Binary search tree
- 1. BINARY SEARCH TREE -RACKSAVI.R, I M.Sc Information Technology, V.V.Vanniaperumal college for women, Virudhunagar.
- 2. OBJECTIVES Definition of binary search tree. Binary search tree operations. Searching data. Inserting data. Deleting data.
- 3. OBJECTIVES Contd… Algorithm for successor. Traversing the tree. Advantages of binary search tree. Disadvantages of binary search tree.
- 4. What is Binary search 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)
- 5. Operations on binary search tree Searching data. Inserting data. Deleting data. Traversing the tree.
- 6. Searching in Binary search 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.
- 7. 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
- 8. 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
- 9. Inserting in Binary search 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.
- 10. 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
- 11. 11. Print “ITEM already exists” 12. Exit 13. EndCase 14. EndWhile 15. If (ptr = NULL) then 16. new = GetNode(NODE) 17. new->DATA = ITEM 18. new->LCHILD = NULL
- 12. 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
- 13. Deletion in Binary search 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.
- 14. 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
- 15. 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
- 16. 16. EndIf *// DECIDE THE 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
- 17. 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
- 18. *// 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
- 19. 45. Else 46. parent->RCHILD = ptr->LCHILD 47. EndIf 48. EndIf 49. EndIf 50. ReturnNode(ptr) 51. EndIf
- 20. *// 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
- 21. 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.
- 22. 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 Binary search 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.
- 24. Advantages of Binary search 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.
- 25. Disadvantages of Binary search 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