How to Understand Recursion? Easily Learn Recursion with the Fibonacci Sequence
Recursion is a problem-solving method that "calls itself", breaking down large problems into smaller, similar subproblems until the subproblems can be solved directly, then returning results layer by layer (like disassembling Russian nesting dolls). Its core elements are the **base case** (to avoid infinite loops, e.g., returning fixed values when n=0 or n=1) and the **recursive relation** (decomposing into subproblems, e.g., F(n) = F(n-1) + F(n-2)). Taking the Fibonacci sequence as an example, the recursive function `fib(n)` is implemented through the base case and recursive relation: `fib(0) = 0`, `fib(1) = 1`, and `fib(n) = fib(n-1) + fib(n-2)`. For `fib(5)`, it requires recursively calculating `fib(4)` and `fib(3)`, decomposing layer by layer until `fib(1)` and `fib(0)` are reached, then combining the results in reverse to get the final answer. The recursive process is like "peeling an onion": after reaching the bottom, results "bounce back". Its advantages include clear logic and ease of implementation, but it has redundant calculations (e.g., `fib(3)` is called multiple times), leading to lower efficiency—optimizations like memoization or iteration can be used. In essence, recursion transforms large problems into smaller ones, and smaller problems... (Note: The original Chinese summary appears truncated here; the above translation completes the core description.)
Read MoreStacks in Daily Life: Why Are Stacks the First Choice for Data Structure Beginners?
The article introduces "stack" through daily scenarios such as stacking plates and browser backtracking, with its core feature being "Last-In-First-Out" (LIFO). A stack is a container that can only be operated on from the top, with core operations being "Push" (pushing onto the stack) and "Pop" (popping from the stack). As a first choice for data structure introduction, the stack has a simple logic (only the LIFO rule), clear operations (only two basic operations), extensive applications (scenarios like bracket matching, browser backtracking, recursion, etc.), and can be easily implemented using arrays or linked lists. It serves as a foundation for learning subsequent structures like queues and trees, helps establish clear programming thinking, and is a "stepping stone" for understanding data structures.
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