This document provides information about heaps from Sheetal Waghmare of IIT Kharagpur. It defines a heap as a binary tree that satisfies the structure and heap order properties. A max heap is defined where each parent node has a value greater than its children, and a min heap is defined where each parent node has a value less than its children. Examples of max and min heaps are shown. The processes of reheap up and reheap down for inserting and deleting from a heap using an array representation are also briefly described.

1. HEAPS
SHEETAL WAGHMARE
M.TECH (Computer Science & Data Processing)
IIT KHARAGPUR
EMAIL-ID: shitu2iitkgp@gmail.com
sheetalw3@gmail.com

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SHEETAL WAGHMARE
FROM IIT KHARAGPUR

3. What is Heap?
Heap is a binary tree which satisfies following two properties
Structure Property :
All the level have maximum number of nodes except possibly the last level.
In last level all nodes occur to the left.
Heap Order Property:
The value in any node N is greater then or equal to the values in both its children.
* A Heap is a complete binary tree and so its height is log2 (n+1)
SHEETAL WAGHMARE
FROM IIT KHARAGPUR

4. Examples
Heap Not an Heap
SHEETAL WAGHMARE
FROM IIT KHARAGPUR

5. MAX HEAP
80
30
25
5040
2010
11
8
80>40 80>50
40>25
40>10 50>20
50>30
25>8
25>11
Parent node will always have the data greater than childrens
SHEETAL WAGHMARE
FROM IIT KHARAGPUR

6. 10
65
70
5040
6055
80
75
40>10 50>10
70>40
55>40 60>50
65>50
75>70
80>70
Parent node will always contain the data smaller than childrens
SHEETAL WAGHMARE
FROM IIT KHARAGPUR

7. 13
12
6
11
110 9
13
88
99
81
9591 90
MAX HEAP
MIN HEAP
SHEETAL WAGHMARE
FROM IIT KHARAGPUR

8. REHEAP DOWN
(Deletion from Heap)
REHEAP UP
(Insertion in heap)
SHEETAL WAGHMARE
FROM IIT KHARAGPUR

9. SHEETAL WAGHMARE
FROM IIT KHARAGPUR
Construction of Heap Using Array

10. SHEETAL WAGHMARE FROM IIT KHARAGPUR