Random Number Generator that Allows "Indexing"

Question

I hope it's not too obvious a question: is there a random number generation algorithm that doesn't depend on previously returned values, so that I can get (for example) the 50th number in the sequence, without computing the previous 49?

The reason is that I am making roguelike that will be persistent (so that I can recreate the exact same level from the same seed), but to compute certain features of each level, I don't want to have to "compute" all previous features just to get the random number generator to the correct "state" of having been used, for example, 100 times so far. I would like to be able to query the 101st random number without determining previous values so that the program can create level features separately.

Answer 1

You can encrypt ordinary sequence number [1..N] with any cipher, and by this way - generate unique pseudorandom value for each SeqNo.

Answer 2

If you use a linear congruential random number generator, it is trivial to compute the $n$-th element generated from a given seed. But it is probably easier just to stash away the state at the "interesting" points of the game.

OTOH, if you want to "restart" the game at a certain point, you'll presumably want to be able to recreate the dungeon's features, but (due to different player actions) the RNG usage will be different from then on. I.e., if started at the same point, if I shoot twice at a monster the RNG will be used more times than if I just run away; the next item generated will get different values. Perhaps what you really want is several independent random number streams, and saving the states as needed?

There are lots of roguelike games around, mostly open source. Some are limited/small (from "build a game in a day" sort of competitions), and might make a good starting point for you. Why start your own, and not hack on an existing one?