Recursion: What is Recursion? An Example with the Fibonacci Sequence, Explained for Beginners

This article explains the concept of recursion using everyday examples and classic cases. Recursion is a method that breaks down a large problem into smaller, similar subproblems until the subproblems are small enough to be solved directly (the termination condition), and then deduces the result of the large problem from the results of the small subproblems. The core lies in "decomposition" and "termination". Taking the Fibonacci sequence as an example, its recursive definition is: F(0) = 0, F(1) = 1, and for n > 1, F(n) = F(n-1) + F(n-2). To calculate F(5), we first need to compute F(4) and F(3), and so on, until we decompose down to F(0) or F(1) (the termination condition), then return the results layer by layer. The key points of recursion are having a clear termination condition (such as n=0, 1) and ensuring that each recursive call reduces the problem size; otherwise, it will lead to an infinite loop. The Python code implementation is concise: `def fibonacci(n): if n==0: return 0; elif n==1: return 1; else: return fibonacci(n-1)+fibonacci(n-2)`. Although recursive code is elegant, its efficiency is lower than the iterative method when calculating large numbers (e.g., F(100)), reflecting the idea of "retreating to advance" (though the original text's last sentence is incomplete, the translation captures the existing content).