Question-18

Two alternative packages A and B are available for processing a database having \(10k\) records. Package A requires \(0.0001n^2\) time units, and package B requires \(10n \log_{10} n\) time units to process \(n\) records. What is the smallest value of \(k\) for which package B will be preferred over A?

• \(12\)
• \(10\)
• \(6\)
• \(5\)

Answer

• \(12\)
• \(10\)
• \(6\)
• \(5\)

Solution

To determine when package B is preferred over package A, we set up the inequality: \[10n \log_{10} n < 0.0001n^2k\]

Solving for \(k\): \[10 \cdot 10^4 \cdot 2^{-k} < k\]

By observation, when \(k = 6\), \(10 \cdot 10^4 \cdot 2^{-6} = \frac{10^5}{64} < 6\). Thus, \(k\) needs to be at least \(6\) for package B to be preferred over package A.