Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy. See our Privacy Policy and User Agreement for details.

Published on Sep 28, Definition of Binary Tree, Introduction to Binary Search Tree, Binary Tree Search Algorithm, Insert a value in BST, Delete a value from BST.

Clipping is a handy way to collect and organize the most important slides from a presentation.

You can keep your great finds in clipboards organized around topics. SlideShare Explore Search You. Binary search tree bst. Show related SlideShares at end.

Hossain Md Shakhawat , Ph. D Student at Tokyo Institute of Technology Follow. Full Name Comment goes here. Are you sure you want to Yes No. This is superbly well explained. Oluwaponmile Adefuwa , Student at Adekunle Ajasin University.

Enmao Liu , ICT engineer at Ericsson at Ericsson. Srinu Vas , Operated at PPL Shipyard Pte Ltd at PPL Shipyard Pte Ltd. Embeds 0 No embeds. No notes for slide. Binary search tree bst 1. Binary Search Tree 2. What is a Binary Tree? Each node can have up to two successor nodes.

A Binary Tree 5. What is the max number of nodes at any level l? What is the total number of nodes N of a full tree with height h? What is the height h of a full tree with N nodes? Why is h important?

Then there is an extremely efficient searching algorithm called Binary Search. That is no one search page by page from the start to end of the book.

This process goes on. How to search a binary tree? Start at the root 2. Search the tree level by level, until you find the element you are searching for or you reach a leaf.

Is this better than searching a linked list? The value stored at a node is greater than the value stored at its left child and less than the value stored at its right child Binary Search Trees Where is the smallest element?

How to search a binary search tree? Compare the value of the item you are searching for with the value stored at the root 3. If the values are equal, then item found; otherwise, if it is a leaf node, then not found If it is less than the value stored at the root, then search the left subtree 5.

If it is greater than the value stored at the root, then search the right subtree 6. Repeat steps for the root of the subtree chosen in the previous step 4 or 5 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. The right subtree of a node is a binary search tree. If y is a node in the right subtree of x, then y.

If the values are equal then the search terminates and x is the desired node. Binary Tree Search Algorithm TREE-SEARCH x,k 1. Binary Tree Search Algorithm 6 6 Example: Animation of How Works in a Sorted Data Array BST - Pseudo code if the tree is empty return NULL else if the key value in the node root equals the target return the node value else if the key value in the node is greater than the target return the result of searching the left subtree else if the key value in the node is smaller than the target return the result of searching the right subtree Search in a BST: The procedure for finding the minimum key: The procedure for finding the maximum key: This is why at step four we always storing the parent of current node x while moving downward.

At the end of step 7 in step 8 we make this node the parent of z z.

Binary search tree(bst)

BST Insertion Algorithm 6 6 2 2 9 9 1 1 4 4 8 8 We are supposed to insert an item value 5 and find an appropriate node z for it Insertion into a BST: If the node has two children then its successor has no left child; copy the successor into the node and delete the successor instead TREE-DELETE T, z removes the node pointed to by z from the tree T. Delete a value from the BST Experimenting the cases: Now while removing the node four cases may happen Delete a value from the BST Case 1: Delete a value from the BST Case 2: Delete a value from the BST Case 3: Delete a value from the BST Case 4: The updating operations cause the tree to become unbalanced.

Used in almost every 3D video game to determine what objects need to be rendered. Used in almost every high-bandwidth router for storing router-tables.

PPT – Binary Trees, Binary Search Trees PowerPoint presentation | free to download - id: 29c3c-OWZjZ

Used in implementing efficient priority-queues. Also used in heap-sort. Constructed by compilers and implicitly calculators to parse expressions. What is a Degenerate BST? Does the order of inserting elements into a tree matter? Better Search Trees Prevent the degeneration of the BST: Binary Search Tree in Data Structure. Trees, Binary Search Tree, AVL Tree in Data Structures.

Start clipping No thanks. You just clipped your first slide! Clipping is a handy way to collect important slides you want to go back to later. Now customize the name of a clipboard to store your clips. Visibility Others can see my Clipboard.