Binary search tree

Binary search tree

• 1.
  BINARY SEARCH TREE -RACKSAVI.R, I M.ScInformation Technology, V.V.Vanniaperumal college for women, Virudhunagar.
• 2.
  OBJECTIVES  Definition ofbinary search tree.  Binary search tree operations.  Searching data.  Inserting data.  Deleting data.
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  OBJECTIVES Contd… Algorithm forsuccessor.  Traversing the tree. Advantages of binary search tree. Disadvantages of binary search tree.
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  What is Binarysearch tree? Binary Search Tree is a binary tree in which every node contains only smaller values in its left subtree and only larger values in its right subtree. left_subtree(Keys) <= node(Keys) <= right_subtree(Keys)
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  Operations on binary searchtree  Searching data.  Inserting data.  Deleting data.  Traversing the tree.
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  Searching in Binarysearch tree Searching operation on a binary search tree, searches for a node in the tree Algorithm Search_BST: Input : ITEM is the data that has to be searched. Output : If found then pointer to the node containing data ITEM else a message. Data Structure : Linked Structure of the binary tree.
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  STEPS: 1. Ptr =ROOT,flag = FALSE 2. While (ptr =! NULL) and (flag = FALSE) do 3. Case: ITEM < ptr->DATA 4. ptr = ptr->LCHILD 5. Case: ptr->DATA = ITEM 6. flag = TRUE
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  7. Case: ITEM> ptr->DATA 8. ptr = ptr->RCHILD 9. EndCase 10. EndWhile 11. If (flag = TRUE) then 12. Print “ITEM has found at the node”, ptr 13. Else 14. Print “Search is unsuccessful” 15. EndIf 16. Stop
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  Inserting in Binarysearch tree Inserting operation on a binary search tree, insert a node in the tree. Algorithm Insert_BST: Input : ITEM is the data component of a node that has to be inserted. Output : If there is no node having data ITEM, it is inserted into the tree else a message.
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  Data Structure :Linked Structure of the binary tree. STEPS: 1. Ptr = ROOT,flag = FALSE 2. While (ptr =! NULL) and (flag = FALSE) do 3. Case: ITEM < ptr->DATA 4. ptr1 = ptr 5. ptr = ptr->LCHILD 6. Case: ITEM > ptr->DATA 7. ptr1 = ptr 8. ptr = ptr->RCHILD 9. Case: ptr->DATA = ITEM 10. flag = TRUE
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  11. Print “ITEMalready exists” 12. Exit 13. EndCase 14. EndWhile 15. If (ptr = NULL) then 16. new = GetNode(NODE) 17. new->DATA = ITEM 18. new->LCHILD = NULL
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  19. new->RCHILD =NULL 20. If(ptr1->DATA < ITEM) then 21. ptr1->RCHILD = new 22. Else 23. ptr->RCHILD = new 24. EndIf 25. EndIf 26. Stop
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  Deletion in Binarysearch tree Deletion operation on a binary search tree, deletes a node from the tree. Deletion of the node depends on the number of its children. Hence, 3 cases may arise : Case 1 : N is the leaf node. Case 2 : N has exactly one child. Case 3 : N has two childs.
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  Algorithm Delete_BST: Input :ITEM is the data of the nodes to be deleted. Output : If the node with data ITEM exists it is deleted else a message. Data Structure : Linked Structure of the binary tree. STEPS: 1. Ptr = ROOT,flag = FALSE 2. While (ptr =! NULL) and (flag = FLASE) do 3. Case: ITEM < ptr->DATA 4. parent = ptr
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  5. Ptr =ptr->LCHILD 6. Case: ITEM > ptr->DATA 7. parent = ptr 8. ptr = ptr->RCHILD 9. Case: ptr->DATA = ITEM 10. flag = TRUE 11. EndCase 12. EndWhile 13. If (flag = FALSE) then 14. Print “ No deletion” 15. Exit
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  16. EndIf *// DECIDETHE CASE OF DELETION //* 17. If(ptr->LCHILD = NULL) and (ptr->RCHILD = NULL) then 18. Case = 1 19. Else 20. If(ptr->LCHILD =! NULL) and (ptr->RCHILD =! NULL) then 21. Case = 3 22. Else 23. Case = 2 24. EndIf
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  25. EndIf *// DELETION: CASE 1 //* 26.If ( Case = 1) then 27. If (parent->LCHILD = ptr)then 28. parent->LCHILD = NULL 29. Else 30. parent->RCHILD = NULL 31. EndIf 32. ReturnNode(ptr) 33. EndIf
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  *// DELETION :CASE 2 //* 34.If (Case = 2) then 35. If (parent->LCHILD = ptr) then 36. If (ptr->LCHILD = NULL) then 37. parent->LCHILD = ptr->RCHILD 38. Else 39. parent->LCHILD = ptr->LCHILD 40. EndIf 41. Else 42. If (parent->RCHILD = ptr) then 43. If (ptr->LCHILD = NULL) then 44. parent->RCHILD = ptr->RCHILD
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  45. Else 46. parent->RCHILD= ptr->LCHILD 47. EndIf 48. EndIf 49. EndIf 50. ReturnNode(ptr) 51. EndIf
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  *// DELETION :CASE 3 //* 52. If (Case = 3 ) 53. ptr1 = SUCC(ptr) 54. item1 = ptr->DATA 55. Delete_BST (item1) 56. ptr->DATA = item1 57. EndIf 58. Stop
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  Algorithm for Succossor Input: Pointer to a node PTR whose inorder successor is to be found. Output : Pointer to the inorder successor of ptr. Data Structure : Linked Structure of the binary tree.
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  1. ptr1 =PTR->RCHILD 2. If ( ptr1 =! NULL) then 3. While(ptr1->LCHILD =! NULL) do 4. ptr1 = ptr1->LCHILD 5. EndWhile 6. EndIf 7. Return( ptr1 ) 8. Stop
• 23.
  Traversal in Binarysearch tree Traversal operation on a binary search tree, visits every node of the tree. There are three types of traversal they are :  In-order traversal.  Pre-order traversal.  Post-order traversal.
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  Advantages of Binarysearch tree The major advantage of binary search trees over other data structures is that the related sorting algorithms and search algorithms such as in – order traversal can be very efficient.
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  Disadvantages of Binarysearch tree The shape of the Binary search tree totally depends on the order of insertions and it can be regenerated  It takes a long time to search an element in a BST because key value of each node has to be compared with the key element to be searched