Cormen Edition 3 Exercise 3.1 Question 1 (Page No. 52)

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Let $f(n)$ and $g(n)$ be asymptotically nonnegative functions. Using the basic definition of $\Theta$ notation, prove that $max(f(n),g(n)) = \Theta(f(n)+g(n))$.

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asked Apr 4, 2019 in Algorithms by akash.dinkar12 Boss (42.5k points) | 26 views

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Cormen Edition 3 Exercise 3.1 Question 2 (Page No. 52)
Show that for any real constants $a$ and $b$, where $b > 0,$ $(n+a)^b=\Theta(n^b)$

asked Apr 4, 2019 in Algorithms by akash.dinkar12 Boss (42.5k points) | 37 views

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Cormen Edition 3 Exercise 8.1 Question 2 (Page No. 194)
Obtain asymptotically tight bounds on $lg\ (n!)$ without using Stirling’s approximation. Instead, evaluate the summation $\sum_{k=1}^{n} lg\ k$.

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Cormen Edition 3 Exercise 3.2 Question 1 (Page No. 60)
Show that if $f(n)$ and $g(n)$ are monotonically increasing functions, then so are the functions $f(n) +g(n)$ and $f(g(n))$, and if $f(n)$ and $g(n)$ are in addition nonnegative, then $f(n) . g(n)$ is monotonically increasing.

asked Apr 4, 2019 in Algorithms by akash.dinkar12 Boss (42.5k points) | 11 views

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Cormen Edition 3 Exercise 3.1 Question 8 (Page No. 53)
We can extend our notation to the case of two parameters $n$ and $m$ that can go to infinity independently at different rates.For a given function $g(n,m)$, we denote by $O(g(n,m))$ the set of functions $O(g(n,m))$ $=$ {$f(n,m) :$ ... all $n \geq n_0$ or $m \geq m_0$ } Give corresponding definitions for $\Omega(g(n,m))$ and $\Theta(g(n,m))$.

asked Apr 4, 2019 in Algorithms by akash.dinkar12 Boss (42.5k points) | 20 views

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Cormen Edition 3 Exercise 3.1 Question 1 (Page No. 52)

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