Design and Analysis of Distributed Algorithms

本书重点在于培养解决问题的能力并充分利用设计工具和技术。作者帮助读者掌握评估复杂设计和协议成本所需的分析工具和技能。本书基于一个直观且完全反应式的计算模型进行讲解。

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Design And Analyze algorithms for distributed computing environments

Design and Analysis of Distributed Algorithms focuses on developing problem-solving skills and fully exploiting design tools and techniques. Moreover, the author helps readers develop the analytical tools and skills needed to evaluate the costs of complex designs and protocols.

This text is based on a simple and fully reactive computational model that allows for intuitive comprehension and logical designs. The principles and techniques that users learn can be applied to any distributed computing environment (e.g., distributed systems, communication networks, data networks, grid networks, internet, etc.). Based on a method developed and refined during the author's twenty years of teaching experience, the text provides a wealth of unique material and learning aids that enable the reader to learn how to design algorithms and protocols to solve problems and perform tasks efficiently in a distributed computing environment. Features include:

*Emphasis on developing problem-solving skills and fully leveraging design tools and techniques with a straightforward, easy-to-follow writing style
*Chapter on distributed data and structures, an important area not covered in comparable texts
*Detailed coverage of synchronous computations, a necessary element for "energy aware" computing Theoretical and experimental exercises in each chapter that allow readers to apply their newfound skills
*All algorithms and protocols presented in the text, as well as those in the exercises, are easily and immediately programmable. References at the end of each chapter lead readers to additional materials for further study.

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资源下载链接为: https://pan.quark.cn/s/9e7ef05254f8 行列式是线性代数的核心概念,在求解线性方程组、分析矩阵特性以及几何计算中都极为关键。本教程将讲解如何用C++实现行列式的计算,重点在于如何输出分数形式的结果。 行列式定义如下:对于n阶方阵A=(a_ij),其行列式由主对角线元素的乘积,按行或列的奇偶性赋予正负号后求和得到,记作det(A)。例如,2×2矩阵的行列式为det(A)=a11×a22-a12×a21,而更高阶矩阵的行列式可通过Laplace展开或Sarrus规则递归计算。 在C++中实现行列式计算时,首先需定义矩阵类或结构体,用二维数组存储矩阵元素,并实现初始化、加法、乘法、转置等操作。为支持分数形式输出,需引入分数类,包含分子和分母两个整数,并提供与整数、浮点数的转换以及加、减、乘、除等运算。C++中可借助std::pair表示分数,或自定义结构体并重载运算符。 计算行列式的函数实现上,3×3及以下矩阵可直接按定义计算,更大矩阵可采用Laplace展开或高斯 - 约旦消元法。Laplace展开是沿某行或列展开,将矩阵分解为多个小矩阵的行列式乘积,再递归计算。在处理分数输出时,需注意避免无限循环和除零错误,如在分数运算前先约简,确保分子分母互质,且所有计算基于整数进行,最后再转为浮点数,以避免浮点数误差。 为提升代码可读性和可维护性,建议采用面向对象编程,将矩阵类和分数类封装,每个类有明确功能和接口,便于后续扩展如矩阵求逆、计算特征值等功能。 总结C++实现行列式计算的关键步骤:一是定义矩阵类和分数类;二是实现矩阵基本操作;三是设计行列式计算函数;四是用分数类处理精确计算;五是编写测试用例验证程序正确性。通过这些步骤,可构建一个高效准确的行列式计算程序,支持分数形式计算,为C++编程和线性代数应用奠定基础。
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