# Time complexity of subset sum problem with reals instead?

It is well known that the conventional subset sum problem with integers is NP-complete. What if the array elements can be any real numbers and also target sum can be any real number? Is it NP-complete still or harder (NP-hard)?

• What model of computation are we talking about here? Most real numbers cannot be encoded as a finite string. – dkaeae Jun 11 at 16:04

What model of real numbers are you using? If it's something like floating point, where everything is really rational, just multiply through by a common denominator and you're back in the world of integers. The bit-length is only polynomially larger than the ones you started with (the common denominator is at most the product of $$n$$ $$n$$-bit numbers, so it has at most $$n^2$$ bits), so nothing has changed, complexity-wise.