###### Asymptotic-Complexity

October 26, 2023###### Asymptotic-Complexity

October 26, 2023# Asymptotic-Complexity

Question 19 |

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 10nlog_{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 |

Question 19 Explanation:

As per given information Package B 10nlog

_{10 n is lesser than or equals to Package A 0.0001n 2 0 because n 2 is asymptotically larger than nlogn. Finally, 10nlog 10 n ≤ 0.0001n 2 Let n = 10 k records. Substitute into 10nlog 10 n ≤ 0.0001n 2 10(10 k )log 10 10 k ≤ 0.0001(10 k ) 2 10 k+1 k ≤ 0.0001 × 10 2k k ≤ 10 2k−k−1−4 k ≤ 10 k−5 According to the problem value 6 is suitable for K.}Correct Answer: C

Question 19 Explanation:

As per given information Package B 10nlog

_{10 n is lesser than or equals to Package A 0.0001n 2 0 because n 2 is asymptotically larger than nlogn. Finally, 10nlog 10 n ≤ 0.0001n 2 Let n = 10 k records. Substitute into 10nlog 10 n ≤ 0.0001n 2 10(10 k )log 10 10 k ≤ 0.0001(10 k ) 2 10 k+1 k ≤ 0.0001 × 10 2k k ≤ 10 2k−k−1−4 k ≤ 10 k−5 According to the problem value 6 is suitable for K.} Subscribe

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