exponential time

简明释义

指数时间

英英释义

例句

1.The algorithm runs in exponential time, which means its performance degrades rapidly as the input size increases.

该算法的运行时间是指数级时间，这意味着随着输入规模的增加，其性能迅速下降。

2.When solving NP-complete problems, the best known algorithms often run in exponential time.

在解决NP完全问题时，已知的最佳算法通常运行在指数级时间内。

3.In certain problems, we often encounter solutions that require exponential time to compute, making them impractical for large datasets.

在某些问题中，我们经常会遇到需要计算指数级时间的解决方案，这使得它们对于大数据集来说不切实际。

4.As the number of variables increases, the complexity can grow to exponential time for certain optimization problems.

随着变量数量的增加，对于某些优化问题，复杂度可能增长到指数级时间。

5.Developers need to be cautious when implementing algorithms with exponential time complexity in production systems.

开发者在生产系统中实现具有指数级时间复杂度的算法时需要谨慎。

作文

In the field of computer science, the term exponential time refers to an algorithm whose growth rate doubles with each addition to the input size. This means that if you have a problem that requires exponential time to solve, the time it takes to compute will increase dramatically as the size of the input increases. For example, consider a simple problem where you need to find all subsets of a given set. If the set has 'n' elements, the number of possible subsets is 2^n, which means that the time complexity of this problem is O(2^n). This is a classic case of exponential time complexity. The implications of exponential time algorithms are significant in practical applications. As the size of the input grows, the time required to solve the problem can become infeasible. For instance, if a problem takes 1 second to solve for 10 items, it might take approximately 1,024 seconds (or about 17 minutes) for 20 items, and over 1,000 seconds for just 30 items. This rapid escalation makes exponential time algorithms impractical for large datasets or complex problems.To illustrate this further, let’s consider the Traveling Salesman Problem (TSP), one of the most well-known problems in combinatorial optimization. The goal of TSP is to find the shortest possible route that visits each city exactly once and returns to the origin city. The brute-force solution for TSP involves calculating the total distance for every possible permutation of cities. For 'n' cities, there are (n-1)! permutations, leading to a time complexity of O(n!). This factorial growth is another example of how quickly exponential time problems can escalate.In contrast to exponential time algorithms, polynomial time algorithms are much more manageable. An algorithm that runs in polynomial time, such as O(n^2) or O(n^3), grows at a much slower rate compared to exponential time algorithms. For many practical applications, polynomial time solutions are preferred because they remain feasible even as the input size increases. This is why researchers continuously seek to find efficient algorithms that can reduce the computational complexity of problems that initially appeared to require exponential time.Moreover, advancements in technology, such as parallel processing and quantum computing, are also being explored to tackle problems that traditionally require exponential time. These technologies promise to revolutionize the way we approach complex computations, potentially allowing us to solve problems previously deemed unsolvable within a reasonable timeframe.In conclusion, understanding exponential time is crucial for anyone involved in computer science or related fields. It highlights the challenges associated with certain algorithms and underscores the importance of developing efficient computational strategies. As we continue to push the boundaries of technology, the quest for faster algorithms remains a primary focus, particularly in an era where data is growing exponentially. By mastering the concept of exponential time, we can better appreciate the intricacies of algorithm design and the impact of computational limits on real-world applications.

在计算机科学领域，术语指数时间指的是一种算法，其增长速度随着输入大小的增加而翻倍。这意味着，如果你有一个需要指数时间来解决的问题，那么计算所需的时间会随着输入的增大而急剧增加。例如，考虑一个简单的问题，你需要找到给定集合的所有子集。如果集合有'n'个元素，则可能的子集数量为2^n，这意味着该问题的时间复杂度为O(2^n)。这是指数时间复杂性的经典案例。指数时间算法的影响在实际应用中是显著的。随着输入大小的增长，解决问题所需的时间可能变得不可行。例如，如果一个问题对于10个项目需要1秒钟来解决，那么对于20个项目，它可能需要大约1,024秒（或约17分钟），而仅仅30个项目就可能需要超过1,000秒。这种快速的升级使得指数时间算法在处理大型数据集或复杂问题时变得不切实际。为了进一步说明这一点，让我们考虑旅行推销员问题（TSP），这是组合优化中最著名的问题之一。TSP的目标是找到一条最短的路径，该路径恰好访问每个城市一次并返回到起始城市。TSP的暴力解决方案涉及计算每个城市排列的总距离。对于'n'个城市，有(n-1)!种排列，导致时间复杂度为O(n!)。这种阶乘增长是另一种示例，说明指数时间问题如何迅速升级。与指数时间算法相比，多项式时间算法要可管理得多。运行在多项式时间的算法，如O(n^2)或O(n^3)，其增长速度远远低于指数时间算法。对于许多实际应用，多项式时间解决方案是首选，因为即使在输入大小增加的情况下，它们仍然是可行的。这就是为什么研究人员不断寻求找到有效的算法，以减少最初似乎需要指数时间的问题的计算复杂性。此外，平行处理和量子计算等技术的进步也正在被探索，以解决传统上需要指数时间的问题。这些技术有望彻底改变我们处理复杂计算的方式，可能使我们能够在合理的时间内解决以前被认为无法解决的问题。总之，理解指数时间对任何参与计算机科学或相关领域的人来说都是至关重要的。它突出了与某些算法相关的挑战，并强调了开发高效计算策略的重要性。随着我们继续推动技术的边界，寻找更快算法的追求仍然是一个主要焦点，特别是在数据呈指数增长的时代。通过掌握指数时间的概念，我们可以更好地理解算法设计的复杂性以及计算限制对现实世界应用的影响。