Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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8,9,10

You are given the following definitions to help you:
O(g(n)) = {f(n): there exist positive constants c and no such that
0 ≤ f(n) ≤ cg(n) for all n ≥ no} .
N(g(n)) = {f(n): there exist positive constants c and no such that
0 ≤ cg (n) ≤ f(n) for all n ≥ no} .
©(g(n)) = {f(n): there exist positive constants C₁, C2, and no such that
0 ≤ c₁g(n) ≤ f(n) ≤ c₂g (n) for all n ≥ no} .
Using above definitions, prove that:
5. T(n) = 6n + 4n+ 3 € 0 (n)
6. T(n) = 100n + 10000 ��� O(n²)
7. T(n) = 5n² - 2n + 16 € O(n³)
8. T(n)=5n² - 2n + 16 is not € O(n)
9. T(n) = n³ + 20n € №(n² )
10. T(n) = 2n³ - 7n + 1 € ☺(n³)
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Transcribed Image Text:You are given the following definitions to help you: O(g(n)) = {f(n): there exist positive constants c and no such that 0 ≤ f(n) ≤ cg(n) for all n ≥ no} . N(g(n)) = {f(n): there exist positive constants c and no such that 0 ≤ cg (n) ≤ f(n) for all n ≥ no} . ©(g(n)) = {f(n): there exist positive constants C₁, C2, and no such that 0 ≤ c₁g(n) ≤ f(n) ≤ c₂g (n) for all n ≥ no} . Using above definitions, prove that: 5. T(n) = 6n + 4n+ 3 € 0 (n) 6. T(n) = 100n + 10000 ��� O(n²) 7. T(n) = 5n² - 2n + 16 € O(n³) 8. T(n)=5n² - 2n + 16 is not € O(n) 9. T(n) = n³ + 20n € №(n² ) 10. T(n) = 2n³ - 7n + 1 € ☺(n³)
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