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计算机代写|算法和结构代写Data Structures and Algorithms代考|The Role of Big O

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计算机代写|算法和结构代写Data Structures and Algorithms代考|The Role of Big O

Despite the fact that Big $\mathrm{O}$ doesn’t distinguish between Bubble Sort and Selection Sort, it is still very important, because it serves as a great way to classify the long-term growth rate of algorithms. That is, for some amount of data, $\mathrm{O}(\mathrm{N})$ will be always be faster than $\mathrm{O}\left(\mathrm{N}^2\right)$. And this is true no matter whether the $\mathrm{O}(\mathrm{N})$ is really $\mathrm{O}(2 \mathrm{~N})$ or even $\mathrm{O}(100 \mathrm{~N})$ under the hood. It is a fact that there is some amount of data at which even $\mathrm{O}(100 \mathrm{~N})$ will become faster than $\mathrm{O}\left(\mathrm{N}^2\right)$. (We’ve seen essentially the same concept in Oh Yes! Big O Notation when comparing a 100-step algorithm with $\mathrm{O}(\mathrm{N})$, but we’ll reiterate it here in our current context.)
Look at the first graph on page 60 , in which we compare $\mathrm{O}(\mathrm{N})$ with $\mathrm{O}\left(\mathrm{N}^2\right)$.
We’ve seen this graph in the previous chapter. It depicts how $\mathrm{O}(\mathrm{N})$ is faster than $\mathrm{O}\left(\mathrm{N}^2\right)$ for all amounts of data.

Now take a look at the second graph on page 60 , where we compare $\mathrm{O}(100 \mathrm{~N})$ with $\mathrm{O}\left(\mathrm{N}^2\right)$.

In this second graph, we see that $\mathrm{O}\left(\mathrm{N}^2\right)$ is faster than $\mathrm{O}(100 N)$ for certain amounts of data, but after a point, even $\mathrm{O}(100 \mathrm{~N})$ becomes faster and remains faster for all increasing amounts of data from that point onward.

It is for this very reason that Big $\mathrm{O}$ ignores constants. The purpose of Big $\mathrm{O}$ is that for different classifications, there will be a point at which one classification supersedes the other in speed, and will remain faster forever. When that point occurs exactly, however, is not the concern of Big $\mathrm{O}$.

Because of this, there really is no such thing as $\mathrm{O}(100 \mathrm{~N})$-it is simply written as $\mathrm{O}(\mathrm{N})$

Similarly, with large amounts of data, $O(\log N)$ will always be faster than $\mathrm{O}(\mathrm{N})$, even if the given $\mathrm{O}(\log \mathrm{N})$ algorithm is actually $\mathrm{O}\left(2^* \log \mathrm{N}\right)$ under the hood.
So Big $\mathrm{O}$ is an extremely useful tool, because if two algorithms fall under different classifications of Big $\mathrm{O}$, you’ll generally know which algorithm to use since with large amounts of data, one algorithm is guaranteed to be faster than the other at a certain point.

计算机代写|算法和结构代写Data Structures and Algorithms代考|A Practical Example

Let’s say you’re tasked with writing a Ruby application that takes an array and creates a new array out of every other element from the original array. It might be tempting to use the each_with_index method available to arrays to loop through the original array as follows:
def every_other(array)
new_array $=[$ ]
array.each_with_index do |element, index|
new_array $\ll$ element if index.even?
end
return new_array
end
In this implementation, we iterate through each element of the original array and only add the element to the new array if the index of that element is an even number.

When analyzing the steps taking place here, we can see that there are really two types of steps. We have one type of step in which we look up each element of the array, and another type of step in which we add elements to the new array.

We perform $\mathrm{N}$ array lookups, since we loop through each and every element of the array. We only perform N / 2 insertions, though, since we only insert every other element into the new array. Since we have $\mathrm{N}$ lookups, and we have $\mathrm{N} / 2$ insertions, we would say that our algorithm technically has an efficiency of $O(N+(N / 2))$, which we can also rephrase as $O(1.5 N)$. But since Big O Notation throws out the constants, we would say that our algorithm is simply $O(N)$.

While this algorithm does work, we always want to take a step back and see if there’s room for any optimization. And in fact, we can.

计算机代写|算法和结构代写Data Structures and Algorithms代考|A Practical Example

def every_other(array)
new_array $=[]$
array.each_with_index 做 lelement, index|

end
return new_array
end

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。