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Cormen Edition 3 Exercise 4.3 Question 1 (Page No. 87)
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Show that the solution of $T(n) = T(n1)+ n$ is $O(n^2)$
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Cormen Edition 3 Exercise 4.3 Question 8 (Page No. 87)
Using the master method, you can show that the solution to the recurrence $T(n) = 4T(n/2) +n^2$ is $T(n) = \Theta(n^2)$.Show that a substitution proof with the assumption $T(n) \leq cn^2$ fails. Then show how to subtract off a lowerorder term to make a substitution proof work.
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Cormen Edition 3 Exercise 4.3 Question 7 (Page No. 87)
Using the master method, you can show that the solution to the recurrence $T(n) = 4T(n/3) +n$ is $T(n) = O(n^{log_34})$.Show that a substitution proof with the assumption $T(n) \leq cn^{log_34}$ fails. Then show how to subtract off a lowerorder term to make a substitution proof work.
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Cormen Edition 3 Exercise 4.3 Question 6 (Page No. 87)
Show that the solution to $T(n) =T(\lfloor n/2 \rfloor+ 17) + n$ is $O(n\ log\ n)$
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Cormen Edition 3 Exercise 4.3 Question 3 (Page No. 87)
We saw that the solution of $T(n) = T(\lceil n/2 \rceil) + n$ is $O(lg\ n)$. Show that the solution of this recurrence is also $\Omega(n\ lg\ n)$. Conclude that the solution is $\Theta(n\log \ n)$.
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