Mway Huffman tree

1
M-way Huffman tree

• Why do we need to add zeroes to our list?
• Given a list of numbers 4, 2, 6, 8, construct a
  3-way huffman tree

2
M-way Huffman tree

• Why do we need to add zeroes to our list?
• 4 2 6 8
• Step 1 find the 3 min members of the list

2
4
6
3
M-way Huffman tree

• Why do we need to add zeroes to our list?
• 8
• Step 2 construct tree and return to list

12
2
4
6
4
M-way Huffman tree

• Why do we need to add zeroes to our list?
• 8
• Step 3 construct next tree with the next 3 min
  members

12
20
12
8
2
4
6
5
M-way Huffman tree

• Why do we need to add zeroes to our list?
• Final tree cost 32

20
12
8
2
4
6
6
M-way Huffman tree

• Now, construct a new 3-way huffman tree, but
  first add (1-n)mod(m-1) zeroes to the list
• List 4 2 6 8, so n 4, m 3
• zeroes to add (1-4)mod(3-1) -3mod2 1

7
M-way Huffman tree

• Why do we need to add zeroes to our list?
• New list 4 2 6 8 0
• Step 1 find the 3 min members of the list

0
2
4
8
M-way Huffman tree

• Why do we need to add zeroes to our list?
• 6 8
• Step 2 construct tree and return tree to list

6
0
2
4
9
M-way Huffman tree

• Why do we need to add zeroes to our list?
• 6 8
• Step 3 construct next tree with the next 3 min
  members

6
20
6
8
6
0
2
4
10
M-way Huffman tree

• Why do we need to add zeroes to our list?
• Final tree cost 26

20
6
8
6
0
2
4
11
M-way Huffman tree

• Why do we need to add zeroes to our list?
• Before adding zeroes, tree cost 32
• After adding zeroes, tree cost 26
• By adding zeroes prior to constructing the m-way
  huffman tree we can reduce the overall cost of
  the tree