Find the suitable constants etc. to prove each of the following (as done in column 3): ( Note: you may use ^ for power, e.g., x square as x^2 ) To prove Find ? f(n)= 4n³+14n²+8 f(n)= n³15+2n²+1 C 4 + 14 + 0 + 8 = 26 no 1 f(n)=O(n³) g(n) Condition f(n) s 26n3 , for n 21 C 4 no f(n)=Q(n³) g(n) n3 Condition 4n³ s f(n) , for n 2 0 C1 4 C2 4 + 14 + 0 + 8 = 26 f(n)=©(n³) g(n) no 1 n3 4n3 s f(n) s 26n³, forn2 1 |Condition

C++ Programming: From Problem Analysis to Program Design
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ISBN:9781337102087
Author:D. S. Malik
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Chapter5: Control Structures Ii (repetition)
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Data structure (java)

Find the suitable constants etc. to prove each of the following (as done in column 3):
( Note: you may use ^ for power, e.g., x square as x^2)
To prove
f(n)= 4n³+14n²+8
f(n)= n³/5+2n²+1
Find ?
4 + 14 + 0 + 8 = 26
no
1
f(n)=O(n³)
g(n)
Condition f(n) < 26n3 , for n 2 1
4
no
ㅇ
f(n)=Q(n³)
n3
g(n)
4n3
s f(n) , for n 2 0
Condition
C1
4
C2
4 + 14 + 0 + 8 = 26
f(n)=©(n³)
g(n)
no
1
n3
4n3
< f(n) < 26n3, for n2
Condition
1
Transcribed Image Text:Find the suitable constants etc. to prove each of the following (as done in column 3): ( Note: you may use ^ for power, e.g., x square as x^2) To prove f(n)= 4n³+14n²+8 f(n)= n³/5+2n²+1 Find ? 4 + 14 + 0 + 8 = 26 no 1 f(n)=O(n³) g(n) Condition f(n) < 26n3 , for n 2 1 4 no ㅇ f(n)=Q(n³) n3 g(n) 4n3 s f(n) , for n 2 0 Condition C1 4 C2 4 + 14 + 0 + 8 = 26 f(n)=©(n³) g(n) no 1 n3 4n3 < f(n) < 26n3, for n2 Condition 1
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