How many times would you need to execute line 2? The more times you need to do this, the more values x needs to be able to represent. So running x++ in O(n) time means the space needed to store the accumulation grows as O(n log_2 n)... under delirium's "pedantic" interpretation of space complexity.
Unknowingly you have allowed me to stumble onto an actual algorithm with O(1) storage pace, that is, one where there are n numbers, and you want to calculated the modulo-k sum. In this case, the algorithm scales logarithmically in the constant parameter k, but O(1) in n.
I agree, but I'm not sure how you can maintain these things without being owned by the people (govt) or a corp. I guess a regulatory body like the FCC then?
