recursion

简明释义

英[rɪˈkɜːʃn]美[rɪˈkɜːrʒn]

n. [数] 递归，循环；递归式

英英释义

单词用法

同义词

反义词

例句

1.The tool even supports recursion to a given depth.

这个工具还支持递归到给定深度。

2.And the reason I want to show you this is to notice that the recursion can be doubled.

如果我来写斐波那契数列你可以看看这儿,原因是我想让你看看这部分的递归可以翻倍。

3.Lisp offers a performance optimization called tail recursion optimization.

Lisp提供一项称作尾部递归优化的性能优化技术。

4.Tail recursion is a common technique in XSLT style sheets.

尾递归是xslt样式表中的常用技术。

5.The question is, can we implement the Visitor pattern without recursion?

问题在于，我们能否在不使用递归的前提下实现访问者模式？

6.Statically forbid polymorphic recursion.

静态禁止多态递归。

7.In programming, recursion refers to a function that calls itself in order to solve a problem.

在编程中，递归指的是一个函数调用自身以解决问题。

8.The recursion technique is often used in algorithms like quicksort and mergesort.

在快速排序和归并排序等算法中，常常使用递归技术。

9.Understanding recursion is essential for mastering data structures such as trees and graphs.

理解递归对于掌握树和图等数据结构至关重要。

10.A classic example of recursion is the calculation of factorials.

计算阶乘是递归的经典例子。

11.Some problems are easier to solve with recursion rather than using iterative methods.

某些问题用递归方法解决比使用迭代方法更容易。

作文

Recursion is a fundamental concept in computer science and mathematics that refers to the process of defining a function or calculating a value by having the function call itself. This method allows for solving complex problems by breaking them down into simpler, more manageable sub-problems. In essence, recursion can be thought of as a way to solve a problem by reducing it to smaller instances of the same problem. For example, when calculating the factorial of a number, we can express it in terms of the factorial of smaller numbers: n! = n * (n-1)!. Here, the function calls itself with a reduced argument until it reaches a base case, which is usually a simple, easily solvable instance of the problem. One of the most famous examples of recursion is the Fibonacci sequence, where each number is the sum of the two preceding ones. The sequence starts with 0 and 1, and the nth Fibonacci number can be defined recursively as follows: F(n) = F(n-1) + F(n-2). This definition clearly shows how recursion works by expressing the nth term in terms of previous terms. Recursion is not only limited to mathematical functions; it also plays a crucial role in programming. Many algorithms utilize recursion to simplify their implementation. For instance, sorting algorithms like quicksort and mergesort often employ recursive techniques to divide the data into smaller subsets before sorting them individually. This approach not only makes the code cleaner but also enhances the efficiency of the algorithm. However, while recursion can be an elegant solution to many problems, it is essential to use it judiciously. Recursive functions can lead to excessive memory usage due to the creation of multiple function calls on the call stack. If the recursion depth becomes too large, it can result in a stack overflow error, causing the program to crash. Therefore, it is crucial to ensure that every recursive function has a well-defined base case to terminate the recursion and prevent infinite loops. In addition to its practical applications in programming, recursion also has philosophical implications. It raises questions about self-reference and the nature of infinity. The idea of a function calling itself can be likened to concepts in art and literature, such as the recursive structures found in fractals or the self-referential narratives in postmodern literature. These themes challenge our understanding of linear progression and invite us to explore the complexities of self-similarity and repetition in various contexts. In conclusion, recursion (递归) is a powerful and versatile concept that extends beyond mathematics and computer science into broader philosophical discussions. Understanding how to implement recursion effectively can significantly enhance problem-solving skills and algorithmic thinking. As we continue to explore the depths of this concept, we uncover not only practical applications but also profound insights into the nature of processes and structures around us.

递归是计算机科学和数学中的一个基本概念，指的是通过让函数调用自身来定义函数或计算值的过程。这种方法允许通过将复杂问题分解为更简单、更易管理的子问题来解决问题。归根结底，递归可以被视为通过将问题简化为同一问题的较小实例来解决问题的一种方式。例如，在计算一个数字的阶乘时，我们可以用较小数字的阶乘来表示它：n! = n * (n-1)!。在这里，该函数以减少的参数调用自身，直到达到一个基本情况，这通常是一个简单且易于解决的问题实例。 递归最著名的例子之一是斐波那契数列，其中每个数字是前两个数字的总和。该序列以0和1开始，第n个斐波那契数可以递归定义如下：F(n) = F(n-1) + F(n-2)。这个定义清楚地展示了递归如何通过将第n项表示为前几项来工作。 递归不仅限于数学函数；它在编程中也发挥着至关重要的作用。许多算法利用递归来简化其实现。例如，排序算法如快速排序和归并排序通常采用递归技术，将数据划分为较小的子集，然后分别进行排序。这种方法不仅使代码更简洁，而且提高了算法的效率。 然而，虽然递归可以是许多问题的优雅解决方案，但必须谨慎使用。递归函数可能会导致过度的内存使用，因为在调用堆栈上创建多个函数调用。如果递归深度变得过大，可能会导致堆栈溢出错误，导致程序崩溃。因此，确保每个递归函数都有一个明确定义的基本情况以终止递归并防止无限循环至关重要。 除了在编程中的实际应用外，递归还具有哲学意义。它引发了关于自我引用和无限本质的问题。函数自我调用的想法可以比作艺术和文学中的概念，例如在分形中发现的递归结构或后现代文学中的自我指涉叙事。这些主题挑战了我们对线性进展的理解，并邀请我们探索各种上下文中自相似性和重复性的复杂性。 总之，recursion（递归）是一个强大而多才多艺的概念，它超越了数学和计算机科学，进入更广泛的哲学讨论。有效理解如何实施递归可以显著增强解决问题的能力和算法思维。随着我们继续探索这一概念的深度，我们不仅揭示了实际应用，还发现了关于我们周围过程和结构本质的深刻见解。