Exercise 2.71.  Suppose we have a Huffman tree for an alphabet of n 
symbols, and that the relative frequencies of the symbols are 1, 2, 4, 
..., 2n-1. Sketch the tree for n=5; for n=10. In such a tree (for 
general n) how may bits are required to encode the most frequent symbol?  
the least frequent symbol?

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n=5:

symbol, frequency pairs are:

(a 1) (b 2) (c 4) (d 8) (e 16)

The tree is:

                  .
                 / \
                .   e
               / \
              .   d
             / \
            .   c
           / \
          a   b

The tree for n=10 is similar.

Since 2^n > 2^1 + 2^2 + ... + 2^(n-1), the most frequent symbol can 
always be encoded in one bit.

The least frequent symbol will require n-1 bits.