Sorting 1 million 8-decimal-digit numbers with 1 MB of RAM

Question

I have a computer with 1 MB of RAM and no other local storage. I must use it to accept 1 million 8-digit decimal numbers over a TCP connection, sort them, and then send the

Answer 1

Now aiming to an actual solution, covering all possible cases of input in the 8 digit range with only 1MB of RAM. NOTE: work in progress, tomorrow will continue. Using arithmetic coding of deltas of the sorted ints, worst case for 1M sorted ints would cost about 7bits per entry (since 99999999/1000000 is 99, and log2(99) is almost 7 bits).

But you need the 1m integers sorted to get to 7 or 8 bits! Shorter series would have bigger deltas, therefore more bits per element.

I'm working on taking as many as possible and compressing (almost) in-place. First batch of close to 250K ints would need about 9 bits each at best. So result would take about 275KB. Repeat with remaining free memory a few times. Then decompress-merge-in-place-compress those compressed chunks. This is quite hard, but possible. I think.

The merged lists would get closer and closer to the 7bit per integer target. But I don't know how many iterations it would take of the merge loop. Perhaps 3.

But the imprecision of the arithmetic coding implementation might make it impossible. If this problem is possible at all, it would be extremely tight.

Any volunteers?