until left child of currentNode becomes a thread. 8. Make currentNode point to its left child. 30 . 50 . 69 80 10. Mark currentNode as successor. 60 Let us find the inorder successor of node 65. Ver. 1.0 Session 14
    22. 22. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. Identify the node for which you want Header Node to locate the inorder successor, and mark it as currentNode. 3. If the right child of currentNode is a thread: a. Mark the right child of currentNode as successor. currentNode . 65 . b. Exit. currentNode • Make currentNode point to its right child. . 40 . . 72 . • Repeat step 5 until left child of currentNode becomes a thread. • Make currentNode point to its left child. 30 . 50 . 69 80 • Mark currentNode as successor. 60 Let us find the inorder successor of node 65. Ver. 1.0 Session 14
    23. 23. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. Identify the node for which you want Header Node to locate the inorder successor, and mark it as currentNode. 3. If the right child of currentNode is a thread: a. Mark the right child of currentNode as successor. . 65 . b. Exit. currentNode • Make currentNode point to its right child. . 40 . . 72 . • Repeat step 5 until left child of currentNode becomes a thread. • Make currentNode point to its left child. 30 . 50 . 69 80 • Mark currentNode as successor. 60 Let us find the inorder successor of node 65. Ver. 1.0 Session 14
    24. 24. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. Identify the node for which you want Header Node to locate the inorder successor, and mark it as currentNode. 3. If the right child of currentNode is a thread: a. Mark the right child of currentNode as successor. . 65 . b. Exit. currentNode • Make currentNode point to its right child. . 40 . . 72 . • Repeat step 5 until left child of currentNode becomes a thread. • Make currentNode point to its left child. 30 . 50 . 69 80 • Mark currentNode as successor. currentNode 60 Let us find the inorder successor of node 65. Ver. 1.0 Session 14
    25. 25. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. Identify the node for which you want Header Node to locate the inorder successor, and mark it as currentNode. 3. If the right child of currentNode is a thread: a. Mark the right child of currentNode as successor. . 65 . b. Exit. • Make currentNode point to its right child. . 40 . . 72 . • Repeat step 5 until left child of currentNode becomes a thread. • Make currentNode point to its left child. 30 . 50 . 69 80 • Mark currentNode as successor. currentNode 60 Let us find the inorder successor of node 65. Ver. 1.0 Session 14
    26. 26. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) Inorder successor 1. Identify the node for which you want Header Node to locate the inorder successor, and located mark it as currentNode. 3. If the right child of currentNode is a thread: a. Mark the right child of currentNode as successor. . 65 . b. Exit. • Make currentNode point to its right child. . 40 . . 72 . • Repeat step 5 until left child of successor currentNode becomes a thread. • Make currentNode point to its left child. 30 . 50 . 69 80 • Mark currentNode as successor. currentNode 60 Let us find the inorder successor of node 65. Ver. 1.0 Session 14
    27. 27. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) Write an algorithm to traverse a threaded binary tree in inorder sequence. Ver. 1.0 Session 14
    28. 28. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread pointing to itself: Header Node a. Display “Tree is empty”. Algorithm to traverse a threaded b. Exit. binary tree in inorder sequence. 2. Mark the left child of the header node as currentNode. 4. Repeat step 4 until the left child of . 65 . currentNode becomes a thread. 6. Make currentNode point to its left child. . 40 . . 72 . 8. Display the information held by currentNode. 10. Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. 12. Find the inorder successor of currentNode, and mark the inorder successor as currentNode. 14. Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    29. 29. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. 2. Mark the left child of the header node as currentNode. 4. Repeat step 4 until the left child of . 65 . currentNode becomes a thread. 6. Make currentNode point to its left child. . 40 . . 72 . 8. Display the information held by currentNode. 10. Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. 12. Find the inorder successor of currentNode, and mark the inorder successor as currentNode. 14. Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    30. 30. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of currentNode . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    31. 31. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of currentNode . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    32. 32. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) • If the left child of the header node is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of currentNode . 65 . currentNode becomes a thread. currentNode • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    33. 33. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. currentNode • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    34. 34. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. currentNode • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder currentNode successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    35. 35. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder currentNode successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    36. 36. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder currentNode successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    37. 37. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder currentNode successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    38. 38. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. currentNode • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder currentNode successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    39. 39. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. currentNode • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    40. 40. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. currentNode • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. currentNode • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    41. 41. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. currentNode • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    42. 42. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. currentNode • Display the information held by the currentNode. 60 currentNode Ver. 1.0 Session 14
    43. 43. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 60 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. • Display the information held by the currentNode. 60 currentNode Ver. 1.0 Session 14
    44. 44. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 60 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of currentNode . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. • Display the information held by the currentNode. 60 currentNode Ver. 1.0 Session 14
