1. 16IT201/Data structure/Unit II/Binary Search Tree
Recap
Binary Search Tree
Node Declaration and Routine Declaration
To make a Empty Tree
Insert a element in a tree
16IT201/Data structure/Unit II/Binary Search Tree

2. Binary Search Tree-Find, FindMin, FindMax and Delete
16IT201/Data structure/Unit II/Binary Search Tree

3. Routine for Find Operation
Int Find(int X, SearchTree T) { If(T==NULL) return NULL; If(X<T->Element) return Find(X,T->left); else If(X>T->Element) return Find(X,T->Right) Return T;//returns the position of the search element
16IT201/Data structure/Unit II/Binary Search Tree

4. 16IT201/Data structure/Unit II/Binary Search Tree
Find Min
Returns the position of the smallest element in the tree
To perform Find Min start the root and go left as long ad there is a left child.
The stopping point is the smallest element
int FindMin (SearchTree T) { If(T==NULL) return NULL; else if(T->left==NULL) return T; else return FindMin (T->left); }
16IT201/Data structure/Unit II/Binary Search Tree

5. 16IT201/Data structure/Unit II/Binary Search Tree
Non Recursive Routine
Int FindMin(SearchTree T) { If(T!=NULL) While(T->left!=NULL) T=T->left Return T }
16IT201/Data structure/Unit II/Binary Search Tree

6. 16IT201/Data structure/Unit II/Binary Search Tree
Find Max
Returns the position of the largest element in the tree
Start at root and go right as long as there is a right child
The stopping point is the largest element
16IT201/Data structure/Unit II/Binary Search Tree

7. 16IT201/Data structure/Unit II/Binary Search Tree
Routine for FindMax
int FindMax(SearchTree T) { If(T==NULL) return NULL; else if(T->Right==NULL) return T; else FindMax(T->Right); }
int Find Max(SearchTree T) { If(T!=NULL) While(T->Right!=NULL) T=T->Right return T; }
16IT201/Data structure/Unit II/Binary Search Tree

8. 16IT201/Data structure/Unit II/Binary Search Tree
Check Point
is the top node in a tree.
is the terminal node in the tree.
traverses the tree in Root,left,right order.
traverses the tree in Left,Right,Root order.
All the child nodes of a parent node are referred as
Neighbors b)Sibilings c)internal nodes d)leaf nodes
6. Which node in a binary tree does not have a parent node?
7. In an Expression tree,the internal odes contain ----
while the leaf nodes contain
8) The Expression (a+b)*(a-b) is stored in an expression tree.What will be preorder sequence.
16IT201/Data structure/Unit II/Binary Search Tree

9. 16IT201/Data structure/Unit II/Binary Search Tree
Deletion Operation
To delete an element consider the following three possibilities CASE 1->Node to be deleted is a leaf node(ie) No children CASE 2 ->Node with one child CASE 3-> Node with two children
16IT201/Data structure/Unit II/Binary Search Tree

10. 16IT201/Data structure/Unit II/Binary Search Tree
Deletion Operation
CASE 1->If the node is a leaf node ,it can be deleted immediately CASE 2:Node with one child If the node has one child, it can be deleted by adjusting in parent pointer that points to its child node CASE 3: To replace the data of the node to be deleted with its smallest data of the right subtree and recursively delete that node
16IT201/Data structure/Unit II/Binary Search Tree

11. 16IT201/Data structure/Unit II/Binary Search Tree
Deletion 12 5 15 3 7 13 15 9 1 8 11
16IT201/Data structure/Unit II/Binary Search Tree

12. 16IT201/Data structure/Unit II/Binary Search Tree
Deletion Operation
SearchTree Delete(int X,SearchTree T) {
Int Tmpcell;
If(T==NULL)
Error(“Element not found”);
else
If(X<T->Element
T->Left=Delete(X,T->Left);
Else
If(X>T->Element)
T->Right=Delete(X,T->Right);
16IT201/Data structure/Unit II/Binary Search Tree

13. 16IT201/Data structure/Unit II/Binary Search Tree
Deletion Operation
If(T->Left&&T->Right)
Tmpcell=FindMin(T->Right);
T->Element=Tmpcell->Element;
T->Right=Delete(T->Element;T->Right); }
Else//one or zero children {
Tmpcell=T;
If(T->Left==NULL)
T=T->Right;
Else if(T->Right==NULL)
T=T->Left;
Free(Tmpcell); }
Return T;
16IT201/Data structure/Unit II/Binary Search Tree

14. 16IT201/Data structure/Unit II/Binary Search Tree
Summarization
16IT201/Data structure/Unit II/Binary Search Tree