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Type:
**Note**Institute:
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ANNA UNIVERSITY
**Course:
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B.Tech
**Specialization:
**Computer Science Engineering**Views:
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**7 months ago**Add to Favourite

1. BINARY SERACH TREE
Binary Search Tree, is a node-based binary tree data structure which has the following
properties:
▪ The left subtree of a node contains only nodes with keys less than the node’s key.
▪ The right subtree of a node contains only nodes with keys greater than the node’s key.
▪ The left and right subtree each must also be a binary search tree.
There must be no duplicate nodes.
Example:
BINARY SERACH TREE
1.Basics
INORDER-TREE-WALK(x)
PREORDER-TREE-WALK(x )
POSTORDER-TREE-WALK(x)
2.Querying a Binary search tree
Search
Minimum
Maximum
Successor
Predecessor
3.Insertion and Deletion
i)
Basics
The binary-search-tree property allows us to print out in 3 ways. Such as

PREORDER-TREE-WALK(x)
if x ≠NIL
print x.key
PREORDER-TREE-WALK(x.left)
PREORDER-TREE-WALK(x,right)
POSTORDER-TREE-WALK(x)
if x ≠NIL
POSTORDER-TREE-WALK(x.left)
POSTORDER-TREE-WALK(x.right)
print x.key
Eg:
(BST)
(a) Inorder (Left, Root, Right) : 4 2 5 1 3
(b) Preorder (Root, Left, Right) : 1 2 4 5 3
(c) Postorder (Left, Right, Root) : 4 5 2 3 1
ii)
Querying a Binary search tree
We often need to search for a key stored in a binary search tree.
It supports,

➢
➢
➢
➢
➢
SEARCH
MINIMUM
MAXIMUM
SUCCESSOR
PREDECESSOR
Searching
We use the following procedure to search for a node with a given key in a binary search
tree.
Explanation
1.The procedure begins its search at the root and compare the key need to be searched with the
root node.
2.If the key is a root node return x
3. If k is smaller than x.key, the search continues in the left subtree of x and the nodes
encountered during the recursion form a simple path downward from the root of the tree until
key is found.
4. If k is larger than x.key, the search continues in the right subtree of x and the nodes
encountered during the recursion form a simple path downward from the root of the tree until
key is found.
Minimum and maximum

Successor
Eg:
Search for the key 13 in the tree, we follow the path 15->6-> 7-> 13 from the root.
The minimum key in the tree is 2, which is found by following left pointers from the root.
The maximum key 20 is found by following right pointers from the root.

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