algorithm - Time Complexity single loop vs multiple sequential loops -

today, me , colleague had small argument 1 particular code snippet. code looks this. @ least, imagined be.

    for(int = 0; < n; i++) {         // operations here     }      (int = 0; < n; i++) {         // more operations here     } 

he wanted me remove second loop, since cause performance issues.

however, sure since don't have nested loops here, complexity o(n), no matter how many sequential loops put ( 2 had ).

his argument if n 1,000,000 , loop takes 5 seconds, code take 10 seconds, since has 2 loops. confused after statement.

what remember dsa lessons ignore such constants while calculating big oh.

what missing here?

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sidenote
in actual code, second loop run m times m smaller n. big n value, m small.

my colleague did not notice , hence pointed out performance issue.

yes,
complexity theory may compare 2 distinct methods of calculation in [?time][?space],
but

do not use [ptime] complexity argument poor efficiency

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fact #1: o( f(n) ) relevant comparing complexities, in areas near n ~ infty, process principal limits being possible compared "there"

fact #2: given n ~ { 10k | 10m | 10g }, none of such cases meets above cited condition

fact #3: if process ( algorithm ) allows loops merged without side-effects ( on resources / blocking / etc ) single pass, single-loop processing may benefit reduced looping overheads.

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a micro benchmark decide, not o( f( n ) ) n ~ infty

as many additional effects stronger influence - better or poor cache-line alignment , amount of possible l1/l2/l3-cache re-uses, smart harnessing of more / less cpu-registers - of driven possible compiler-optimisations , may further increase code-execution speeds small n-s, beyond expectations above.

so,
perform several scaling-dependent microbenchmarking, before resorting argue limits of o( f( n ) )

always do.