Practice question · True or false
simplifies to in Big-O notation, since constant factors are dropped.
Hints
- Is the 2 a factor or an exponent?
- and are different claims.
Show the answer
False
Why
False. Big-O drops constant multipliers, so , but is a different growth class entirely and never reduces to . Confusing a coefficient with an exponent is the single most common Big-O error, and it changes the answer by orders of magnitude at scale.
Practise Complexity and efficiency basics
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More questions on Complexity and efficiency basics
- An O(n²) algorithm can beat an O(nlog n) one on real data. How is that consistent with the complexity classes?
- Two nested loops each running n times give O(n²). Why does the analysis not simply add the two loops?
- Match each everyday task to the growth rate of its work as n grows.
- An O(n²) simulation takes 2 seconds for n = 1000 particles. Predict its runtime for n = 5000, in seconds.