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BINARY TREE data structure and algorithm-1.pptx
- 1. Atal Bihari VajpayeeVishwavidyalaya Bilaspur Chhattisgarh Session 2025- 26 Guidance By:- Mr.Jitendra Kumar Sir Assistant Professor Presented By:- Ravindra Singh Rathore Binary Tree And Its Operation Subject:- Data StructureAndArchitecture
- 2. Outline • Tree • Binarytree Implementation • Binary Search Tree • BST Operations • Traversal • Insertion • Deletion • Types of BST • Complexity in BST • Applications of BST
- 3. Trees Tree • Each nodecan have 0 or more children • A node can have at most one parent Binary tree • Tree with 0–2 children per node • Also known as Decision Making Tree
- 4. Trees Terminology • Root no parent • Leaf no child • Interior non-leaf • Height distance from root to leaf (H)
- 5. Why is himportant? The Tree operations like insert, delete, retrieve etc. are typically expressed in terms of the height of the tree h. So, it can be stated that the tree height h determines running time!
- 6. Binary Search Tree Keyproperty is value at node • Smaller values in left subtree • Larger values in right subtree Example X > Y X < Z Y X Z
- 7. Binary Search Tree Examples Binarysearch trees Not a binary search tree 5 10 30 2 25 45 5 10 45 2 25 30 5 10 30 2 25 45
- 8. Difference between BTand BST • A binary tree is simply a tree in which each node can have at most two children. • A binary search tree is a binary tree in which the nodes are assigned values, with the following restrictions : 1. No duplicate values. 2. The left subtree of a node can only have values less than the node 3. The right subtree of a node can only have values greater than the node and recursively defined 4. The left subtree of a node is a binary search tree. 5. The right subtree of a node is a binary search tree.
- 9. Binary Tree SearchAlgorithm TREE-SEARCH(x,k) • If x==NIL or k==x.key • return x • If k < x.key • return TREE-SEARCH(x.left,k) • else • return TREE-SEARCH(x.right,k)
- 10. BST Operations Four basicBST operations 1 2 3 4 Traversal Search Insertion Deletion
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- 13. Preorder Traversal 23 1812 20 44 35 52 Root Left Right
- 14. Postorder Traversal 12 2018 35 52 44 23 Left Right Root
- 15. Inorder Traversal 12 1820 23 35 44 52 Produces a sequenced list Left Root Right
- 17. Complexity in BST OperationAverage Worst Case Best Case Search O(log n) O(n) O(1) Insertion O(log n) O(n) O(1) Deletion O(log n) O(n) O(1)
- 18. Applications of BST •Used in many search applications where data is constantly entering/leaving, such as the map and set objects in many languages' libraries. • Storing a set of names, and being able to lookup based on a prefix of the name. (Used in internet routers.) • Storing a path in a graph, and being able to reverse any subsection of the path in O(log n) time. (Useful in travelling salesman problems). • Finding square root of given number • allows you to do range searches efficiently.
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