Following are the various algorithms time complexities expressions. Find the dominant terms and specify the Big-Oh complexity of each algorithm.

C++ Programming: From Problem Analysis to Program Design
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Chapter15: Recursion
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  1. 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

 

 

Following are the various algorithms time complexities expressions. Find the dominant terms and
specify the Big-Oh complexity of each algorithm.
Expression
75 + 0.001n.3 +0.025n + (1000)
500n + 100n + 50n log1o n
(10n1.5)4 +0.3n + 5nº.5 + 2.5 · n².75
150n3 + n² log2 n+n(log2 n)*
3 log10 n + log2 log, n
100n4 + 0.01n² + 200(log2 n)
n3 + 0.01n + 100n? + 5n3
2n0.3 +n0.35 +0.5n0.25
0.01n² log2 n + n(log2 n)
50n3 log3 n + n log3 n + 100nt
S. No.
Dominant term(s)
O(.)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Transcribed Image Text:Following are the various algorithms time complexities expressions. Find the dominant terms and specify the Big-Oh complexity of each algorithm. Expression 75 + 0.001n.3 +0.025n + (1000) 500n + 100n + 50n log1o n (10n1.5)4 +0.3n + 5nº.5 + 2.5 · n².75 150n3 + n² log2 n+n(log2 n)* 3 log10 n + log2 log, n 100n4 + 0.01n² + 200(log2 n) n3 + 0.01n + 100n? + 5n3 2n0.3 +n0.35 +0.5n0.25 0.01n² log2 n + n(log2 n) 50n3 log3 n + n log3 n + 100nt S. No. Dominant term(s) O(.) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
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