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Advanced Data Structures - Binary Heap

This presentation is brought to you by Prof. Ajitkumar Shitole, Department of Computer Engineering of International Institute of Information Technology, I²IT, Pune. The presentation explains the advanced data structure of Binary heap, a special kind of binary tree.

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Advanced Data Structures - Binary Heap

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  1. BINARY HEAP

  2. HOPE FOUNDATION’S INTERNATIONAL INSTITUTE OF INFORMATION TECHNOLOGY, (I²IT) www.isquareit.edu.in +91 20 22933441 / 2

  3. Binary Heap A special kind of binary tree. It has two properties that are not generally true for other trees: Completeness / Heap Structure: The tree is complete, which means that nodes are added from top to bottom, left to right, without leaving any spaces. A binary tree is completely full if it is of height, h, and has 2h+1-1 nodes. Heapness / Heap Order: The item in the tree with the highest priority is at the top of the tree, and the same is true for every sub tree.

  4. Binary Heap • Max Heap: A heap is a binary tree in which every parent is greater than its child(ren). 2. Min Heap: A Reverse Heap is one in which the rule is “every parent is less than the child(ren)”.

  5. Binary Heap To build a heap, data is placed in the tree as it arrives. Algorithm: • add a new node at the next leaf position • use this new node as the current position • While new data is greater than that in the parent of the current node: ● move the parent down to the current node ● make the parent (now vacant) the current node ● Place data in current node

  6. Binary Heap New nodes are always added on the deepest level in an orderly way. The tree never becomes unbalanced. A heap is not a sorted structure. Can be regarded as partially ordered. A given set of data can be formed into many different heaps (depends on the order in which the data arrives.)

  7. Binary Heap Example: Data arrives to be heaped in the order: 54, 87, 27, 67, 19, 31, 29, 18, 32

  8. 54 87 87 87 87 87 27 27 27 27 67 87 54 54 67 54 67 54 54 19 Binary Heap 54, 87, 27, 67, 19, 31, 29, 18, 32 54 Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  9. 87 87 67 67 27 27 19 19 54 54 Binary Heap 54, 87, 27, 67, 19, 31, 29, 18, 32 31 Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  10. 87 87 67 67 31 31 27 27 29 29 19 19 54 54 Binary Heap 54, 87, 27, 67, 19, 31, 29, 18, 32 18 32 Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  11. THANK YOU For further information please contact Prof. AjitkumarShitole Department of Computer Engineering Hope Foundation’s International Institute of Information Technology, I²IT Hinjawadi, Pune – 411 057 Phone - +91 20 22933441 www.isquareit.edu.in | ajitkumars@isquareit.edu.in

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