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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 计算机代写|组合优化代写Combinatorial optimization代考|Priority Queue

Although Dijkstra algorithm with simple buckets runs faster for small $c$. it cannot be counted as a polynomial-time solution. In fact, the input size of $c$ is $\log c$. Therefore, we would like to select a data structure which implements Dijkstra algorithm in polynomial-time. This data structure is priority queue.

A priority queue is a data structure for maintaining a set $S$ of elements, each with an associated value, called a key. All keys are stored in an array $A$ such that an element belongs to set $S$ if and only if its key is in array $A$. There are two types of priority queues, the min-priority queue and the max-priority queue. Since they are similar, we introduce one of them, the min-priority queue.

A min-priority queue supports the following operations: $\operatorname{Minimum}(S)$, Extract$\operatorname{Min}(S)$, Increase-Key $(S, x, k)$, and $\operatorname{Insert}(S, x)$.
The min-heap can be employed in implementation of those operations.
$\operatorname{Minimum}(S)$ returns the element of $S$ with the smallest key, which can be implemented as follows.
Heap-Minimum $(A)$ $\quad$ return $A[1]$.
Extract-Min $(S)$ removes and returns the element of $S$ with the smallest key, which can be implemented by using min-heap as follows.

Decrease-Key $(S, x, k)$ decreases the value of element $x$ ‘s key to the new value $k$, which is assumed to be no more than $x$ ‘s current key value. Suppose that $A[i]$ contains $x$ ‘s key. Then, Decrease-Key $(S, x, k)$ can be implemented as an operation of min-heap as follows.

## 计算机代写|组合优化代写Combinatorial optimization代考|All Pairs Shortest Paths

In this section, we study the following problem.
Problem 3.6.1 (All-Pairs-Shortest-Paths) Given a directed graph $G=(V, E)$, find the shortest path from $s$ to $t$ for all pairs ${s, t}$ of nodes.

If we apply the Bellman-Ford algorithm for single pair of nodes for each of $U\left(n^2\right)$ pairs, then the total time for computing a solution of the all-pairs-shortestpaths problem is $O\left(n^3 m\right)$. In the following, we will present two faster algorithms, with running time $O\left(n^3 \log n\right)$ and $O\left(n^3\right)$, respectively, with only restriction that no negative weight cycle exists. Before doing so, let us consider an example on which we introduce an approach which can be used for the all-pairs-shortest-paths problem.

Example 3.6.2 (Path Counting) Given a directed graph $G=(V, E)$ and a positive integer $k$, count the number of paths with exactly $k$ arcs from $s$ to $t$ for all pairs ${s, t}$ of nodes

Let $a_{s t}^{(k)}$ denote the number of paths with exactly $k$ arcs from $s$ to $t$. Then, we have
$$a_{s t}^{(1)}=\left{\begin{array}{l} 1 \text { if }(s, t) \in E \ 0 \text { otherwise. } \end{array}\right.$$
This means that $\left(a_{s t}^{(1)}\right)$ is the adjacency matrix of graph $G$. Denote
$$A(G)=\left(a_{s t}^{(1)}\right) .$$

# 组合优化代考

## 计算机代写|组合优化代写Combinatorial optimization代考|Priority Queue

Extract-Min(小号)移除并返回元素小号使用最小的键，可以通过使用 min-heap 来实现，如下所示。

## 计算机代写|组合优化代写Combinatorial optimization代考|All Pairs Shortest Paths

$$a_{st}^{(1)}=\left{1 如果 (s,吨)∈和 0 否则。 \正确的。 吨H一世s米和一个ns吨H一个吨(一个s吨(1))一世s吨H和一个dj一个C和nC是米一个吨r一世X○FGr一个pHG.D和n○吨和 A(G)=\left(a_{st}^{(1)}\right) 。$$

## 有限元方法代写

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## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师