Project Euler 219: Skewcost coding
Problem Description
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 prefixfree 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 prefixfree 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 prefixfree 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(10^{9}) ?
Project Euler 219 Solution
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