SNS COLLEGE OF TECHNOLOGY (Autonomous ) COIMBATORE-35

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Presentation transcript:

SNS COLLEGE OF TECHNOLOGY (Autonomous ) COIMBATORE-35 Recap AVL Tree (Double Rotation) Double Rotation(Left Right Rotation) Double Rotation(Right Left Rotation) 16IT201/Data Structuress- Unit - II/Binary Heaps

SNS COLLEGE OF TECHNOLOGY (Autonomous ) COIMBATORE-35

16IT201/Data Structuress- Unit - II/Binary Heaps Binary Heap Refereed to as Heaps. Heap have two property -Structure Property & Heap Order Property 16IT201/Data Structuress- Unit - II/Binary Heaps

16IT201/Data Structuress- Unit - II/Binary Heaps Types of Heap 16IT201/Data Structuress- Unit - II/Binary Heaps

16IT201/Data Structuress- Unit - II/Binary Heaps Heap Strucutre Binary Tree with Structure and Heap Order property Binary Tree with Structure but violating Heap Order property 16IT201/Data Structuress- Unit - II/Binary Heaps

Binary Heap Operations Insert Operations & DeleteMin Operations To Perform Insert and DeleteMin operations ensure that heap order property is maintained 16IT201/Data Structuress- Unit - II/Binary Heaps

Insert a node - percolate up If the new node has a greater value than the parent of the hole - we insert the node in the hole. Thus, if the new value to be inserted is 18, our new binary heap would be: A hole is created at the bottom of the tree, in the next available position. 16IT201/Data Structuress- Unit - II/Binary Heaps

Insert a node - percolate up we want to insert 16. 16 is less than 17, so we slide down 17, and the hole appears at the node where 17 used to be Since 16 is less than 10, we can insert it in the hole: Complexity of insertion: O(logN) in the worst case. 16IT201/Data Structuress- Unit - II/Binary Heaps

Can u find the error in this pic 16IT201/Data Structuress- Unit - II/Binary Heaps

16IT201/Data Structuress- Unit - II/Binary Heaps

16IT201/Data Structuress- Unit - II/Binary Heaps

16IT201/Data Structuress- Unit - II/Binary Heaps

16IT201/Data Structuress- Unit - II/Binary Heaps Explanation: From Equation 1: 1 Shape = 45/3 = 15 Now if you notice there are 15 sides in 1 shape, thus each side contributes to value of 1. From 2nd Equation: 4 Bananas + 4 Bananas + 15 sides shape = 23 8 bananas = 23 – 15 = 8 => 1 Banana = 1 From 3rd equation => 2 clocks = 10 – 4 = 6 => 1 clock = 3 now here also if you notice, clock time in hour represents its value in the equation thus Clock with 2 o clock + 3 Bananas + 3 Bananas * Shape with 11 sides = 2 + 3 + 3 *11 = 5 + 33 = 38 16IT201/Data Structuress- Unit - II/Binary Heaps

16IT201/Data Structuress- Unit - II/Binary Heaps DeleteMin 16IT201/Data Structuress- Unit - II/Binary Heaps

16IT201/Data Structuress- Unit - II/Binary Heaps For Each of the following list construct an AVL tree by inserting their element successfully starting with the empty tree A) 1,2,3,4,5,6 B)6,5,4,3,2,1 C)2,1,4,5,9,3,6,7 D) 15, 20, 24, 10, 13, 7, 30, 36, 25 16IT201/Data Structuress- Unit - II/Binary Heaps

Binary Heap Properties Summarization Binary Heap Properties Min Heap & Max Heap Heap Opeartions 16IT201/Data Structuress- Unit - II/Binary Heaps

A wonderful moving bicycle illusion 16IT201/Data Structuress- Unit - II/Binary Heaps