Complexity Theory Trivia Questions

Sample Complexity Theory Questions

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1. 1.Written as a capital letter with parentheses like O(n²), this mathematical shorthand describes how an algorithm's runtime scales with input size.

   • Big O notation
   • Lambda calculus
   • Set-builder notation
   • Sigma notation

2. 2.An algorithm that runs in the same amount of time regardless of input size is said to have this type of time behavior.

   • Linear time
   • Constant time
   • Quadratic time
   • Logarithmic time

3. 3.When an algorithm's runtime doubles each time you add one more element to the input, it exhibits this explosive scaling behavior.

   • Polynomial growth
   • Linear growth
   • Exponential growth
   • Logarithmic growth

4. 4.This famous unsolved question asks whether every problem whose solution can be quickly verified can also be quickly solved.

   • The Halting Problem
   • The Riemann Hypothesis
   • Goldbach's Conjecture
   • P versus NP

5. 5.This computational class contains all problems solvable in a reasonable amount of time, growing at most as a power of the input size.

   • P (Polynomial time)
   • NP (Nondeterministic Polynomial time)
   • EXPTIME
   • PSPACE

6. 6.A binary search achieves its speed by repeatedly halving the search space, resulting in this efficient runtime.

   • O(1)
   • O(n)
   • O(log n)
   • O(n²)

7. 7.This class of problems can have their solutions verified quickly, even if finding the solution might be much harder.

   • NP
   • P
   • EXPTIME
   • Undecidable

8. 8.Merge sort and quicksort achieve this runtime by dividing problems into smaller subproblems and combining results.

   • O(n)
   • O(log n)
   • O(n²)
   • O(n log n)

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