And in my exercise, we are fixing two computers & two competing algorithms, and varying only the input sizes to these algorithms. So I prefer to treat memory lookup time as a constant.
Sure, when you start performing your algorithmic analysis, there's nothing preventing from stating as an axiom...
- memory lookup is O(1)
Just be aware that this is an axiom
after all and only true for a particular set of von Neumann type machines. Or stated another way, for certain given problems and the same finite amount of silicon, there are better ways to arrange the wires between the transistors (like say into a shift register instead of a tree (RAM)). And your complexity analysis (with Axiom #1 from above) will be incorrect and lead to answers which aren't consistent with the actual performance of the physical machine.
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