The document presents a detailed overview of greedy algorithms, specifically focusing on the optimal merge pattern and Huffman coding. It explains how greedy algorithms determine optimal solutions among feasible alternatives and demonstrates the mechanics of Huffman coding, including character frequency and encoding. The presentation illustrates various examples and calculations to highlight the efficiency and application of these concepts in data compression.

1. Presentation
on
Greedy Algorithm (Optimal merge
pattern – Huffman coding)
Md. Monirul Alom - 162422011 (Group Leader)
Md. Moshiur Rahman Khan - 162422507
Md. Jahangir Alam - 162422004
Md. Rokan Uzzaman - 163432024
Md. Sanowar Hossain - 163432021
Md. Raisul Islam Ripon - 163432027
1

2. Greedy Algorithm
Greedy Algorithm finds the optimal solution from
the set of feasible solutions
2

3. X → Y
Possible solutions:
S1: Go by feet (walking)
S2: Go by bus
S3: Go by train
S4: Go by flight
….
….
Sn: There may be n solutions
3

4. X → Y
Possible solutions:
S1: Go by feet (walking)
S2: Go by bus
S3: Go by train
S4: Go by flight
….
….
Sn: There may be n solutions
Feasible solutions:
S3: Go by train
S4: Go by flight
8 hours
4

5. X → Y
Possible solutions:
S1: Go by feet (walking)
S2: Go by bus
S3: Go by train
S4: Go by flight
….
….
Sn: There may be n solutions
Feasible solutions:
S3: Go by train
S4: Go by flight
Optimal Solution:
S3: Go by train (Costs less)
5

6. Optimal merge pattern
A B
3 5
8 9
12 11
20 16
C
3
5
8
9
11
12
16
20
m n
4 4
Complexity: ϴ(m+n) = 8
6

7. List A B C D
Size 6 5 2 3
A
6
B
5
C
2
D
3
11
13
16
Cost = 11+13+16 = 40
7

8. List A B C D
Size 6 5 2 3
A
6
B
5
C
2
D
3
11 5
16
Cost = 11+5+16 = 32
8

9. List A B C D
Size 6 5 2 3
A
6
B
5
C
2
D
3
16
10
5
Cost = 5+10+16 = 31
9

10. List A B C D E
Size 6 5 2 3 7
C
2
D
3
B
5
A
6
E
7
Sorted in ascending order
10

11. List A B C D E
Size 6 5 2 3 7
C
2
D
3
B
5
A
6
E
7
5
10
23
13
11

12. List A B C D E
Size 6 5 2 3 7
C
2
D
3
B
5
A
6
Cost
5+10+13+23 = 51
E
7
5
10
23
13
2*3+3*3+5*2+6*2+7*2 = 51
12

13. Huffman Coding
Message: BCCABBDDAECCBBAEDDCC
Character
A
B
C
D
E
Length: 20
Size: 20*8 = 160 bits
13

14. Huffman Coding
Message: BCCABBDDAECCBBAEDDCC
Character
Code
A 000
B 001
C 010
D 011
E 100
Length: 20
Size: 20*3 = 60 bits
001010010000………
14

15. Huffman Coding
Message: BCCABBDDAECCBBAEDDCC
Character
Code
A 000
B 001
C 010
D 011
E 100
40
bits
15
bits
55 bits
Length: 20
Size: 20*3 = 60 bits
001010010000………
Total size = 60 +55
= 115 bits
15

16. Huffman Coding
Message: BCCABBDDAECCBBAEDDCC
Character
Frequency
A 3
B 5
C 6
D 4
E 2
2 3 4 5 6
E A D B C
Sorted in ascending order according to frequency
16

17. Huffman Coding
Message: BCCABBDDAECCBBAEDDCC
2 3 4 5 6
E A D B C
5
9
11
20
Character
Frequency
A 3
B 5
C 6
D 4
E 2
17

18. Huffman Coding
Message: BCCABBDDAECCBBAEDDCC
Character
Frequency
Code
A 3 001 3*3= 9
B 5 10 5*2=10
C 6 11 6*2=12
D 4 01 4*2=8
E 2 000 2*3=6
40
bits
20 12
bits
45 bits
2 3 4 5 6
E A D B C
5
9
11
200
0
0
0
1
11
1
Total = Message + table
= 45 + 52 = 97 bits
18

19. Decoding
Message: BCCABBDDAECCBBAEDDCC
2 3 4 5 6
E A D B C
5
9
11
200
0
0
0
1
11
1
101111001……..
19

20. Thank you
20