Youwrite an optimal huffman code for a:1 b:1 c:2 d:3 e:5 f:8 g:13 h:21

To create an optimal Huffman code, we need to follow these steps:

1. Create a frequency table:

   • Count the frequency of each symbol in the given data.
   • In this case, the frequency table would be:
     • a: 1
     • b: 1
     • c: 2
     • d: 3
     • e: 5
     • f: 8
     • g: 13
     • h: 21

2. Create a priority queue:

   • Initialize a priority queue with the symbols and their frequencies.
   • The priority queue will be sorted based on the frequencies.
   • In this case, the priority queue would be:
     • a: 1
     • b: 1
     • c: 2
     • d: 3
     • e: 5
     • f: 8
     • g: 13
     • h: 21

3. Build the Huffman tree:

   • Take the two symbols with the lowest frequencies from the priority queue.
   • Create a new node with a combined frequency equal to the sum of the two symbols' frequencies.
   • Make the two symbols as the left and right children of the new node.
   • Insert the new node back into the priority queue.
   • Repeat these steps until there is only one node left in the priority queue, which will be the root of the Huffman tree.
   • In this case, the Huffman tree would be: _________ /
     h: 21 _________ /
     g: 13 _________ /
     f: 8 _________ /
     e: 5 _________ /
     d: 3 _________ /
     c: 2 _________ /
     a: 1 b: 1

4. Assign binary codes:

   • Traverse the Huffman tree from the root to each leaf node.
   • Assign a '0' for each left branch and a '1' for each right branch.
   • The binary codes for each symbol would be:
     • a: 1111111
     • b: 1111110
     • c: 111110
     • d: 11110
     • e: 1110
     • f: 110
     • g: 10
     • h: 0

Therefore, the optimal Huffman code for the given symbols and frequencies would be:

• a: 1111111
• b: 1111110
• c: 111110
• d: 11110
• e: 1110
• f: 110
• g: 10
• h: 0