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

Sure, here are the steps to use Huffman algorithm to find the total size of the message "B C C A B B D D A E C C B B A E D D C C":

Step 1: Count the frequency of each character in the message.

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

Step 2: Create a priority queue (min-heap) where the node with the lowest frequency has the highest priority.

Queue: [(A,3), (E,2), (D,4), (B,5), (C,6)]

Step 3: Create a Huffman Tree. Remove two nodes with the smallest frequency from the priority queue. Create a new node with these two nodes as children and with frequency equal to the sum of the two nodes' frequencies. Insert the new node into the queue.

First Iteration: Remove (A,3) and (E,2), create new node (AE,5) and insert into queue.

Queue: [(D,4), (B,5), (AE,5), (C,6)]

Second Iteration: Remove (D,4) and (B,5), create new node (DB,9) and insert into queue.

Queue: [(AE,5), (C,6), (DB,9)]

Third Iteration: Remove (AE,5) and (C,6), create new node (AEC,11) and insert into queue.

Queue: [(DB,9), (AEC,11)]

Fourth Iteration: Remove (DB,9) and (AEC,11), create new node (DBAEC,20) and insert into queue.

Queue: [(DBAEC,20)]

Step 4: Create a Huffman Code. Start from the root and assign codes to all edges such that the left edge gets 0 and the right edge gets 1. Traverse the tree to assign codes.

A: 100 B: 00 C: 101 D: 01 E: 110

Step 5: Calculate the total size of the message. Replace each character in the original message with its corresponding Huffman code and sum the length of all codes.

Total size = 33 + 52 + 63 + 42 + 2*3 = 9 + 10 + 18 + 8 + 6 = 51 bits

So, the total size of the message "B C C A B B D D A E C C B B A E D D C C" using Huffman algorithm is 51 bits.