big o - What is constant factors and low-order term in algorithms? -


in following video described asymptotic analyzes issues: https://class.coursera.org/algo-004/lecture/169

but can't understand "low-order term" , "constant factor" itself? (it @ 4th minute of video).

the merge sort 6n*log2(n)+6n. why 6n low-order term in case mentioned in video , 6 constant factor? these terms have concrete definition?

lower-order term:

"order" here refers order of magnitude.

the concept easy understand , explain when dealing simple terms such x or x2. x has order of magnitude 1, since can written x1, , x2 has order 2 - order of magnitude equal power of variable in term. things little more hazy (at least me) when complicate things by, example, adding log. [1]

in informal terms, f(x) lower order g(x) if f(x) < g(x) x tends infinity.

it's easy see f(n) = 6n lower order g(n) = 6n*log2(n) substituting large value n (the correct approach mathematically prove it, substituting large value tends work simple terms).

the terms things separated plus / minus symbols.

so lower-order term term of lower order other term.

presumably opposite of the leading-order term, term largest order of magnitude.

[1]: deal big-o lot, it's been while (high-school?) since i've dealt basics of order of magnitude, apologies if might have missed or forgotten regarding part.

constant factor:

"factor" term in multiplication. 6n, 6 , n factors.

a constant factor doesn't depend on input parameter(s) (which n in case).

here, regardless of make n, 6 stay 6, it's constant.


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