Algorithm Question on File Search Indexing

Question

There is one question and I have the solution to it also. But I couldn\'t understand the solution. Kindly help with some set of examples and shower some experience.

Answer 1

To make the explanation simpler, let's say you have a list of two-digit numbers, where each digit is between 0 and 3, but you can't spare the 16 bits to remember for each of the 16 possible numbers, whether you have already encountered it. What you do is to create an array a of 4 3-bit integers and in a[i], you store how many numbers with the first digit i you encountered. (Two-bit integers wouldn't be enough, because you need the values 0, 4 and all numbers between them.)

If you had the file

00, 12, 03, 31, 01, 32, 02

your array would look like this:

4, 1, 0, 2

Now you know that all numbers starting with 0 are in the file, but for each of the remaining, there is at least one missing. Let's pick 1. We know there is at least one number starting with 1 that is not in the file. So, create an array of 4 bits, for each number starting with 1 set the appropriate bit and in the end, pick one of the bits that wasn't set, in our example if could be 0. Now we have the solution: 10.

In this case, using this method is the difference between 12 bits and 16 bits. With your numbers, it's the difference between 32 kB and 119 MB.