I have given message encoded with non-optimal Huffman code. I need to decode the message and encode it again, but this time with optimal Huffman code, so after that I can find average_number_of_bits_per_symbols = num_of_bits_in_message / num_of_characters_in_message

Example:

input:

6
A 11
B 10
C 01
D 0001
E 001
F 0000
101100000001000010001001100011000000010001010010000000100001000110001100011000000010000000000000100110001000100000000000000011011111010100100101011001010000111001010110000100000010010000000111010000001100100100001010001000100000000001

output:

2.469

Here is what I got from decoding:

// Third column is occurrence of the letter
A 11 5
B 10 19
C 01 12
D 0001 8
E 001 18
F 0000 19

BAFDFBEEBEBFEDCEFDFBEBEBEBFEFFFCEBEDFFFDBAABBBCECCBCCFABCCCBDFEEFDACFEBCEFBBEDFFE

num_of_characters: 81

So now I have to find optimal codes for these letters. I’ve tried tree like this one:

19      19     18     12      8     5
  B      F      E      C      D     A
        /            /           /
   0   /1       0   /1      0   /1
      /            /           /
                               /
                              /
                    0        /1
                            /
                           /
                          /
          0              /
                         /
                        /
                       /1
                ______/

And with this I will get:

A 111 => 3 * 5  = 15
D 110 => 3 * 8  = 24
C 101 => 3 * 12 = 36
E 100 => 3 * 18 = 54
F 01  => 2 * 19 = 38
B 00  => 2 * 19 = 38
num_of_bits     = 205

So 205 / 81 = 2.530 => which is not equal with the example output...

So what I am doing wrong?