Java语言实现的SAT4J求解器基础教程

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资源摘要信息:"SAT4J_JAVA.zip_Java solv_Sat4j_Java_WalkS_sat_sat4j" SAT4J是一个用Java编写的SAT求解器库。SAT(布尔可满足性问题)是一个著名的NP-完全问题,广泛应用于逻辑推理、电子设计自动化、人工智能等领域。求解器的目标是判断一组布尔变量的赋值是否能满足一组逻辑表达式,即找到一个赋值,使得所有表达式都为真。 描述中提到的"基于miniSAT",意味着SAT4J可能采用了miniSAT作为其核心算法或者启发式方法的一部分。miniSAT是一个高效且被广泛使用的SAT求解器,由Niklas Een和 Niklas Sorensson于2003年开发。它采用DPLL算法和子句学习技术,是研究和工业界中应用较为广泛的一个求解器。 SAT4J提供了Java开发者一个易于使用的接口,使得他们可以快速地将SAT求解功能集成到自己的Java应用程序中。通过SAT4J,开发者可以创建SAT实例、添加约束、求解问题,并获取解决方案。它还允许用户进行更高级的SAT问题操作,例如满足性判断、最优解搜索、不相容核心提取等。 SAT4J适用于各种需要逻辑推理和决策支持的场景,例如: - 软件和硬件验证:在设计阶段,通过SAT求解器来验证系统设计是否满足特定的规范和属性。 - 人工智能:在AI领域,SAT求解器用于各种逻辑规划和推理任务,如知识表示、问题求解等。 - 产品配置:在配置系统中,SAT求解器可以帮助解决产品配置问题,确保客户的配置请求在技术上是可行的。 - 调度与优化问题:在生产调度、资源分配等优化问题中,SAT技术可用于表达复杂的约束条件。 SAT4J的出现,降低了Java开发者在面对需要逻辑运算和决策支持的复杂问题时的门槛。它不仅是一个可重用的库,而且还可以作为一个强大的工具,帮助开发者快速构建起基于SAT问题求解的解决方案。 从提供的文件名称列表中可以看出,除了主程序和相关的库文件之外,可能还包含了一个名为"***.txt"的文本文件。这个文件可能是用来说明SAT4J_JAVA.zip包中文件的详情,或者是提供额外的文档和示例,比如如何安装、使用SAT4J库以及其API文档。由于文件列表中包含"SAT"这一关键词,这表明该压缩包可能还包含了与SAT问题相关的一些示例或测试文件,用以展示如何使用SAT4J解决SAT问题。而这些示例文件对于理解SAT4J的使用方法和其背后算法的实现细节非常有帮助。 SAT4J不仅仅是一个求解器,它也是Java在逻辑编程和推理领域的扩展。它提升了Java在处理逻辑问题上的能力,为Java开发者提供了一个强大的逻辑处理工具,使得在Java环境中解决复杂逻辑问题是可行的,这对于推动Java在更多领域的应用有着积极的作用。

用代码解决这个问题The program committee of the school programming contests, which are often held at the Ural State University, is a big, joyful, and united team. In fact, they are so united that the time spent together at the university is not enough for them, so they often visit each other at their homes. In addition, they are quite athletic and like walking. Once the guardian of the traditions of the sports programming at the Ural State University decided that the members of the program committee spent too much time walking from home to home. They could have spent that time inventing and preparing new problems instead. To prove that, he wanted to calculate the average distance that the members of the program committee walked when they visited each other. The guardian took a map of Yekaterinburg, marked the houses of all the members of the program committee there, and wrote down their coordinates. However, there were so many coordinates that he wasn't able to solve that problem and asked for your help. The city of Yekaterinburg is a rectangle with the sides parallel to the coordinate axes. All the streets stretch from east to west or from north to south through the whole city, from one end to the other. The house of each member of the program committee is located strictly at the intersection of two orthogonal streets. It is known that all the members of the program committee walk only along the streets, because it is more pleasant to walk on sidewalks than on small courtyard paths. Of course, when walking from one house to another, they always choose the shortest way. All the members of the program committee visit each other equally often. Input The first line contains the number n of members of the program committee (2 ≤ n ≤ 105). The i-th of the following n lines contains space-separated coordinates xi, yi of the house of the i-th member of the program committee (1 ≤ xi, yi ≤ 106). All coordinates are integers. Output Output the average distance, rounded down to an integer, that a member of the program committee walks from his house to the house of his colleague.

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