lower bound

简明释义

下际

英英释义

例句

1.Our financial model sets a lower bound 下界 on revenue projections to ensure conservative estimates.

我们的财务模型为收入预测设定了一个lower bound 下界，以确保保守的估计。

2.In optimization problems, finding a lower bound 下界 can help identify feasible solutions.

在优化问题中，找到一个lower bound 下界可以帮助识别可行解。

3.The lower bound 下界 on the number of operations required to solve this problem is logarithmic.

解决这个问题所需操作的lower bound 下界是对数级别的。

4.In algorithm analysis, we often establish a lower bound 下界 for the time complexity of sorting algorithms.

在算法分析中，我们通常会为排序算法的时间复杂度建立一个lower bound 下界。

5.The researchers determined a lower bound 下界 for the minimum required sample size in their study.

研究人员确定了他们研究中所需最小样本量的lower bound 下界。

作文

In mathematics and computer science, the concept of a lower bound is crucial in understanding the limitations of algorithms and data structures. A lower bound refers to the minimum value or performance that can be expected from an algorithm in the worst-case scenario. This idea is particularly important when analyzing the efficiency of sorting algorithms, searching techniques, and many other computational processes. For instance, if we consider sorting algorithms, we can establish that any comparison-based sorting algorithm has a lower bound of O(n log n) for its time complexity. This means that no matter how optimized the algorithm is, it cannot perform better than this threshold in the average case. Understanding this lower bound helps developers and researchers set realistic expectations for their algorithms and motivates them to explore alternative methods when the traditional approaches fall short.Furthermore, the concept of a lower bound is not limited to theoretical applications; it also plays a significant role in practical scenarios. For example, when developing software that handles large datasets, knowing the lower bound of resource consumption can help in planning and allocating resources efficiently. If a developer understands that their algorithm has a lower bound on memory usage, they can make informed decisions about hardware requirements and optimize their code accordingly to stay within those limits.Additionally, the lower bound concept extends beyond algorithms into various fields such as economics, engineering, and statistics. In economics, for instance, the lower bound can refer to the minimum price at which a product can be sold without incurring losses. This understanding allows businesses to set pricing strategies that ensure profitability while remaining competitive in the market.In engineering, particularly in structural analysis, the lower bound can signify the minimum load that a structure can support before failure occurs. Engineers must account for these limits during the design phase to ensure safety and reliability. Similarly, in statistics, a lower bound may represent the minimum expected value of a dataset based on certain conditions or assumptions, guiding researchers in their analyses and interpretations.Moreover, the exploration of lower bounds often leads to deeper insights and innovations. Researchers frequently challenge existing lower bounds by discovering new algorithms that achieve better performance or by proving that certain problems cannot be solved more efficiently than previously established limits. This ongoing pursuit drives the advancement of technology and enhances our understanding of complex systems.In conclusion, the concept of a lower bound serves as a fundamental principle across various disciplines, providing essential insights into the limitations and capabilities of algorithms, economic models, engineering designs, and statistical analyses. By grasping the significance of a lower bound, individuals can make informed decisions, optimize processes, and foster innovation in their respective fields. Understanding these boundaries not only enhances problem-solving skills but also encourages a mindset of continuous improvement and exploration. As we move forward in an increasingly complex world, recognizing and respecting the lower bounds of our endeavors will be key to achieving success and sustainability.

在数学和计算机科学中，lower bound的概念对于理解算法和数据结构的限制至关重要。lower bound指的是在最坏情况下可以预期的算法的最小值或性能。这个理念在分析排序算法、搜索技术以及许多其他计算过程时尤其重要。例如，如果我们考虑排序算法，我们可以确定任何基于比较的排序算法在时间复杂度上有一个lower bound为O(n log n)。这意味着无论算法如何优化，它在平均情况下都不能表现得比这个阈值更好。理解这个lower bound有助于开发人员和研究人员对他们的算法设定现实的期望，并激励他们在传统方法无法达到目标时探索替代方法。此外，lower bound的概念不仅限于理论应用；它在实际场景中也发挥着重要作用。例如，在开发处理大数据集的软件时，了解资源消耗的lower bound可以帮助有效地规划和分配资源。如果开发人员了解他们的算法在内存使用上有一个lower bound，他们就可以做出明智的决策，合理配置硬件需求，并相应地优化代码，以保持在这些限制之内。此外，lower bound的概念超越了算法，扩展到经济学、工程学和统计学等多个领域。在经济学中，例如，lower bound可以指产品在不产生损失的情况下能够销售的最低价格。这种理解使企业能够制定定价策略，确保盈利，同时在市场中保持竞争力。在工程学中，特别是在结构分析中，lower bound可以表示结构在发生故障之前能够承受的最小载荷。工程师必须在设计阶段考虑这些限制，以确保安全性和可靠性。同样，在统计学中，lower bound可能表示基于某些条件或假设的数据集的最小预期值，引导研究人员进行分析和解释。此外，对lower bounds的探索往往会带来更深入的见解和创新。研究人员经常挑战现有的lower bounds，通过发现能够实现更好性能的新算法，或通过证明某些问题不能以比先前确立的限制更高效的方式解决。这种持续的追求推动了技术的进步，增强了我们对复杂系统的理解。总之，lower bound的概念作为各个学科的基本原则，提供了对算法、经济模型、工程设计和统计分析的限制和能力的重要见解。通过掌握lower bound的重要性，个人可以做出明智的决策，优化流程，并在各自的领域促进创新。理解这些边界不仅增强了问题解决能力，还鼓励了持续改进和探索的思维方式。随着我们在日益复杂的世界中前进，认识和尊重我们努力的lower bounds将是取得成功和可持续发展的关键。