canonical ordering

简明释义

典序

英英释义

例句

1.The algorithm uses canonical ordering 规范顺序 to maintain a standard format for all entries.

该算法使用 规范顺序 canonical ordering 来保持所有条目的标准格式。

2.The software applies canonical ordering 规范顺序 to ensure that similar data is grouped together.

该软件应用 规范顺序 canonical ordering 以确保相似数据被分组在一起。

3.In computer science, canonical ordering 规范顺序 is often used to simplify data structures.

在计算机科学中，规范顺序 canonical ordering 通常用于简化数据结构。

4.In database management, canonical ordering 规范顺序 helps in optimizing query performance.

在数据库管理中，规范顺序 canonical ordering 有助于优化查询性能。

5.When sorting lists, applying canonical ordering 规范顺序 ensures uniformity in the output.

在排序列表时，应用 规范顺序 canonical ordering 确保输出的一致性。

作文

In the realm of mathematics and computer science, the concept of canonical ordering plays a crucial role in organizing and simplifying complex structures. To understand this concept better, we must first recognize what it entails. Canonical ordering refers to a standard way of arranging elements within a set or structure so that they can be easily compared and manipulated. This method is particularly useful when dealing with data structures, algorithms, and mathematical objects, as it provides a consistent framework for analysis.For instance, consider a set of numbers. If we were to arrange them in ascending order, we would achieve a canonical ordering of that particular set. This arrangement allows for straightforward comparisons between the numbers, making it easier to identify the smallest or largest values. In programming, canonical ordering can be employed to ensure that data is processed in a uniform manner, which is essential for functions such as sorting and searching.Moreover, canonical ordering is not limited to numeric data. It can also be applied to strings, trees, and graphs. For example, in the context of trees, a canonical ordering might involve traversing the tree in a specific sequence, such as pre-order, in-order, or post-order traversal. This systematic approach allows for a unique representation of the tree structure, which can be beneficial for tasks like serialization or comparison with other trees.In addition to its practical applications, canonical ordering has significant implications in theoretical computer science. It aids in the establishment of equivalence classes, where different representations of the same object can be identified and categorized under a single canonical form. This process is vital in areas such as algebra, where different polynomial expressions can be transformed into a canonical ordering to facilitate easier manipulation and understanding.Furthermore, the concept extends beyond mathematics and computer science into fields like linguistics and philosophy. In linguistics, canonical ordering can refer to the arrangement of words in a sentence that adheres to grammatical rules, ensuring clarity and coherence in communication. Similarly, in philosophy, the idea of a canonical ordering can be applied to arguments and propositions, where a structured presentation is necessary for logical reasoning.In conclusion, the significance of canonical ordering cannot be overstated. It serves as a foundational principle across various disciplines, providing a means to organize, compare, and analyze complex structures. By adhering to a canonical ordering, we can enhance our understanding of data and relationships, leading to more effective problem-solving and decision-making processes. As we continue to explore the vast landscape of knowledge, the concept of canonical ordering will undoubtedly remain a pivotal tool in our intellectual arsenal.

在数学和计算机科学领域，canonical ordering（规范排序）的概念在组织和简化复杂结构方面发挥着至关重要的作用。要更好地理解这个概念，我们必须首先认识到它所包含的内容。Canonical ordering指的是一种标准方式，用于排列集合或结构中的元素，以便于比较和操作。当处理数据结构、算法和数学对象时，这种方法特别有用，因为它提供了一个一致的分析框架。例如，考虑一组数字。如果我们将它们按升序排列，我们就会得到该特定集合的canonical ordering。这种排列允许对数字进行简单的比较，使得识别最小或最大值变得更加容易。在编程中，canonical ordering可以用于确保数据以统一的方式进行处理，这对于排序和搜索等功能至关重要。此外，canonical ordering并不仅限于数字数据。它还可以应用于字符串、树和图。例如，在树的上下文中，canonical ordering可能涉及以特定顺序遍历树，例如前序、中序或后序遍历。这种系统化的方法允许树结构的唯一表示，这对于序列化或与其他树的比较等任务是有益的。除了其实际应用，canonical ordering在理论计算机科学中也具有重要意义。它有助于建立等价类，其中不同表示形式的同一对象可以被识别并归类为单一的规范形式。这个过程在代数等领域中至关重要，在这些领域中，不同的多项式表达式可以转化为canonical ordering，以便于更简单的操作和理解。此外，这个概念不仅仅局限于数学和计算机科学，还扩展到语言学和哲学等领域。在语言学中，canonical ordering可以指符合语法规则的句子中单词的排列，从而确保交流的清晰性和连贯性。同样，在哲学中，canonical ordering的概念可以应用于论证和命题，其中结构化的呈现对逻辑推理是必要的。总之，canonical ordering的重要性不容小觑。它作为各种学科的基础原则，提供了一种组织、比较和分析复杂结构的手段。通过遵循canonical ordering，我们可以增强对数据和关系的理解，从而导致更有效的问题解决和决策过程。随着我们继续探索知识的广阔领域，canonical ordering的概念无疑将继续成为我们智力工具箱中的关键工具。