The document discusses heap data structures, which are complete binary trees that can be classified into max-heaps and min-heaps based on their node value properties. It describes the array representation of heaps, including the construction process and insertion algorithms for nodes. Heaps are also highlighted for their applications in sorting and implementing priority queues.

1. Presented By:
Arun Brijwasi
MCA/25021/18

2. Heap data structure
Array implementation of heap
Constructing heap
Application of heap

3. A Heap is a special Tree-based data
structure in which the tree is a complete
binary tree.
Generally, Heaps can be of two types:
1. 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. 2. 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. A Binary Heap is a Complete Binary Tree.
A binary heap is typically represented as
array.
The representation is done as:
• The root element will be at Arr[0].
• Indexes of other nodes :
 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

6. The traversal method use to achieve Array
representation is Level Order.

7. Construction of heap can be:
• Max heap construction
• Min heap construction
Both trees are constructed using the same
input and order of arrival.

8. The algorithm for inserting one element in
max heap is as follows:
• Step 1 − Create a new node at the end of heap.
• Step 2 − Assign new value to the node.
• Step 3 − Compare the value of this child node with
its parent.
• Step 4 − If value of parent is less than child, then
swap them.
• Step 5 − Repeat step 3 & 4 until Heap property
holds.

9. Suppose we have the following elements
in an array:
To construct a max heap from tree built
from above sequence we need following
steps:

11. After we obtain the max heap the elements
in array will be as follows:

12. The algorithm for inserting one element in
max heap is as follows:
• Step 1 − Create a new node at the end of heap.
• Step 2 − Assign new value to the node.
• Step 3 − Compare the value of this child node
with its parent.
• Step 4 − If value of parent is more than child, then
swap them.
• Step 5 − Repeat step 3 & 4 until Heap property
holds.

13. Consider elements in array:
{10, 8, 9, 7, 6, 5, 4}
To construct a max heap from tree built
from above sequence we need following
steps:

15. Heaps can be used in sorting the elements
in a specific order in efficient time. It is
known as Heap sort.
Priority queues can be efficiently
implemented using Binary Heap.