Assume that each of the expressions below gives the processing time T(n) spent by an algorithm for solving a problem of size n. Select the dominant term(s) having the steepest increase in n and specify the lowest Big-Oh complexity of each algorithm. For example, the dominant term in 0.1n + 10n4 is 10n4 and it is O(n4).                                                                                                   Expression Dominant term(s) O(. . .) 5 + 0.001n3 + 0.025n     500n + 100n1.5 + 50n log10 n     0.3n + 5n1.5 + 2.5 · n1.75     n2 log2 n + n(log2 n)2     n log3 n + n log2 n     100n + 0.01n2     0.01n + 100n2     2n + n0.5 + 0.5n1.25     0.01n log2 n + n(log2 n)2     100n log3 n + n3 + 100n

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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Assume that each of the expressions below gives the processing time T(n) spent by an algorithm for solving a problem of size n. Select the dominant term(s) having the steepest increase in n and specify the lowest Big-Oh complexity of each algorithm. For example, the dominant term in 0.1n + 10n4 is 10n4 and it is O(n4).                                                                                                

 

Expression

Dominant term(s)

O(. . .)

5 + 0.001n3 + 0.025n

   

500n + 100n1.5 + 50n log10 n

   

0.3n + 5n1.5 + 2.5 · n1.75

   

n2 log2 n + n(log2 n)2

   

n log3 n + n log2 n

   

100n + 0.01n2

   

0.01n + 100n2

   

2n + n0.5 + 0.5n1.25

   

0.01n log2 n + n(log2 n)2

   

100n log3 n + n3 + 100n

   
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