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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Give an algorithm for the following problem, Given a list of \(n\) distinct positive integers, partition the list into two sublists, each of size \(n / 2,\) such that the difference between the sums of integers in the two sublists is minimized. Determine the time complexity of your algorithm. You may assume that \(n\) is a multiple of 2
Write a \(\Theta(n)\) algorithm that sorts \(n\) distinct integers, ranging in size between 1 and \(k n\) inclusive, where \(k\) is a constant positive integer. (Hint: Use a kn-element array.)
Suppose you have a computer that requires 1 minute to solve problem instances of size \(n=1,000 .\) Suppose you buy a new computer that runs 1,000 times faster than the old one. What instance sizes can be run in 1 minute, assuming the following time complexities \(T(n)\) for our algorithm? a. \(T(n)=n\) b. \(T(n)=n^{3}\) c. \(T(n)=10^{n}\)
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?
Write an algorithm that finds the \(m\) smallest numbers in a list of \(n\) numbers.
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