    45. 45. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 60 65 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of currentNode . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    46. 46. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 60 65 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of currentNode . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. currentNode • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    47. 47. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 60 65 69 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. currentNode • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    48. 48. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 60 65 69 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. currentNode • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. currentNode • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    49. 49. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 60 65 69 72 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. currentNode • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    50. 50. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 60 65 69 72 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of . 65 . currentNode becomes a thread. currentNode • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder currentNode successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    51. 51. Data Structures and AlgorithmsTraversing a Threaded Binary Tree (Contd.) 1. If the left child of the header node 30 40 50 60 65 69 72 80 is a thread pointing to itself: Header Node a. Display “Tree is empty”. b. Exit. • Mark the left child of the header node as currentNode. • Repeat step 4 until the left child of Traversal complete . 65 . currentNode becomes a thread. • Make currentNode point to its left child. . 40 . . 72 . • Display the information held by currentNode. • Repeat steps 7 and 8 until right child of currentNode points to the 30 . 50 . 69 80 header node. • Find the inorder successor of currentNode, and mark the inorder currentNode successor as currentNode. • Display the information held by the currentNode. 60 Ver. 1.0 Session 14
    52. 52. Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree Insert an algorithm to locate the position inserting a newto be Write operation refers to the process of of a new node node at its appropriatebinary tree. inserted in a threaded position. To implement an insert operation in a threaded binary tree, you first need to locate the position for the new node to be inserted. For this, you first need to implement a search operation. Ver. 1.0 Session 14
    53. 53. Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread Insert node 35 pointing to itself: a. Mark head as parent. AlgorithmHeader Node the to locate b. Exit. position of a new node in 2. Mark the left child of head as currentNode. . a threaded binary tree. 3. 4. Mark head as parent. Repeat steps a, b, c, d, and e until currentNode becomes NULL: a. Mark currentNode as parent. . 65 . b. If the value of the new node is less than that of currentNode and the left child of currentNode is a normal link: i. Make currentNode point to its left child and go to step 4. . 40 . . 72 . c. If the value of the new node is less than that of currentNode and the left child of currentNode is a thread: i. Mark currentNode as NULL and go to step 4. d. If the value of the new node is greater than 30 . 50 . 69 80 that of currentNode and the right child of currentNode is a normal link: i. Make currentNode point to its right child and go to step 4. e. If the value of the new node is greater than that of currentNode and the right child of currentNode is a thread: 60 i. Mark currentNode as NULL and go to step 4. Ver. 1.0 Session 14
    54. 54. Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread Insert node 35 pointing to itself: a. Mark head as parent. Header Node b. Exit. 2. Mark the left child of head as currentNode. . 3. 4. Mark head as parent. Repeat steps a, b, c, d, and e until currentNode becomes NULL: a. Mark currentNode as parent. . 65 . b. If the value of the new node is less than that of currentNode and the left child of currentNode is a normal link: i. Make currentNode point to its left child and go to step 4. . 40 . . 72 . c. If the value of the new node is less than that of currentNode and the left child of currentNode is a thread: i. Mark currentNode as NULL and go to step 4. d. If the value of the new node is greater than 30 . 50 . 69 80 that of currentNode and the right child of currentNode is a normal link: i. Make currentNode point to its right child and go to step 4. e. If the value of the new node is greater than that of currentNode and the right child of currentNode is a thread: 60 i. Mark currentNode as NULL and go to step 4. Ver. 1.0 Session 14
    55. 55. Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread Insert node 35 pointing to itself: a. Mark head as parent. Header Node b. Exit. • Mark the left child of head as currentNode. . • • Mark head as parent. Repeat steps a, b, c, d, and e until currentNode becomes NULL: a. Mark currentNode as parent. currentNode . 65 . b. If the value of the new node is less than that of currentNode and the left child of currentNode is a normal link: i. Make currentNode point to its left child and go to step 4. . 40 . . 72 . c. If the value of the new node is less than that of currentNode and the left child of currentNode is a thread: i. Mark currentNode as NULL and go to step 4. d. If the value of the new node is greater than 30 . 50 . 69 80 that of currentNode and the right child of currentNode is a normal link: i. Make currentNode point to its right child and go to step 4. e. If the value of the new node is greater than that of currentNode and the right child of currentNode is a thread: 60 i. Mark currentNode as NULL and go to step 4. Ver. 1.0 Session 14
    56. 56. Data Structures and AlgorithmsInserting Nodes in a Threaded Binary Tree (Contd.) 1. If the left child of the header node is a thread Insert node 35 pointing to itself: a. Mark head as parent. Header Node b. Exit. • Mark the left child of head as currentNode. parent . • • Mark head as parent. Repeat steps a, b, c, d, and e until currentNode becomes NULL: a. Mark currentNode as parent. currentNode . 65 . b. If the value of the new node is less than that of currentNode and the left child of currentNode is a normal link: i. Make currentNode point to its left child and go to step 4. . 40 . . 72 . c. If the value of the new node is less than that of currentNode and the left child of currentNode is a thread: i. Mark currentNode as NULL and go to step 4. d. If the value of the new node is greater than 30 . 50 . 69 80 that of currentNode and the right child of currentNode is a normal link: i. Make currentNode point to its right child and go to step 4. e. If the value of the new node is greater than that of currentNode and the right child of currentNode is a thread: 60 i. Mark currentNode as NULL and go to step 4. Ver. 1.0 Session 14

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