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Cormen Edition 3 Exercise 4.6 Question 3 (Page No. 106)
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Show that case 3 of the master theorem is overstated, in the sense that the regularity condition $af(n/b)\geq cf(n)$ for some constant $c<1$ implies that there exists a constant $\epsilon >0$ such that $f(n)=\Omega(n^{log_ba+\epsilon})$.
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Cormen Edition 3 Exercise 4.6 Question 2 (Page No. 106)
Show that if $f(n)=\Theta(n^{log_ba}\lg^kn )$, where $k\geq0$ then the master recurrence has solution $T(n) =\Theta(n^{log_ba} \lg^{k+1}n)$.For simplicity, confine your analysis to exact powers of $b$.
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Cormen Edition 3 Exercise 4.5 Question 5 (Page No. 97)
Consider the regularity condition $af(n/b) \leq cf(n)$ for some constant $c<1$,which is part of case 3 of the master theorem. Give an example of constants $a\geq 1$ and $b>1$ and a function $f(n)$ that satisfies all the conditions in case 3 of the master theorem except the regularity condition.
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Apr 5, 2019
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Cormen Edition 3 Exercise 4.5 Question 4 (Page No. 97)
Can the master method be applied to the recurrence $T(n)=4T(n/2)+n^2\ lg\ n$ ?Why or why not? Give an asymptotic upper bound for this recurrence.
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Cormen Edition 3 Exercise 4.5 Question 3 (Page No. 97)
Use the master method to show that the solution to the binarysearch recurrence $T(n)=T(n/2) + \Theta(1)$ is $T(n)=\Theta(lg\ n)$.
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