recursively

简明释义

英[rɪˈkɜːsɪvli]美[rɪˈkɜr.sɪv.li]

adv. 递归地；递回地

英英释义

单词用法

同义词

反义词

例句

1.It recursively walks through a set of directories, applying the style sheet as it goes along.

它递归地遍历一组目录，在这个过程中应用样式表。

2.Software architecture can be used recursively.

软件架构可以递归地使用。

3.A lock can be acquired in one of two ways, recursively or non-recursively.

可以通过两种方式(递归地或非递归地)的其中一种来请求锁。

4.In this case, you're recursively selecting all files starting with the 'SRC' directory.

本例中递归选择了“src”目录下的所有文件。

5.These two steps repeat recursively and depth first.

这两步递归地以深度优先的方式重复。

6.If a subtree is found, the method calls itself recursively, as shown in Listing 18.

如果找到子树，递归地调用其本身，见清单18。

7.This algorithm repeats recursively until all newly resolved subgroups contain no further subgroups.

此算法递归地重复，直到所有新解析的子组不再包含子组。

8.The function calculates the factorial of a number recursively 递归地 by calling itself.

这个函数通过调用自身来计算一个数字的阶乘递归地。

9.In this algorithm, we will sort the list recursively 递归地 using the quicksort method.

在这个算法中，我们将使用快速排序方法递归地对列表进行排序。

10.The tree structure can be traversed recursively 递归地 to access each node.

树结构可以通过递归地遍历来访问每个节点。

11.We can define the Fibonacci sequence recursively 递归地 as each number being the sum of the two preceding ones.

我们可以将斐波那契数列定义为递归地每个数字是前两个数字的和。

12.The algorithm divides the problem into smaller subproblems and solves them recursively 递归地.

该算法将问题分解为更小的子问题，并递归地解决它们。

作文

In the world of computer science, the concept of recursion is fundamental. Recursion refers to a method where the solution to a problem depends on solutions to smaller instances of the same problem. When we say that a function operates recursively, we mean that it calls itself in order to solve a problem. This approach can be incredibly powerful, allowing for elegant solutions to complex problems. For example, consider the task of calculating the factorial of a number. The factorial of n, denoted as n!, is the product of all positive integers up to n. A recursive definition of factorial can be expressed as: n! = n × (n-1)! for n > 0, and 0! = 1. In this case, the function calls itself with a reduced value until it reaches the base case of 0. The beauty of using recursion lies in its simplicity and clarity. Instead of writing lengthy loops, a recursive function can express the same logic in a more straightforward manner. However, it’s essential to understand that recursion can be less efficient than iterative solutions in some cases, particularly when dealing with large input sizes. Each recursive call adds a layer to the call stack, which can lead to increased memory usage and potential stack overflow errors if not managed properly. Moreover, recursion is not limited to mathematical computations. It is widely used in data structures such as trees and graphs. For instance, traversing a binary tree can be done recursively by visiting the left subtree, then the root, and finally the right subtree, a process known as in-order traversal. This method allows for a clean and intuitive way to navigate complex structures. In the broader context of programming and algorithm design, understanding how to implement functions recursively is a critical skill. Many algorithms, including those for sorting and searching, leverage recursion to achieve their goals. Quick sort and merge sort are classic examples of sorting algorithms that utilize recursively defined processes to sort elements efficiently. However, one must also be cautious about the potential pitfalls of recursion. Infinite recursion can occur if the base case is not correctly defined, leading to programs that never terminate. Therefore, it is crucial to ensure that each recursive call brings the function closer to its base case, thereby preventing infinite loops. In conclusion, the concept of recursion and the use of recursively defined functions play a significant role in computer science. They offer a powerful tool for solving problems, particularly those that can be broken down into smaller, more manageable parts. While recursion may not always be the most efficient method, its elegance and simplicity make it a valuable technique in the programmer's toolkit. Understanding and mastering recursion will undoubtedly enhance one’s ability to tackle a wide range of computational challenges effectively.

在计算机科学的世界中，递归的概念是基础性的。递归指的是一种方法，其中问题的解决依赖于该问题较小实例的解决。当我们说一个函数以递归方式操作时，我们的意思是它调用自身来解决问题。这种方法可以非常强大，允许对复杂问题进行优雅的解决。例如，考虑计算一个数字的阶乘的任务。n的阶乘，记作n!，是所有正整数乘积直到n。阶乘的递归定义可以表示为：n! = n × (n-1)! 对于 n > 0，且 0! = 1。在这种情况下，该函数以减少的值调用自身，直到达到基例0。 使用递归的美在于其简洁性和清晰性。与其编写冗长的循环，不如用递归函数以更直接的方式表达相同的逻辑。然而，必须理解，在某些情况下，递归可能比迭代解决方案效率低下，特别是在处理大输入时。每次递归调用都会向调用栈添加一层，这可能导致内存使用增加，并且如果管理不当，可能会导致堆栈溢出错误。 此外，递归不仅限于数学计算。它在树和图等数据结构中被广泛使用。例如，遍历二叉树可以通过访问左子树，然后是根，最后是右子树，以递归的方式完成，这个过程称为中序遍历。这种方法允许以干净和直观的方式导航复杂结构。 在编程和算法设计的更广泛背景下，理解如何实现递归函数是一项关键技能。许多算法，包括排序和搜索，利用递归来实现其目标。快速排序和归并排序是利用递归定义过程有效排序元素的经典排序算法示例。 然而，人们也必须小心递归的潜在陷阱。如果基案例未正确定义，可能会发生无限递归，导致程序无法终止。因此，确保每次递归调用使函数更接近其基案例至关重要，从而防止无限循环。 总之，递归的概念和递归定义的函数在计算机科学中扮演着重要角色。它们为解决问题提供了一种强大的工具，特别是那些可以分解为更小、更易管理部分的问题。虽然递归可能不是最有效的方法，但其优雅和简洁使其成为程序员工具箱中的宝贵技术。理解和掌握递归无疑将增强一个人有效应对各种计算挑战的能力。