upper bound

简明释义

高限

英英释义

例句

1.The upper bound for the total cost of the project is estimated at $100,000.

项目的总成本上界估计为100,000美元。

2.To ensure safety, we set an upper bound on the temperature of the reactor.

为了确保安全，我们对反应堆的温度设置了上界。

3.The upper bound of the dataset indicates the maximum value recorded.

数据集的上界表示记录的最大值。

4.The algorithm has an upper bound of O(n^2) for its time complexity.

该算法的时间复杂度具有上界为O(n^2)。

5.In this optimization problem, we need to find the upper bound on resource usage.

在这个优化问题中，我们需要找到资源使用的上界。

作文

In mathematics and computer science, the concept of an upper bound is crucial for understanding limits and constraints. An upper bound refers to a value that a given function or sequence cannot exceed. This concept is particularly important in algorithms, where determining the maximum time or space complexity can significantly impact performance and efficiency. For example, when analyzing sorting algorithms, we often look for an upper bound on their running time to ensure that they will perform adequately under worst-case scenarios.To illustrate this further, consider a simple algorithm that sorts a list of numbers. If we say that the algorithm has a time complexity of O(n^2), we are stating that the upper bound for the time it takes to sort n numbers is proportional to n squared. This means that as the size of the input increases, the time taken by the algorithm will not grow faster than a quadratic function of n. Knowing this upper bound helps developers make informed decisions about which algorithm to use based on the expected size of the input data.In addition to algorithms, the notion of an upper bound can also be applied in various fields such as economics, physics, and engineering. For instance, in economics, the upper bound might represent the maximum price that consumers are willing to pay for a product, which can help businesses set pricing strategies. In physics, an upper bound could denote the maximum force that a material can withstand before failing, guiding engineers in designing safe structures.Understanding the implications of an upper bound enables researchers and practitioners to approach problems with a clearer perspective. It allows them to identify potential limitations and work within those constraints to optimize their solutions. Furthermore, recognizing an upper bound can lead to more robust designs and analyses, as it encourages consideration of worst-case scenarios.Moreover, the concept of an upper bound is not limited to theoretical applications; it also has practical implications. For example, in project management, knowing the upper bound of resources required for a project can help in budgeting and resource allocation. It ensures that teams do not overcommit resources, which can lead to project failure or financial loss.In conclusion, the term upper bound serves as a vital tool in various disciplines, providing a framework for understanding limits and constraints. Whether in mathematics, economics, or engineering, recognizing an upper bound aids in decision-making processes and enhances problem-solving capabilities. By grasping the significance of an upper bound, individuals can better navigate complex systems and develop effective strategies to achieve their goals. As we continue to encounter increasingly complex challenges in our respective fields, the ability to identify and work with upper bounds will undoubtedly remain an essential skill for success.

在数学和计算机科学中，“upper bound”的概念对于理解限制和约束至关重要。“upper bound”指的是一个给定函数或序列无法超过的值。这个概念在算法中尤为重要，因为确定最大时间或空间复杂度可以显著影响性能和效率。例如，在分析排序算法时，我们常常寻找其运行时间的“upper bound”，以确保它们在最坏情况下能够表现得足够好。进一步说明这一点，考虑一个简单的算法，该算法对数字列表进行排序。如果我们说该算法的时间复杂度为O(n^2)，这意味着排序n个数字所需的时间的“upper bound”与n的平方成正比。这意味着随着输入大小的增加，算法所需的时间不会超过n的平方函数。了解这个“upper bound”有助于开发人员根据预期的输入数据规模做出明智的决策。除了算法外，“upper bound”的概念还可以应用于经济学、物理学和工程等各个领域。例如，在经济学中，“upper bound”可能代表消费者愿意为某个产品支付的最高价格，这可以帮助企业制定定价策略。在物理学中，“upper bound”可以表示材料在失效之前能够承受的最大力，这指导工程师设计安全的结构。理解“upper bound”的含义使研究人员和从业者能够以更清晰的视角解决问题。它使他们能够识别潜在的限制，并在这些约束内工作，以优化解决方案。此外，认识到“upper bound”可以导致更稳健的设计和分析，因为它鼓励考虑最坏情况。此外，“upper bound”的概念不仅限于理论应用；它还有实际意义。例如，在项目管理中，了解项目所需资源的“upper bound”可以帮助预算和资源分配。它确保团队不会过度承诺资源，从而导致项目失败或财务损失。总之，“upper bound”一词在各个学科中都作为一个重要工具，为理解限制和约束提供了框架。无论是在数学、经济学还是工程中，识别“upper bound”都有助于决策过程并增强解决问题的能力。通过掌握“upper bound”的重要性，个人可以更好地应对复杂系统并制定有效的策略以实现目标。随着我们在各自领域中继续面临日益复杂的挑战，识别和利用“upper bounds”的能力无疑将继续成为成功的基本技能。