The following Message "B C C A B B D D A E C C B B A E D D C C", is given. Use Huffman algorithm to find the total size of the message 1 point43 bits45 bits40 bits41 bits

To solve this problem, we need to follow the steps of Huffman's algorithm:

1. First, we need to calculate the frequency of each character in the message:

   A: 3 B: 5 C: 6 D: 4 E: 2

2. Then, we create a priority queue (or a min-heap) and insert all characters with their frequencies. The character with the lowest frequency has the highest priority:

   E: 2 A: 3 D: 4 B: 5 C: 6

3. We create a new internal node with a frequency equal to the sum of the two nodes with the smallest frequency. This new node becomes the parent of the two nodes. The character with the lowest frequency is assigned a '0' and the character with the next lowest frequency is assigned a '1'. We remove these two nodes from our priority queue:

   AD: 7 (A: '0', D: '1') B: 5 C: 6 E: 2

4. We repeat step 3 until we have only one node left in our priority queue. This node represents the root of our Huffman tree:

   AD: 7 (A: '0', D: '1') B: 5 C: 6 E: 2

   ADB: 12 (AD: '0', B: '1') C: 6 E: 2

   ADBE: 14 (ADB: '0', E: '1') C: 6

   ADBEC: 20 (ADBE: '0', C: '1')

5. Now, we can assign a binary code to each character according to the paths from the root to the leaves:

   A: '000' D: '001' B: '01' E: '10' C: '11'

6. Finally, we replace each character in the original message with its corresponding binary code and calculate the total size of the message:

   B: '01' C: '11' C: '11' A: '000' B: '01' B: '01' D: '001' D: '001' A: '000' E: '10' C: '11' C: '11' B: '01' B: '01' A: '000' E: '10' D: '001' D: '001' C: '11' C: '11'

The total size of the message is 43 bits. So, the answer is 43 bits.

To solve this problem, we need to follow the steps of Huffman's algorithm:

1. First, we need to calculate the frequency of each character in the message:

   A: 3 B: 5 C: 6 D: 4 E: 2

2. Then, we create a priority queue (or a min-heap) and insert all characters along with their frequencies. The character with the lowest frequency has the highest priority:

   E: 2 A: 3 D: 4 B: 5 C: 6

3. We remove two nodes with the highest priority (lowest frequency) from the queue:

   A: 3 D: 4 B: 5 C: 6

   And create a new node with these two nodes as children. The frequency of the new node is the sum of the frequencies of the two nodes. This new node is inserted back into the queue:

   AD: 7 B: 5 C: 6

4. We repeat steps 3 until there is only one node left in the queue. This node represents the root of the Huffman tree.

5. Now, we assign binary codes to each character. If we go left from a node, we add a '0' to the code. If we go right, we add a '1'. The code assigned to each character is the code assigned to the path from the root to the character:

   A: 110 B: 10 C: 0 D: 111 E: 101

6. Finally, we calculate the total size of the message by multiplying the frequency of each character by the length of its code, and summing all these values:

   A: 3 * 3 = 9 B: 5 * 2 = 10 C: 6 * 1 = 6 D: 4 * 3 = 12 E: 2 * 3 = 6

   Total size = 9 + 10 + 6 + 12 + 6 = 43 bits

So, the total size of the message using Huffman's algorithm is 43 bits.

To solve this problem using Huffman's algorithm, we need to follow these steps:

1. First, we need to calculate the frequency of each character in the message:

   A: 4 B: 5 C: 6 D: 4 E: 2

2. Then, we create a priority queue (or a min-heap) and insert all characters along with their frequencies. The character with the lowest frequency has the highest priority:

   E: 2 A: 4 D: 4 B: 5 C: 6

3. We remove two nodes with the highest priority (lowest frequency) from the queue and create a new node. The frequency of the new node is the sum of the two nodes and this node is inserted back into the queue. We repeat this step until there is only one node left in the queue:

   E, A: 6 D, B: 9 C: 6 E, A, D, B: 15 C, E, A, D, B: 21

4. The last node is the root of the Huffman tree. We assign codes to each character by traversing the tree. Characters are the leaves of the tree. We add a '0' when we move left and a '1' when we move right:

   E: 00 A: 01 D: 10 B: 11 C: 1

5. Finally, we calculate the total size of the message. The size of the message is the sum of the frequency of each character times the length of its code:

   A: 4 * 2 = 8 bits B: 5 * 2 = 10 bits C: 6 * 1 = 6 bits D: 4 * 2 = 8 bits E: 2 * 2 = 4 bits

   Total size = 8 + 10 + 6 + 8 + 4 = 36 bits

So, none of the options given in the question are correct. The total size of the message using Huffman's algorithm is 36 bits.

To solve this problem, we need to follow the steps of Huffman's algorithm:

1. First, we need to calculate the frequency of each character in the message:

   A: 3 B: 5 C: 6 D: 4 E: 2

2. Then, we create a priority queue (or a min-heap) where the node with the lowest frequency has the highest priority:

   E: 2 A: 3 D: 4 B: 5 C: 6

3. We remove two nodes with the highest priority (lowest frequency) from the queue and create a new node with these two nodes as children. The new node's frequency is the sum of the two nodes' frequencies. We insert the new node into the queue.

   After the first iteration, the queue looks like this:

   AD: 7 (A: 3, D: 4) B: 5 C: 6 E: 2

   After the second iteration, the queue looks like this:

   AD: 7 BC: 11 (B: 5, C: 6) E: 2

   After the third and final iteration, the queue looks like this:

   ADBCE: 20 (AD: 7, BC: 11, E: 2)

4. Now, we assign codes to each character. The left child gets a '0' and the right child gets a '1'. We start from the root and assign codes to all characters:

   A: 00 D: 01 B: 10 C: 11 E: 100

5. Finally, we calculate the total size of the message. We multiply the frequency of each character by the length of its code and sum up all the results:

   A: 3 * 2 = 6 bits B: 5 * 2 = 10 bits C: 6 * 2 = 12 bits D: 4 * 2 = 8 bits E: 2 * 3 = 6 bits

   Total size = 6 + 10 + 12 + 8 + 6 = 42 bits

So, none of the options provided are correct. The total size of the message using Huffman's algorithm is 42 bits.