Chapter 1: Problem 1
Write an algorithm that finds the largest number in a list (an array) of \(n\) numbers.
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These are the key concepts you need to understand to accurately answer the question.
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Chapter 1: Problem 1
Write an algorithm that finds the largest number in a list (an array) of \(n\) numbers.
These are the key concepts you need to understand to accurately answer the question.
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Using the definitions of \(O\) and \(\Omega\), show that $$6 n^{2}+20 n \in O\left(n^{3}\right) \quad \text { but } \quad 6 n^{2}+20 n \notin \Omega\left(n^{3}\right)$$
Write an algorithm that finds the \(m\) smallest numbers in a list of \(n\) numbers.
Group the following function by complexity category. $$\begin{aligned}&n \ln n \quad(\lg n)^{2} \quad 5 n^{2}+7 n \quad n^{5 / 2}\\\&n ! \quad 2^{n !} \quad 4^{n} \quad n^{n} \quad n^{n}+\ln n\\\&5^{\lg n} \lg (n !) \quad(\lg n) ! \quad \sqrt{n} \quad e^{n} \quad 8 n+12 \quad 10^{n}+n^{20}\end{aligned}$$
Discuss the reflexive, symmetric, and transitive properties for asymptotic comparisons \((O, \Omega, \Theta, o)\)
Algorithm A performs \(10 n^{2}\) basic operations, and algorithm \(\mathrm{B}\) performs 300 In \(n\) basic operations. For what value of \(n\) does algorithm B start to show its better performance?
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