Heap Data Structure

Heap Data Structure-its application in
shorting domain
Saumya Som
BWU/BCA/17/207
BCA-D (2nd Semester)
Teacher- SOUMIK GUHA ROY

CONTENTS
1 Binary Tree
Types of Binary Tree
Heap Data Structure
Heapsort
Array Representation of
Heaps
Heap Types
2
3
4
5
6

1
Binary
Tree
In a normal tree, every node can
have any number of children.
Binary tree is a special type of
tree data structure in which
every node can have a maximum
of 2 children. One is known as left
child and the other is known as
right child

2
Types of Binary
Tree• Def: Full binary tree = a binary tree in
which each node is either a leaf or has
degree exactly 2.
• Def: Complete binary tree = a binary
tree in which all leaves are on the same
level and all internal nodes have degree
2.
Fig 1:Full binary tree
2
14 8
1
16
7
4
3
9 10
12
Fig 2:Complete binary tree
2
1
16
4
3
9 10

3
Heap Data
Structure
A heap is a nearly complete binary tree with the
following two properties:
• Structural property: all levels are full, except possibly
the last one, which is filled from left to right
• Order (heap) property: for any node x
Parent(x) ≥ x
5
7
8
4
2
Fig 3:Heap

4
Array Representation of Heaps
• A heap can be stored as an
array A.
• Root of tree is A[1]
• Left child of A[i] = A[2i]
• Right child of A[i] = A[2i + 1]
• Parent of A[i] = A[ i/2 ]
Fig 4 :Array Representation of Heaps

5
Heap Types
• Max-heaps (largest element at root), have the max-heap property:
• for all nodes i, excluding the root:
A[PARENT(i)] ≥ A[i]
• Min-heaps (smallest element at root), have the min-heap property:
• for all nodes i, excluding the root:
A[PARENT(i)] ≤ A[i]
MAX Heap
MIN Heap

6
Heapsort
• Goal:
• Sort an array using heap representations
• Idea:
• Build a max-heap from the array
• Swap the root (the maximum element) with the last element in the
array
• Repeat this process until only one node remains

7
Example: 4 1 3 2 16 9 10 14 8 7
2
14 8
1
16
7
4
3
9 10
1
2 3
4 5 6 7
8 9 10
2
14 8
1
16
7
4
3
9 10
1
2 3
4 5 6 7
8 9 10 14
2 8
1
16
7
4
3
9 10
1
2 3
4 5 6 7
8 9 10
14
2 8
1
16
7
4
10
9 3
1
2 3
4 5 6 7
8 9 10
14
2 8
16
7
1
4
10
9 3
1
2 3
4 5 6 7
8 9 10 8
2 4
14
7
1
16
10
9 3
1
2 3
4 5 6 7
8 9 10

Heap Data Structure

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