number of unique names (algorithmically)

gistfile1.txt

B = 8     # 8 bytes for the fixed name length
total = 0 # accumulator for the number of names
for b in range(1, B + 1):
    # Compute the number of unique partitions for all possible values of k
    l = [0] * b
    partition_total = 0
    for k in range(1, b):
        partition_total += num_partitions(l, k)

    # Multiply the partition total by the number of possible names of length b
    num_unique = 2 ** (8 * b)
    total += (partition_total * num_unique)

    # Debug
    print "For b=%d, partition_total=%d" % (b, partition_total)
    print "For b=%d, num_unique=%d" % (b, num_unique)

print "Total: %d" % (total)