Question

This is part of a search function on a website. So im trying to find a way to get to the end result as fast as possible.

Have a binary number where digit order matters.

Input Number = 01001

Have a database of other binary numbers all the same length.

01000, 10110, 00000, 11111

I dont know how to write what im doing, so im going to do it more visually below.

// Zeros mean nothing & the location of a 1 matters, not the total number of 1's.    
input num > 0 1 0 0 1 = 2 possible matches
number[1] > 0 1 0 0 0 = 1 match = 50% match
number[2] > 1 0 1 1 0 = 0 match = 0% match
number[3] > 0 0 0 0 0 = 0 match = 0% match
number[4] > 1 1 1 1 1 = 2 match = 100% match

Now obviously, you could go digit by digit, number by number and compare it that way (using a loop and what not). But I was hoping there might be an algorithm or something that will help. Mostly because in the above example I only used 5 digit numbers. But im going to be routinely comparing around 100,000 numbers with 200 digits each, that’s a lot of calculating.

I usually deal with php and MySQL. But if something spectacular comes up I could always learn.

Answer 1

If it’s possible to somehow chop up your bitstrings in integer-size chunks some elementary boolean arithmetic would do, and that kind of instructions is generally pretty fast

$matchmask = ~ ($inputval ^ $tomatch) & $inputval

What this does:

• the xor determines the bits that are different in the inputval and tomatch
• negation gives a value where all bits that are equal in inputval and tomatch are set
• and that with inputval and only the bits that are 1 in both inputval and tomatch remain set.

Then count the number of bits set in the result, look at How to count the number of set bits in a 32-bit integer? for an optimal solution, easily translated into php