n.递归

In computer science, recursion is a powerful technique where a function calls itself to solve smaller instances of the same problem.
在计算机科学中，递归是一种强大的技术，其中函数通过调用自身来解决同一问题的较小实例。
The algorithm employs recursion to traverse the binary tree, visiting each node exactly once.
该算法使用递归来遍历二叉树，确保每个节点恰好被访问一次。
Understanding recursion can be challenging at first, but it's essential for mastering advanced programming concepts.
初次理解递归可能颇具挑战性，但它是掌握高级编程概念的关键。
The mathematician used recursion to define the Fibonacci sequence, where each number is the sum of the two preceding ones.
数学家使用递归来定义斐波那契数列，其中每个数字都是前两个数字的和。
To avoid infinite recursion, every recursive algorithm must have one or more base cases that stop the recursion when a certain condition is met.
为了避免无限递归，每个递归算法都必须有一个或多个基本情况，在满足特定条件时停止递归。
这些句子涵盖了递归在不同场景下的应用，从计算机科学到数学，展示了递归的重要性和实用性。
The factorial of 5 can be calculated recursively as 5 * factorial(4).
可以递归地计算5的阶乘为5*factorial(4)。
The Fibonacci sequence is a classic example of recursion, where each number is the sum of the two preceding ones.
斐波那契数列是递归的经典示例，其中每个数字都是前两个数字之和。
To solve this problem, we need to break it down into smaller sub-problems using recursion.
要解决这个问题，我们需要使用递归将其分解为更小的子问题。
The recursive function calls itself until it reaches the base case, which stops the recursion.
递归函数会一直调用自身，直到达到基本情况，这将停止递归。
The depth-first search algorithm uses recursion to traverse a tree or graph by exploring as far as possible along each branch before backtracking.
深度优先搜索算法使用递归来遍历树或图，沿着每个分支尽可能深入探索，然后回溯。
In programming, recursion can lead to elegant and concise solutions for certain problems, but it can also cause stack overflow if not properly managed.
在编程中，递归可以为某些问题提供优雅简洁的解决方案，但如果管理不当，可能会导致堆栈溢出。
The Tower of Hanoi puzzle requires recursive thinking to move all disks from one peg to another, obeying specific rules.
汉诺塔谜题需要递归思维以遵守特定规则将所有盘子从一个柱子移动到另一个柱子。
Recursive algorithms often involve defining a general case and a simpler base case, then solving the general case in terms of the base case.
递归算法通常涉及定义一般情况和更简单的基本情况，然后根据基本情况求解一般情况。
A binary search algorithm utilizes recursion to repeatedly divide a sorted list in half until finding the target element.
二分查找算法利用递归反复将有序列表分成两半，直到找到目标元素。
When designing a recursive function, it's crucial to identify the stopping condition, otherwise the function will continue calling itself indefinitely.
设计递归函数时，确定终止条件至关重要，否则函数将继续无限自我调用。