Sorry , I think, I haven't been clear. My question is 'What are the input of random sets given as input?' because I feel if we write ANY algorithm, however bad

Sorry , I think, I haven't been clear. My question is 'What are the input of random sets given as input?' because I feel if we write ANY algorithm, however bad it may be, until it gives us a path, saying that that it is only x% longer is a property of the input given by us. I am saying that x could turn out to be 25 in most of the cases who knows.