![Traversal Method:
• The traversal method use to achieve Array representation is
Level Order
Arr[(i-1)/2]
Returns the parent
node
Arr[(2*i)+1]
Returns the left child
node
Arr[(2*i)+2]
Returns the right child
node
Below table shows indexes of other nodes for the ith
node, i.e., Arr[i]:](https://image.slidesharecdn.com/heapminmaxunit7-250112064728-07d21045/85/Max-Heap-Min-Heap-Heapify-Heap-sort-Build-max-Heap-5-320.jpg)
Max Heap, Min Heap, Heapify, Heap sort, Build max Heap
- 1. Heap (Max/ Min /Heapify) Prepared By: Mr. Zeeshan Mubeen (Senior Lecturer, RSCI) Unit No. 10
- 2. What is a Heap? • A Heap is a special Tree-based data structure in which the tree is a complete binary tree. It’s a complete tree (All levels are completely filled except possibly the last level and the last level has all keys as left as possible). • Generally, Heaps can be of two types: • Max Heap • Min Heap
- 3. Max Heap: • In a Max-Heap the key present at the root node must be greatest among the keys present at all of it’s children. The same property must be recursively true for all sub-trees in that Binary Tree.
- 4. Min Heap: • In a Min-Heap the key present at the root node must be minimum among the keys present at all of it’s children. The same property must be recursively true for all sub-trees in that Binary Tree.
- 5. Traversal Method: • The traversal method use to achieve Array representation is Level Order Arr[(i-1)/2] Returns the parent node Arr[(2*i)+1] Returns the left child node Arr[(2*i)+2] Returns the right child node Below table shows indexes of other nodes for the ith node, i.e., Arr[i]:
- 6. Build Max Heap • Build Max-Heap : Using MAX-HEAPIFY() we can construct a max-heap by starting with the last node that has children (which occurs at A.length/2 the elements the array A. BUILD-MAX-HEAP(A) A.heapsize = A.length for i = A.length/2 downto 0 MAX-HEAPIFY(A,i)
- 7. Max-Heapify: • Max-Heapify : Given a tree that is a heap except for node i,Max-Heapify function arranges node i and it’s subtrees to satisfy the heap property.
- 10. Build max Heap….
- 11. Build max Heap….
- 12. Heap Sort:
- 13. Heap Sort….
- 14. Heap Sort….
- 15. Heap Sort….
- 16. Heap Sort….
- 17. Heap Sort….
- 18. Heap Sort….
- 19. Heap Sort….
- 20. How Heap Sort Works? 1. Since the tree satisfies Max-Heap property, then the largest item is stored at the root node. 2. Swap: Remove the root element and put at the end of the array (nth position) Put the last item of the tree (heap) at the vacant place. 3. Remove: Reduce the size of the heap by 1. 4. Heapify: Heapify the root element again so that we have the highest element at root. 5. The process is repeated until all the items of the list are sorted.