If an algorithm has a running time of 3N2 + 5N + 10, what is its asymptotic Big-O complexity?
Options
- A. O(N)
- B. O(N log N)
- C. O(N2)
- D. More than one of the above
- E. None of the above
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Quiz Practice:
Correct Answer (Detailed Explanation is Below)
C. O(N2)
Detailed Explanation
For 3N2 + 5N + 10, the dominant term for large N is N2. In Big-O analysis, constant coefficients and lower-order terms are ignored, so the expression is O(N2). This does not mean the actual running time equals N2; Big-O describes asymptotic growth. Identifying the dominant term is a fundamental technique for analyzing algorithm complexity.