Following are the various algorithms time complexities expressions. Find the dominant terms and specify the Big-Oh complexity of each algorithm. S. No. Expression Dominant term(s) O (. . .) 1. 75 + 0.001n1.3 + 0.025n + (1000)4     2. 500n + 100n + 50n log10 n     3. (10n1.5)4 + 0.3n + 5n6.5 + 2.5 · n2.75     4. 150n3 + n2 log2 n + n(log2 n)4     5. 3 log10 n + log2 log2 n     6. 100n4 + 0.01n2 + 200(log2 n)4     7. n3 + 0.01n + 100n2 + 5n3     8. 2n0.5 + n0.35 + 0.5n0.25     9. 0.01n2 log2 n + n(log2 n)     10. 50n3 log3 n + n5 log3 n + 100n4

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Following are the various algorithms time complexities expressions. Find the dominant terms and specify the Big-Oh complexity of each algorithm.


S. No.

Expression

Dominant term(s)

O (. . .)

1.

75 + 0.001n1.3 + 0.025n + (1000)4

 

 

2.

500n + 100n + 50n log10 n

 

 

3.

(10n1.5)4 + 0.3n + 5n6.5 + 2.5 · n2.75

 

 

4.

150n3 + n2 log2 n + n(log2 n)4

 

 

5.

3 log10 n + log2 log2 n

 

 

6.

100n4 + 0.01n2 + 200(log2 n)4

 

 

7.

n3 + 0.01n + 100n2 + 5n3

 

 

8.

2n0.5 + n0.35 + 0.5n0.25

 

 

9.

0.01n2 log2 n + n(log2 n)

 

 

10.

50n3 log3 n + n5 log3 n + 100n4

 

 

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