# Problem 219: Skew-cost coding
Let A and B be bit strings (sequences of 0's and 1's). If A is equal to
the leftmost length(A) bits of B, then A is said to be a prefix of B.
For example, 00110 is a prefix of 001101001, but not of 00111 or 100110.
A prefix-free code of size n is a collection of n distinct bit strings
such that no string is a prefix of any other. For example, this is a
prefix-free code of size 6: 0000, 0001, 001, 01, 10, 11 Now suppose that
it costs one penny to transmit a '0' bit, but four pence to transmit a
'1'. Then the total cost of the prefix-free code shown above is 35
pence, which happens to be the cheapest possible for the skewed pricing
scheme in question. In short, we write Cost(6) = 35. What is Cost(109) ?