Concept explainers
(a)
To prove that the asymptotic notation
(a)
Explanation of Solution
Given Information:Let
Explanation:
Consider that there exists some constants
The last line ensures the fact that
Therefore,
(b)
To prove that the asymptotic notation
(b)
Explanation of Solution
Explanation:
Consider that there exists some constants
The last line ensures the fact that
Therefore,
(c)
To prove that the asymptotic notation
(c)
Explanation of Solution
Explanation:
Consider that there exists some constants
It is already proved that for
Therefore,
(d)
To prove that the asymptotic notation
(d)
Explanation of Solution
Explanation:
It can be easily prove by removing the equality from the part (a).
The limit definition of
The limit is equal to 0since
Therefore,
(e)
To prove that the asymptotic notation
(e)
Explanation of Solution
Explanation:
It can be easily prove by removing the equality from the part (b).
The limit definition of
notation is as follows:
The limit is equal to
Therefore,
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Chapter 3 Solutions
Introduction to Algorithms
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